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https://opentextbc.ca/alfm3/chapter/review-change-and-the-metric-system/screen-shot-2023-01-24-at-12-24-54-pm/ Tue, 24 Jan 2023 20:25:02 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-24-at-12.24.54-PM.png 1311 1309 0 0 https://opentextbc.ca/alfm3/chapter/review-change-and-the-metric-system/printer/ Tue, 24 Jan 2023 20:49:41 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/printer.jpg 1314 1309 0 0 https://opentextbc.ca/alfm3/chapter/review-change-and-the-metric-system/cordless-phone/ Tue, 24 Jan 2023 20:49:47 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/cordless-phone.jpg 1315 1309 0 0 https://opentextbc.ca/alfm3/chapter/review-change-and-the-metric-system/screen-shot-2023-01-24-at-2-56-07-pm/ Tue, 24 Jan 2023 22:56:29 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-24-at-2.56.07-PM.png 1318 1309 0 0 https://opentextbc.ca/alfm3/chapter/review-change-and-the-metric-system/screen-shot-2023-01-24-at-2-55-58-pm/ Tue, 24 Jan 2023 22:56:30 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-24-at-2.55.58-PM.png 1319 1309 0 0 https://opentextbc.ca/alfm3/chapter/review-change-and-the-metric-system/screen-shot-2023-01-24-at-2-58-08-pm/ Tue, 24 Jan 2023 22:58:29 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-24-at-2.58.08-PM.png 1320 1309 0 0 https://opentextbc.ca/alfm3/chapter/review-change-and-the-metric-system/screen-shot-2023-01-24-at-2-58-21-pm/ Tue, 24 Jan 2023 22:58:30 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-24-at-2.58.21-PM.png 1321 1309 0 0 https://opentextbc.ca/alfm3/screen-shot-2023-01-25-at-10-52-34-am/ Wed, 25 Jan 2023 18:52:44 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-25-at-10.52.34-AM.png 1361 0 0 0 https://opentextbc.ca/alfm3/breadmaker/ Wed, 25 Jan 2023 18:58:56 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/breadmaker.jpg 1362 0 0 0 https://opentextbc.ca/alfm3/shop-vacuum/ Wed, 25 Jan 2023 18:59:06 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/shop-vacuum.jpg 1363 0 0 0 https://opentextbc.ca/alfm3/screen-shot-2023-01-25-at-12-19-21-pm/ Wed, 25 Jan 2023 20:19:53 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-25-at-12.19.21-PM.png 1364 0 0 0 https://opentextbc.ca/alfm3/screen-shot-2023-01-25-at-12-19-11-pm/ Wed, 25 Jan 2023 20:19:54 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-25-at-12.19.11-PM.png 1365 0 0 0 https://opentextbc.ca/alfm3/screen-shot-2023-01-25-at-12-18-59-pm/ Wed, 25 Jan 2023 20:19:54 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-25-at-12.18.59-PM.png 1366 0 0 0 https://opentextbc.ca/alfm3/screen-shot-2023-01-25-at-12-18-50-pm/ Wed, 25 Jan 2023 20:19:54 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-25-at-12.18.50-PM.png 1367 0 0 0 https://opentextbc.ca/alfm3/chapter/the-metric-system/screen-shot-2023-01-24-at-7-46-34-am/ Thu, 26 Jan 2023 20:37:30 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-24-at-7.46.34-AM.png 1409 1249 0 0 https://opentextbc.ca/alfm3/chapter/the-metric-system/screen-shot-2023-01-24-at-7-47-16-am-2/ Thu, 26 Jan 2023 20:39:44 +0000 https://opentextbc.ca/alfm3/wp-content/uploads/sites/424/2023/01/Screen-Shot-2023-01-24-at-7.47.16-AM-1.png 1410 1249 0 0 https://opentextbc.ca/alfm3/chapter/multiplying-larger-numbers/ Thu, 05 Jan 2023 23:24:51 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1024 To find the product of a one digit multiplier, use as many of these steps as you need to complete each multiplication question:

• Step 1: Multiply the ones digit in the large number by the one-digit multiplier.
• Step 2: Multiply the tens digit in the large number by the multiplier.
• Step 3: Multiply the hundreds digit in the large number by the multiplier.
• Step 4: Multiply the thousands digit in the large number by the multiplier.

Example A

62 × 4 = Step 1: 4 × 2 ones = 8

[latex]\begin{array}{rr}&62\\\times&4\\\hline&8\end{array}[/latex]

Step 2: 4 × 6 tens = 24 tens = 2 hundreds and 4 tens

[latex]\begin{array}{rr}&62\\\times&4\\\hline&248\end{array}[/latex]

The product of 62 × 4 is 248.

Exercise 1

Find the product. Check your work using the answer key at the end of the exercise.

1. [latex]\begin{array}{rr}&72\\\times&2\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&81\\\times&5\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&21\\\times&8\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&80\\\times&6\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&73\\\times&3\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&71\\\times&3\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&40\\\times&7\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&90\\\times&9\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&82\\\times&4\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&40\\\times&5\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&92\\\times&4\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&83\\\times&3\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&90\\\times&8\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&71\\\times&9\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&53\\\times&2\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&30\\\times&6\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&81\\\times&7\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&61\\\times&2\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&70\\\times&8\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&41\\\times&6\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&90\\\times&5\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&60\\\times&9\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&92\\\times&3\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&81\\\times&4\\\hline\\\end{array}[/latex]

Answers to Exercise 1

1. 144
2. 405
3. 168
4. 480
5. 219
6. 213
7. 280
8. 810
9. 328
10. 200
11. 368
12. 249
13. 720
14. 639
15. 106
16. 180
17. 567
18. 122
19. 560
20. 246
21. 450
22. 540
23. 276
24. 324

Example B

523 × 3 =

[latex]\begin{array}{rr}&523\\\times&3\\\hline&1569\end{array}[/latex]

Step 1: 3 × 3 ones = 9 ones Step 2: 3 × 2 tens = 6 tens Step 3: 3 × 5 hundreds = 15 hundreds = 1 thousand and 5 hundreds The product of 523 × 3 is 1569.

Example C

901 × 8 =

[latex]\begin{array}{rr}&901\\\times&8\\\hline&7208\end{array}[/latex]

Step 1: 8 × 1 one = 8 ones Step 2: 8 × 0 tens = 0 tens Step 3: 8 × 9 hundreds = 72 hundreds = 7 thousands and 2 hundreds The product of 901 × 8 is 7208.

Exercise 2

Find the product. Check your work using the answer key at the end of the exercise.

1. [latex]\begin{array}{rr}&601\\\times&7\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&423\\\times&3\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&641\\\times&2\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&922\\\times&4\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&820\\\times&4\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&211\\\times&5\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&803\\\times&2\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&542\\\times&2\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&813\\\times&3\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&610\\\times&4\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&901\\\times&6\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&711\\\times&8\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&720\\\times&3\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&910\\\times&5\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&801\\\times&6\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&932\\\times&3\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&731\\\times&2\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&701\\\times&5\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&521\\\times&2\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&632\\\times&3\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&720\\\times&4\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&942\\\times&2\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&710\\\times&9\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&601\\\times&8\\\hline\\\end{array}[/latex]

Answers to Exercise 2

1. 4207
2. 1269
3. 1282
4. 3688
5. 3280
6. 1055
7. 1606
8. 1084
9. 2439
10. 2440
11. 5406
12. 5688
13. 2160
14. 4550
15. 4806
16. 2796
17. 1462
18. 3505
19. 1042
20. 1896
21. 2880
22. 1884
23. 6390
24. 4808

Renaming and Carrying

In the times tables, the products are often two digit numbers. You must rename and carry. The amount you carry is added onto the product of the next column.

Example D

[latex]\begin{array}{rr}&68\\\times&7\\\hline\end{array}[/latex] Step 1: Multiply the ones by the multiplier. 7 × 8 ones = 56 ones = 5 tens + 6 ones Write the 6 ones in the product. Carry the 5 tens to the tens column and make a note of it for yourself. You might write it above the tens column.

[latex]\begin{array}{rrr}&_5\hspace{0.5em}\\&68\\\times&7\\\hline&6\end{array}[/latex]

Step 2: Multiply the tens by the multiplier. 7 × 6 tens = 42 tens Now add on the 5 tens that you carried. 42 tens + 5 tens = 47 tens = 4 hundreds and 7 tens

[latex]\begin{array}{rrr}&_5\hspace{0.5em}\\&68\\\times&7\\\hline&476\end{array}[/latex]

Exercise 3

Find the product. Check your work using the answer key at the end of the exercise.

1. [latex]\begin{array}{rr}&16\\\times&8\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&62\\\times&6\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&37\\\times&4\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&14\\\times&9\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&36\\\times&7\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&92\\\times&9\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&48\\\times&6\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&17\\\times&2\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&26\\\times&4\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&54\\\times&7\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&58\\\times&8\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&45\\\times&4\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&56\\\times&3\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&47\\\times&5\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&39\\\times&6\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&75\\\times&6\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&38\\\times&5\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&82\\\times&7\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&98\\\times&3\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&29\\\times&5\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&47\\\times&3\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&74\\\times&8\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&56\\\times&5\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&98\\\times&4\\\hline\\\end{array}[/latex]

Answers to Exercise 3

1. 128
2. 372
3. 148
4. 126
5. 252
6. 828
7. 288
8. 34
9. 104
10. 378
11. 464
12. 180
13. 168
14. 235
15. 234
16. 450
17. 190
18. 574
19. 294
20. 145
21. 141
22. 592
23. 280
24. 392

Example E

[latex]4\times224=[/latex]          [latex]\begin{array}{rr}&224\\\times&4\\\hline\end{array}[/latex] Step 1: 4 × 4 ones = 16 ones = 1 ten and 6 ones

Write the 6 ones in the product and carry the one ten.

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&6\end{array}[/latex]

Step 2: 4 × 2 tens = 8 tens

8 tens + 1 ten we carried = 9 tens

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&96\end{array}[/latex]

Step 3: 4 × 2 hundreds = 8 hundreds

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&224\\\times&4\\\hline&896\end{array}[/latex]

 

Example F

[latex]4\times456=[/latex]          [latex]\begin{array}{rr}&456\\\times&5\\\hline\end{array}[/latex] Step 1: 5 × 6 ones = 30 ones = 3 ten and 0 ones

The 0 must be written to hold the ones place. Carry the 3 tens.

[latex]\begin{array}{rr}&_3\hspace{0.5em}\\&456\\\times&5\\\hline&0\end{array}[/latex]

Step 2: 5 × 5 tens = 25 tens

25 tens + 3 tens = 28 tens = 2 hundreds and 8 tens

Write the 8 tens in the product. Carry the 2 hundreds.

[latex]\begin{array}{rr}&_{2\text{ }3}\hspace{0.5em}\\&456\\\times&5\\\hline&80\end{array}[/latex]

Step 3: 5 × 4 hundreds = 20 hundreds + 2 hundreds = 22 hundreds = 2 thousands and 2 hundreds

[latex]\begin{array}{rr}&_{2\text{ }3}\hspace{0.5em}\\&456\\\times&5\\\hline&2280\end{array}[/latex]

Exercise 4

Find the products. Check your work using the answer key at the end of the exercise.

1. [latex]\begin{array}{rr}&648\\\times&9\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&240\\\times&7\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&457\\\times&8\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&404\\\times&2\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&106\\\times&9\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&156\\\times&4\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&407\\\times&8\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&239\\\times&6\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&118\\\times&9\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&425\\\times&7\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&139\\\times&8\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&565\\\times&2\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&248\\\times&3\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&604\\\times&6\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&239\\\times&4\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&576\\\times&3\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&857\\\times&6\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&478\\\times&9\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&674\\\times&7\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&629\\\times&8\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&893\\\times&5\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&583\\\times&8\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&952\\\times&9\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&293\\\times&7\\\hline\\\end{array}[/latex]

Answers to Exercise 4

1. 5832
2. 1680
3. 3656
4. 808
5. 954
6. 624
7. 3256
8. 1434
9. 1062
10. 2975
11. 1112
12. 1130
13. 744
14. 3624
15. 956
16. 1728
17. 5142
18. 4302
19. 4718
20. 5032
21. 4465
22. 4664
23. 8568
24. 2051

 

Example G

[latex]\begin{array}{rr}&2408\\\times&9\\\hline\end{array}[/latex]

[latex]\begin{array}{rr}&_3\hspace{0.7em}_7\hspace{0.5em}\\&2408\\\times&9\\\hline&21672\end{array}[/latex]

Step 1: 9 × 8 ones = 72 ones = 7 tens and 2 ones Step 2: 9 × 0 = 0 tens. 0 tens + 7 tens = 7 tens Step 3: 9 × 4 hundreds = 36 hundreds = 3 thousands and 6 hundreds Step 4: 9 × 2 thousands = 18 thousands. 18 thousands + 3 thousands = 21 thousands

Exercise 5

Find the products. Check your work using the answer key at the end of the exercise.

1. [latex]\begin{array}{rr}&4103\\\times&8\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&6087\\\times&4\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&3280\\\times&6\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&7034\\\times&5\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&8456\\\times&2\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&4758\\\times&7\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&4735\\\times&3\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&5402\\\times&9\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&5394\\\times&4\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&2034\\\times&8\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&8652\\\times&5\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&6392\\\times&7\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&4187\\\times&6\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&1376\\\times&9\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&3297\\\times&2\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&9628\\\times&3\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&7689\\\times&8\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&5160\\\times&3\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&4256\\\times&7\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&5491\\\times&5\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&8032\\\times&9\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&8645\\\times&6\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&6453\\\times&2\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&8129\\\times&4\\\hline\\\end{array}[/latex]

Answers to Exercise 5

1. 32824
2. 24348
3. 19680
4. 35170
5. 16912
6. 33306
7. 14205
8. 48618
9. 21576
10. 16272
11. 43260
12. 44744
13. 25122
14. 12384
15. 6594
16. 28884
17. 61512
18. 15480
19. 29792
20. 27455
21. 72288
22. 51870
23. 12906
24. 32516

Topic A: Self-Test

Mark   /14    Aim 11/14

1. Find the products. (6 marks)
   1. [latex]\begin{array}{rr}&62\\\times&4\\\hline\\\end{array}[/latex]
   2. [latex]\begin{array}{rr}&31\\\times&4\\\hline\\\end{array}[/latex]
   3. [latex]\begin{array}{rr}&423\\\times&3\\\hline\\\end{array}[/latex]
   4. [latex]\begin{array}{rr}&734\\\times&2\\\hline\\\end{array}[/latex]
   5. [latex]\begin{array}{rr}&8342\\\times&2\\\hline\\\end{array}[/latex]
   6. [latex]\begin{array}{rr}&5231\\\times&3\\\hline\\\end{array}[/latex]
2. Multiply these numbers. (4 marks)
   1. [latex]\begin{array}{rr}&44\\\times&7\\\hline\\\end{array}[/latex]
   2. [latex]\begin{array}{rr}&69\\\times&8\\\hline\\\end{array}[/latex]
   3. [latex]\begin{array}{rr}&207\\\times&9\\\hline\\\end{array}[/latex]
   4. [latex]\begin{array}{rr}&184\\\times&6\\\hline\\\end{array}[/latex]
3. Find the products. (4 marks)
   1. [latex]\begin{array}{rr}&2834\\\times&5\\\hline\\\end{array}[/latex]
   2. [latex]\begin{array}{rr}&4037\\\times&6\\\hline\\\end{array}[/latex]
   3. [latex]\begin{array}{rr}&9241\\\times&8\\\hline\\\end{array}[/latex]
   4. [latex]\begin{array}{rr}&3652\\\times&4\\\hline\\\end{array}[/latex]

Answers to Topic A Self-Test

1. Find the products.
   1. 249
   2. 124
   3. 1269
   4. 1468
   5. 16684
   6. 15693
2. Multiply these numbers.
   1. 308
   2. 552
   3. 1863
   4. 1104
3. Find the products.
   1. 14170
   2. 24222
   3. 73928
   4. 14608

]]> 1024 1022 6 0 https://opentextbc.ca/alfm3/chapter/two-and-three-digit-multipliers/ Fri, 06 Jan 2023 16:53:11 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1048 Multiplying by Two-Digit Multipliers

Example A

[latex]24\times23=[/latex] Part 1: Multiply by the ones digit in the multiplier.

Multiply 3 ones by 24 using the method you already know. The first partial product is 72.

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&24\\\times&23\\\hline&72\end{array}[/latex]

Part 2: Multiply by the tens digit in the multiplier. First, put a 0 to hold the ones place in your partial product. We are multiplying by a ten, so we hold the ones place.

Step 1: Multiply 2 tens by 4 ones = 8 tens

Write the 8 tens under the tens in your first partial product. It is very important to keep the columns straight – ones under one, tens under tens.

Step 2: Multiply 2 tens by 2 tens = 4 hundreds

Write the 4 hundreds in your partial product. The second partial product is 480.

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&24\\\times&23\\\hline&72\\&480\end{array}[/latex]

Part 3: Add the partial products together, being sure to add ones to ones, tens to tens, hundreds to hundreds. The sum is the final product.

Draw a line under the partial products. Add. Check your addition.

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&24\\\times&23\\\hline&72\\+&480\\\hline&552\end{array}[/latex]

Example B

[latex]36\times425 =[/latex] Part 1: Multiply by the ones digit in the multiplier. 6 × 425 = 2550

[latex]\begin{array}{rr}&_1\hspace{0.15em}_3\hspace{0.5em}\\&425\\\times&36\\\hline&2550\end{array}[/latex]

Part 2: Multiply by the tens digit in the multiplier. First put a 0 to hold the ones place in the second partial product.

• Step 1: 3 tens × 5 tens = 15 tens = 1 hundred and 5 tens Write the 5 tens in the second partial product and carry the 1 hundred. Now you can see why it is best to cross out the numbers you carry as soon as you have added them to the product.
• Step 2: 3 tens × 2 tens = 6 hundreds 6 hundreds + 1 hundred (carried) = 7 hundreds. There is nothing to carry.
• Step 3: 3 tens × 4 hundreds = 12 thousands

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&_1\hspace{0.15em}_3\hspace{0.5em}\\&425\\\times&36\\\hline&2550\\&12750\end{array}[/latex]

Part 3: Add the partial products together.

[latex]\begin{array}{rr}&_1\hspace{0.5em}\\&_1\hspace{0.15em}_3\hspace{0.5em}\\&425\\\times&36\\\hline&2550\\+&12750\\\hline&15300\end{array}[/latex]

Tip: Keeping the columns straight with ones under ones, tens under tens, hundreds under hundreds is very important. Working on large-squared graphing paper using one digit per square is often helpful.

tens × tens = hundreds tens × hundreds = thousands

Exercise 1

Multiply, being very careful to keep the columns straight when you write your partial products. Check your work using the answer key at the end of the exercise.

[latex]\begin{array}{rr}&84\\\times&12\\\hline&168\\+&840\\\hline&1008\end{array}[/latex]

1. [latex]\begin{array}{rr}&73\\\times&12\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&50\\\times&42\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&62\\\times&31\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&61\\\times&42\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&91\\\times&53\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&92\\\times&31\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&91\\\times&49\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&72\\\times&48\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&53\\\times&30\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&41\\\times&53\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&42\\\times&94\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&80\\\times&86\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&31\\\times&79\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&54\\\times&40\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&61\\\times&48\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&60\\\times&31\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&55\\\times&73\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&84\\\times&56\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&53\\\times&38\\\hline\\\end{array}[/latex]

Answers to Exercise 1

1. 876
2. 2100
3. 1922
4. 2562
5. 4823
6. 2852
7. 4459
8. 3456
9. 1590
10. 2173
11. 3948
12. 6880
13. 2449
14. 2160
15. 2928
16. 1860
17. 4015
18. 4704
19. 2014

When the multiplier has a zero in the ones place, use this shortcut.

Example C

[latex]\begin{array}{rr}&48\\\times&80\\\hline&3840\end{array}[/latex]

• Step 1: 0 ones × 48 = 0. Place one zero in the product and that will hold the ones place.
• Step 2: Multiply by the tens digit and write the product beside the zero.

Example D

[latex]\begin{array}{rr}&97\\\times&20\\\hline&1940\end{array}[/latex]

Exercise 2

Find the products. Use the shortcut for multipliers with a zero in them. Check your work using the answer key at the end of the exercise. [latex]\begin{array}{rr}&76\\\times&70\\\hline&5320\end{array}[/latex]

1. [latex]\begin{array}{rr}&52\\\times&70\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&91\\\times&70\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&83\\\times&70\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&49\\\times&70\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&61\\\times&70\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&16\\\times&70\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&36\\\times&70\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&398\\\times&70\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&432\\\times&70\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&863\\\times&70\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&907\\\times&70\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&503\\\times&70\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&452\\\times&70\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&943\\\times&70\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&248\\\times&70\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&6287\\\times&70\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&9025\\\times&70\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&8907\\\times&70\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&300\\\times&70\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&9075\\\times&70\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&3952\\\times&70\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&1528\\\times&70\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&7106\\\times&70\\\hline\\\end{array}[/latex]

Answers to Exercise 2

1. 3640
2. 6370
3. 5810
4. 3430
5. 4270
6. 1120
7. 2520
8. 27860
9. 30240
10. 60410
11. 63490
12. 35210
13. 31640
14. 66010
15. 17360
16. 440090
17. 631750
18. 623490
19. 21000
20. 635250
21. 276640
22. 106960
23. 497420

How are you doing? Ask your instructor for help if you are not comfortable with multiplying.

Multiplying by Three-Digit Multipliers

To multiply by three digit multipliers, use the same method with one more part.

Example E

[latex]417\times368 =[/latex]

[latex]\begin{array}{rr}&417\\\times&368\\\hline&3336\\&25020\\+&125100\\\hline&153456\end{array}[/latex]

• Part 1: Multiply by the 8 ones.
• Part 2: Multiply the 6 tens; hold the ones place with 0.
• Part 3: Multiply by the 3 hundreds. Put 00 to hold the ones and tens places in the third partial product.
  • Step 1: 3 hundreds × 7 ones = 21 hundreds = 2 thousands and 1 hundred. Write the 1 hundred and carry the 2 thousands.
  • Step 2: 3 hundreds × 1 ten = 3 thousands. 3 thousands + 2 thousands (carried) = 5 thousands.
  • Step 3: 3 hundreds × 4 hundreds = 12 ten thousands.
• Part 4: Add the partial products.

Exercise 3

Find the products. Check your work using the answer key at the end of the exercise.

1. [latex]\begin{array}{rr}&416\\\times&213\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&375\\\times&291\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&361\\\times&475\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&275\\\times&863\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&984\\\times&469\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&489\\\times&578\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&498\\\times&123\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&267\\\times&854\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&613\\\times&368\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&725\\\times&547\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&269\\\times&912\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&752\\\times&697\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&983\\\times&357\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&835\\\times&148\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&386\\\times&296\\\hline\\\end{array}[/latex]

Answers to Exercise 3

1. 88608
2. 109125
3. 171475
4. 237325
5. 461496
6. 282642
7. 61254
8. 228018
9. 225584
10. 396575
11. 245328
12. 524144
13. 350931
14. 123580
15. 114256

You know to hold the ones place with a zero if the multiplier has a zero in the ones place. Use the same skill if the multiplier has a zero in the tens place.

Example F

[latex]927\times405 =[/latex]

[latex]\begin{array}{rr}&927\\\times&405\\\hline&4635\\+&370800\\\hline&375435\end{array}[/latex]

• Part 1: Multiply by the 5 ones.
• Part 2: Multiply by the 0 tens. Hold the ones place with a 0; 0 × 927 = 0; Place one zero in the tens place in the second partial product.
• Part 3: Multiply by the 4 hundreds. The ones and tens places are already held by zeros. Start this partial product in the hundreds place on the same line.
• Part 4: Add the partial products.

Exercise 4

Find the products. Check your work using the answer key at the end of the exercise.

[latex]\begin{array}{rr}&_2\hspace{0.15em}_2\hspace{0.5em}\\&698\\\times&301\\\hline&698\\+&209400\\\hline&210098\end{array}[/latex]

1. [latex]\begin{array}{rr}&923\\\times&403\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&830\\\times&108\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&482\\\times&206\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&432\\\times&205\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&625\\\times&405\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&275\\\times&306\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&765\\\times&506\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&1576\\\times&702\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&432\\\times&405\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&625\\\times&409\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&175\\\times&306\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&5874\\\times&309\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&7384\\\times&104\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&6538\\\times&603\\\hline\\\end{array}[/latex]

Answers to Exercise 4

1. 371969
2. 89640
3. 99292
4. 88560
5. 253125
6. 84150
7. 387090
8. 1106352
9. 174960
10. 255625
11. 53550
12. 1815066
13. 767936
14. 3942414

Multiplying by 10, 100, and 1000

Exercise 5

Do the following questions and see if you can find the pattern. Check your work using the answer key at the end of the exercise.

1. [latex]\begin{array}{rr}&83\\\times&10\\\hline&830\end{array}[/latex]
2. [latex]\begin{array}{rr}&46\\\times&10\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&97\\\times&10\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&123\\\times&10\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&70\\\times&10\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&129\\\times&10\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&1852\\\times&10\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&29871\\\times&10\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&45\\\times&100\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&26\\\times&100\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&432\\\times&100\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&679\\\times&100\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&2482\\\times&100\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&9037\\\times&100\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&46207\\\times&100\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&97512\\\times&100\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&23\\\times&1000\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&452\\\times&1000\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&207\\\times&1000\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&348\\\times&1000\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&2118\\\times&1000\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&2431\\\times&1000\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&23681\\\times&1000\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&48203\\\times&1000\\\hline\\\end{array}[/latex]

Answers to Exercise 5

1. 830
2. 460
3. 970
4. 1230
5. 700
6. 1290
7. 18520
8. 298710
9. 4500
10. 2600
11. 43200
12. 67900
13. 248200
14. 903700
15. 4620700
16. 9751200
17. 23000
18. 452000
19. 207000
20. 348000
21. 2118000
22. 2431000
23. 23681000
24. 48203000

And the pattern is … When multiplying by 10, 100, 1000, 10000, etc., place as many zeros to the right of the number as there are zeros in the 10, 100, 1000, etc.

• To multiply by 10 put one zero after the number.
• To multiply by 100 put two zeros after the number.
• To multiply by 1000 put three zeros after the number.

Exercise 6

Find the products using the short method.  Do not rewrite the questions. Check your work using the answer key at the end of the exercise.

1. 12 × 10 = 120
2. 10 × 3175 =
3. 162 × 10 =
4. 10 × 53821 =
5. 10 × 123 =
6. 27342 × 10 =
7. 10 × 98 =
8. 1134 × 10 =
9. 15 × 100 =
10. 100 × 278 =
11. 9134 × 100 =
12. 651 × 100 =
13. 100 × 5169 =
14. 100 × 24815 =
15. 10 × 905 =
16. 45683 × 10 =
17. 1000 × 87 =
18. 521 × 1000 =
19. 1000 × 68935 =
20. 1000 × 8902 =
21. 1576 × 1000 =
22. 31584 × 1000 =
23. 1000 × 426 =
24. 72 × 1000 =

Answers for Exercise 6

1. 120
2. 31750
3. 1620
4. 538210
5. 1230
6. 273420
7. 980
8. 11340
9. 1500
10. 27800
11. 913400
12. 65100
13. 516900
14. 2481500
15. 9050
16. 456830
17. 87000
18. 521000
19. 68935000
20. 8902000
21. 1576000
22. 31584000
23. 426000
24. 72000

Topic B: Self-Test

Mark  /12    Aim  10/12

1. Multiply these numbers.
   1. [latex]\begin{array}{rr}&47\\\times&39\\\hline\\\end{array}[/latex]
   2. [latex]\begin{array}{rr}&58\\\times&93\\\hline\\\end{array}[/latex]
   3. [latex]\begin{array}{rr}&48\\\times&100\\\hline\\\end{array}[/latex]
   4. [latex]\begin{array}{rr}&982\\\times&1000\\\hline\\\end{array}[/latex]
   5. [latex]\begin{array}{rr}&678\\\times&39\\\hline\\\end{array}[/latex]
   6. [latex]\begin{array}{rr}&4579\\\times&86\\\hline\\\end{array}[/latex]
   7. [latex]\begin{array}{rr}&8703\\\times&93\\\hline\\\end{array}[/latex]
   8. [latex]\begin{array}{rr}&7390\\\times&85\\\hline\\\end{array}[/latex]
   9. [latex]\begin{array}{rr}&8047\\\times&236\\\hline\\\end{array}[/latex]
   10. [latex]\begin{array}{rr}&4238\\\times&197\\\hline\\\end{array}[/latex]
   11. [latex]\begin{array}{rr}&8200\\\times&444\\\hline\\\end{array}[/latex]
   12. [latex]\begin{array}{rr}&7265\\\times&409\\\hline\\\end{array}[/latex]

Answers to Topic B Self-Test

1. Multiply these numbers.
   1. 1833
   2. 5394
   3. 4800
   4. 982000
   5. 26442
   6. 393794
   7. 809379
   8. 628150
   9. 1899092
   10. 834886
   11. 3640800
   12. 2971385

]]> 1048 1022 7 0 https://opentextbc.ca/alfm3/chapter/estimating-products/ Fri, 06 Jan 2023 21:18:57 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1058 000, etc... You can find the products in questions like these using regular multiplication: But here is a shortcut:

1. Count all the zeros at the end of the numbers in both factors.
2. Write down that many zeros at the end of the product.
3. Multiply the other digits in the usual way and put them before the zeros.

Example A

30 × 500 =

• How many zeros at the end of the factors? 3
• Write them down. 000
• Multiply the other digits and put them before the zeros. 3 × 5 = 15

30 × 500 = 15000

Example B

400 × 3000 =

• How many zeros at the end of the factors? 5
• Write them down. 00000
• Multiply the other digits and put them before the zeros. 4 × 3 = 12

400 × 3000 = 1200000

Exercise 1

Find the products using the shortcut. Check your work using the answer key at the end of the exercise.

1. [latex]\begin{array}{rr}&300\\\times&20\\\hline&6000\end{array}[/latex]
2. [latex]\begin{array}{rr}&6000\\\times&200\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&210\\\times&20\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&800\\\times&600\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&400\\\times&500\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&6000\\\times&90\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&50000\\\times&6000\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&80000\\\times&30\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&5000\\\times&50\\\hline\\\end{array}[/latex]
10. [latex]\begin{array}{rr}&70\\\times&80\\\hline\\\end{array}[/latex]
11. [latex]\begin{array}{rr}&3000\\\times&700\\\hline\\\end{array}[/latex]
12. [latex]\begin{array}{rr}&50000\\\times&900\\\hline\\\end{array}[/latex]
13. [latex]\begin{array}{rr}&9000\\\times&8000\\\hline\\\end{array}[/latex]
14. [latex]\begin{array}{rr}&60000\\\times&90\\\hline\\\end{array}[/latex]
15. [latex]\begin{array}{rr}&90000\\\times&2000\\\hline\\\end{array}[/latex]
16. [latex]\begin{array}{rr}&600\\\times&600\\\hline\\\end{array}[/latex]
17. [latex]\begin{array}{rr}&40000\\\times&800\\\hline\\\end{array}[/latex]
18. [latex]\begin{array}{rr}&2400\\\times&70\\\hline\\\end{array}[/latex]
19. [latex]\begin{array}{rr}&390\\\times&40\\\hline\\\end{array}[/latex]
20. [latex]\begin{array}{rr}&7200\\\times&5000\\\hline\\\end{array}[/latex]
21. [latex]\begin{array}{rr}&7000\\\times&7000\\\hline\\\end{array}[/latex]
22. [latex]\begin{array}{rr}&61000\\\times&400\\\hline\\\end{array}[/latex]
23. [latex]\begin{array}{rr}&5200\\\times&300\\\hline\\\end{array}[/latex]
24. [latex]\begin{array}{rr}&40\\\times&60\\\hline\\\end{array}[/latex]

Answers to Exercise 1

1. 6 000
2. 1 200 000
3. 4 200
4. 480 000
5. 200 000
6. 540 000
7. 300 000 000
8. 2 400 000
9. 250 000
10. 5 600
11. 2 100 000
12. 45 000 000
13. 72 000 000
14. 5 400 000
15. 180 000 000
16. 360 000
17. 32 000 000
18. 168 000
19. 15 600
20. 36 000 000
21. 49 000 000
22. 24 400 000
23. 1 560 000
24. 2 400

To find an estimated product, round the factors before you multiply. If a factor has only one digit, do not round it.

Example C

[latex]\begin{array}{rr}&6258\\\times&3\\\hline\end{array}[/latex] 6258 rounds to 6000. Leave 3 as is. [latex]\begin{array}{rr}&6000\\\times&3\\\hline&18000\end{array}[/latex] 18000 is the estimated product.

Example D

[latex]\begin{array}{rr}&491\\\times&24\\\hline\end{array}[/latex] 491 rounds to 500. 24 rounds to 20. [latex]\begin{array}{rr}&500\\\times&20\\\hline&10000\end{array}[/latex] 10000 is the estimated product.

Topic C: Self-Test

Mark  /18    Aim  15/18

1. Multiply these numbers.
   1. [latex]\begin{array}{rr}&600\\\times&70\\\hline\end{array}[/latex]
   2. [latex]\begin{array}{rr}&9000\\\times&30\\\hline\end{array}[/latex]
   3. [latex]\begin{array}{rr}&5000\\\times&600\\\hline\end{array}[/latex]
   4. [latex]\begin{array}{rr}&3000\\\times&500\\\hline\end{array}[/latex]
   5. [latex]\begin{array}{rr}&400\\\times&50\\\hline\end{array}[/latex]
   6. [latex]\begin{array}{rr}&8000\\\times&1000\\\hline\end{array}[/latex]
2. Find an estimated product.
   1. [latex]\begin{array}{rr}&87\\\times&23\\\hline\end{array}[/latex]
   2. [latex]\begin{array}{rr}&268\\\times&25\\\hline\end{array}[/latex]
   3. [latex]\begin{array}{rr}&9421\\\times&75\\\hline\end{array}[/latex]
   4. [latex]\begin{array}{rr}&2632\\\times&49\\\hline\end{array}[/latex]
   5. [latex]\begin{array}{rr}&365\\\times&455\\\hline\end{array}[/latex]
   6. [latex]\begin{array}{rr}&7264\\\times&590\\\hline\end{array}[/latex]

Answers to Topic C Self-Test

1. Multiply these numbers.
   1. 42000
   2. 270000
   3. 3000000
   4. 1500000
   5. 20000
   6. 8000000
2. Find an estimated product.
   1. 90 × 20 = 1800
   2. 300 × 30 = 9000
   3. 9000 × 80 = 720000
   4. 3000 × 50 = 150000
   5. 400 × 500 = 200000
   6. 7000 × 600 = 4200000

]]> 1058 1022 8 0 https://opentextbc.ca/alfm3/chapter/multiplication-problems/ Fri, 06 Jan 2023 22:51:15 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1062 Key words that point to multiplication:

• altogether
• combined
• in all
• total
• the average is
• product
• how many?
• how much?
• each

Exercise 1

Do these problems by following the five problem-solving steps. Remember to circle the information and underline what is being asked. Be sure to write down your estimation before you find the actual solution. Check your work using the answer key at the end of the exercise.

1. Maria spent $151 a month to ride to work. How much did it cost her to ride to work for the whole year? (1 year = 12 months)
2. Fred travels 121 km a day on his delivery route. How far does he travel in 5 working days?
3. Manuel buys 340 L of gas a month. In 6 months, how many litres of gas does Manual buy?
4. An apartment building has 16 apartments, each rented for $870 a month. What is the total monthly rental income from this building?
5. A farmer sells potatoes at $53 per 50 kg sack. How much will he get for 75 sacks?
6. Bob is paid $12 per hour. If he worked 39 hours last week and 24 hours this week, how much did he earn for the two weeks? (two operations)
7. It costs $35260 per working day to run the factory. How much does it cost to run this factory for a month of 23 working days?
8. The train has an average speed of 75 km an hour. How far does this train travel in 14 hours?
9. Lee’s sports car averages 18 km per litre. How far can she drive on 12 L of gasoline?
10. Frank bought a used car and paid for it over 15 months. He made 15 monthly payments of $325 each. How much did he pay?

Answers to Exercise 1

1. $1812
2. 605 km
3. 2040 L
4. $13920
5. $3975
6. 63hours, $756
7. $810, 980
8. 1050 km
9. 216 km
10. $4875

Topic D: Self-Test

Mark  /8    Aim  6/8

1. Solve these problems. Show all your work. Give yourself one mark for the correct method and one mark for the correct answer.
   1. A freight train has 70 cars. Each car can hold 22680 kilograms of cargo. How much cargo can the train hold in all?
   2. The highway distance between Fernie and Edmonton is 621 kilometres. How many kilometres will a bus travel in 68 trips from Fernie to Edmonton?
   3. A tanker truck made 275 trips in one year. The truck hauled 23 800 litres each time. How many litres did the truck haul during the year?
   4. The college cafeteria hopes to serve 425 people each day. Estimate how many meals will be served if the cafeteria is open 175 days.

Answers to Topic D Self-Test

1. Solve these problems. Show all your work. Give yourself one mark for the correct method and one mark for the correct answer.
   1. 1587600 kilograms
   2. 42228 kilometres
   3. 6545000 litres
   4. 400 × 200 = 80000 meals

]]> 1062 1022 9 0 https://opentextbc.ca/alfm3/chapter/review-multiplication/ Fri, 06 Jan 2023 23:17:58 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1066

Find the products.

1. [latex]\begin{array}{rr}&81\\\times&5\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&73\\\times&3\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&441\\\times&2\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&512\\\times&4\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&9342\\\times&2\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&8132\\\times&3\\\hline\\\end{array}[/latex]

Find the products.

1. [latex]\begin{array}{rr}&48\\\times&7\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&78\\\times&9\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&892\\\times&8\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&536\\\times&6\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&2375\\\times&4\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&5649\\\times&3\\\hline\\\end{array}[/latex]

Find the products.

1. [latex]\begin{array}{rr}&67\\\times&19\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&581\\\times&34\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&7310\\\times&46\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&754\\\times&692\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&2735\\\times&846\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&857\\\times&308\\\hline\\\end{array}[/latex]
7. [latex]\begin{array}{rr}&629\\\times&407\\\hline\\\end{array}[/latex]
8. [latex]\begin{array}{rr}&2805\\\times&15\\\hline\\\end{array}[/latex]
9. [latex]\begin{array}{rr}&5102\\\times&743\\\hline\\\end{array}[/latex]

Find the products. Use the shortcut.

1. [latex]\begin{array}{rr}&1000\\\times&82\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&100\\\times&26\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&6263\\\times&1000\\\hline\\\end{array}[/latex]
4. 407 × 100 =
5. 100 × 9482 =
6. 3614 × 10 =
7. 1000 × 1795 =

Find the products. Use the shortcut.

1. [latex]\begin{array}{rr}&50\\\times&40\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&600\\\times&800\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&9000\\\times&500\\\hline\\\end{array}[/latex]

Find an estimated product.

1. [latex]\begin{array}{rr}&68\\\times&39\\\hline\\\end{array}[/latex]
2. [latex]\begin{array}{rr}&185\\\times&94\\\hline\\\end{array}[/latex]
3. [latex]\begin{array}{rr}&6763\\\times&69\\\hline\\\end{array}[/latex]
4. [latex]\begin{array}{rr}&853\\\times&399\\\hline\\\end{array}[/latex]
5. [latex]\begin{array}{rr}&2735\\\times&846\\\hline\\\end{array}[/latex]
6. [latex]\begin{array}{rr}&68924\\\times&268\\\hline\\\end{array}[/latex]

Word problems.

1. The Yellow River in China is 5464 kilometres long. How many kilometres will 75 boats cover if they travel the length of the river?
2. Mount Logan in Canada is 5959 metres high. How many metres would 24 climbers cover if they were able to climb to the top of Mt. Logan?
3. How many pieces of candy are needed to pack 500 boxes, if each box has 8 rows and each row has 15 pieces of candy? (2-step question)
4. The distance between Prince Rupert and Kelowna is 1409 km. Estimate how many kilometres 42 trucks will travel if each truck makes one trip.

Answers to Unit 1 Review

1. Find the products.
   1. 405
   2. 219
   3. 882
   4. 2048
   5. 18684
   6. 24396
2. Find the products.
   1. 336
   2. 702
   3. 7136
   4. 3216
   5. 9500
   6. 16947
3. Find the products.
   1. 1273
   2. 19754
   3. 336260
   4. 521768
   5. 2313810
   6. 263956
   7. 256003
   8. 42075
   9. 3790786
4. Find the products. Use the shortcut.
   1. 82000
   2. 2600
   3. 6263000
   4. 40700
   5. 948200
   6. 36140
   7. 1795000
5. Find the products. Use the shortcut.
   1. 2000
   2. 480000
   3. 4500000
6. Find an estimated product.
   1. 70 × 40 = 2800
   2. 200  × 90  = 18000
   3. 7000 × 70 = 490000
   4. 900  × 400  =  360000
   5. 3000 × 800 = 2400000
   6. 70000  × 300  =  21000000
7. Word problems.
   1.  409800 kilometres
   2. 143016 metres or 286032 there and back
   3. 60000 pieces of candy
   4. 1000 × 40  =  40000 kilometres

CONGRATULATIONS!!

Now you have finished Unit 1.

TEST TIME!

Ask your instructor for the practice test for this unit. Once you’ve done the practice test, you need to do the unit 1 test. Again, ask your instructor for this. Good luck!

]]> 1066 1022 10 0 https://opentextbc.ca/alfm3/chapter/introduction-and-division-facts/ Fri, 06 Jan 2023 23:48:51 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1078 [latex]8\div4[/latex]              [latex]\require{enclose}4\enclose{longdiv}{8}[/latex]

Division is the opposite of multiplication. Multiplication takes equal-sized groups and puts the groups together to find the total.

3 × 4 = 12

Division takes the total and separates that amount into equal groups. You can find the number of equal groups or the size of each group.

12 ÷ 4 = 3

[latex]4 × 3 = 12[/latex]	[latex]12 ÷ 3 = 4[/latex]	[latex]\begin{array}{r}4\\3 \enclose{longdiv}{12} \end{array}[/latex]
[latex]3 × 4 = 12[/latex]	[latex]12 ÷ 4 = 3[/latex]	[latex]\begin{array}{r}3\\4 \enclose{longdiv}{12} \end{array}[/latex]

Learn this vocabulary for division:

• Dividend – The number or quantity to be divided; the amount altogether.
• Divisor – The number we divide by. The divisor tells us the number of groups or the quantity in each group that the dividend is to be separated into.
• Quotient – (“kw ō shent”) The answer to a division question.

[latex]\begin{array}{r}\text{quotient}\\\text{divisor} \enclose{longdiv}{\text{dividend}}\end{array}[/latex]             [latex]\text{dividend}\div\text{divisor}=\text{quotient}[/latex]

If you have learned your times tables well, the division facts will be easier. The times table chart can be used to find division facts.

To use the times table chart for division facts:

• Find the divisor in the column on the left of the times table chart.
• Run your finger in a straight line across the divisor row until you come to the dividend.
• Go straight up that column and the quotient should be the top number.

Try a few while you are doing Exercise 1.

Exercise 1

Complete this chart to help yourself understand the connection between multiplication and division. The first one is done for you. Check your work using the answer key at the end of the exercise.

#	Multiplication	Division	Division	"Say"
a	5 × 3 = 15 3 × 5 = 15	15 ÷ 3 = 5 15 ÷ 5 = 3	[latex]\begin{array}{r}5\\3 \enclose{longdiv}{15} \end{array}[/latex] [latex]\begin{array}{r}3\\5 \enclose{longdiv}{15} \end{array}[/latex]	15 divided by 3 is 5 15 divided by 5 is 3
b	8 × 6 = 48 6 × 8 = 48	48 ÷ 6 = 8 48 ÷ 8 = 6	[latex]\begin{array}{r}8\\6 \enclose{longdiv}{48} \end{array}[/latex] [latex]\begin{array}{r}6\\8 \enclose{longdiv}{48} \end{array}[/latex]	48 divided by 6 is 8.
c	3 × 7 = 21
d	5 × 9 = 45
e	4 × 6 = 24
f	2 × 8 = 16
g	7 × 10 = 70
h	6 × 9 = 54
i	9 × 4 = 36
j	6 × 7 = 42

Answers to Exercise 1

#	Multiplication	Division	Division	"Say"
a	5 × 3 = 15 3 × 5 = 15	15 ÷ 3 = 5 15 ÷ 5 = 3	[latex]\begin{array}{r}5\\3 \enclose{longdiv}{15} \end{array}[/latex] [latex]\begin{array}{r}3\\5 \enclose{longdiv}{15} \end{array}[/latex]	15 divided by 3 is 5 15 divided by 5 is 3
b	8 × 6 = 48 6 × 8 = 48	48 ÷ 6 = 8 48 ÷ 8 = 6	[latex]\begin{array}{r}8\\6 \enclose{longdiv}{48} \end{array}[/latex] [latex]\begin{array}{r}6\\8 \enclose{longdiv}{48} \end{array}[/latex]	48 divided by 6 is 8. 48 divided by 8 is 6.
c	3 × 7 = 21 7 × 3 = 21	21 ÷ 7 = 3 21 ÷ 3 = 7	[latex]\begin{array}{r}3\\7 \enclose{longdiv}{21} \end{array}[/latex] [latex]\begin{array}{r}7\\3 \enclose{longdiv}{21} \end{array}[/latex]	21 divided by 7 is 3. 21 divided by 3 is 7.
d	5 × 9 = 45 9 × 5 = 45	45 ÷ 9 = 5 45 ÷ 5 = 9	[latex]\begin{array}{r}5\\9 \enclose{longdiv}{45} \end{array}[/latex] [latex]\begin{array}{r}9\\5 \enclose{longdiv}{45} \end{array}[/latex]	45 divided by 9 is 5. 45 divided by 5 is 9.
e	4 × 6 = 24 6 × 4= 24	24 ÷ 6 = 4 24 ÷ 4 = 6	[latex]\begin{array}{r}4\\6 \enclose{longdiv}{24} \end{array}[/latex] [latex]\begin{array}{r}6\\4 \enclose{longdiv}{24} \end{array}[/latex]	24 divided by 6 is 4. 24 divided by 4 is 6.
f	2 × 8 = 16 8 × 2 = 16	16 ÷ 8 = 2 16 ÷ 2 = 8	[latex]\begin{array}{r}2\\8 \enclose{longdiv}{16} \end{array}[/latex] [latex]\begin{array}{r}8\\2 \enclose{longdiv}{16} \end{array}[/latex]	16 divided by 8 is 2. 16 divided by 2 is 8.
g	7 × 10 = 70 10 × 7 = 70	70 ÷ 10 = 7 70 ÷ 7 = 10	[latex]\begin{array}{r}7\\10 \enclose{longdiv}{70} \end{array}[/latex] [latex]\begin{array}{r}10\\7 \enclose{longdiv}{70} \end{array}[/latex]	70 divided by 10 is 7. 70 divided by 7 is 10.
h	6 × 9 = 54 9 × 6 = 54	54 ÷ 9 = 6 54 ÷ 6 = 9	[latex]\begin{array}{r}6\\9 \enclose{longdiv}{54} \end{array}[/latex] [latex]\begin{array}{r}9\\6 \enclose{longdiv}{54} \end{array}[/latex]	54 divided by 9 is 6. 54 divided by 6 is 9.
i	9 × 4 = 36 4 × 9 = 36	36 ÷ 4 = 9 36 ÷ 9 = 4	[latex]\begin{array}{r}9\\4 \enclose{longdiv}{36} \end{array}[/latex] [latex]\begin{array}{r}4\\9 \enclose{longdiv}{36} \end{array}[/latex]	36 divided by 4 is 9. 36 divided by 9 is 4.
j	6 × 7 = 42 7 × 6 = 42	42 ÷ 7 = 6 42 ÷ 6 = 7	[latex]\begin{array}{r}6\\7 \enclose{longdiv}{42} \end{array}[/latex] [latex]\begin{array}{r}7\\6 \enclose{longdiv}{42} \end{array}[/latex]	42 divided by 7 is 6. 42 divided by 6 is 7.

Exercise 2

Check your division facts by quickly doing this exercise. Check your work using the answer key at the end of the exercise.

1. 72 ÷ 6 =
2. 12 ÷ 2 =
3. 3 ÷ 1 =
4. 80 ÷ 10 =
5. 18 ÷ 6 =
6. 40 ÷  4 =
7. 21 ÷ 7 =
8. 50 ÷ 5 =
9. 54 ÷ 9 =
10. 8 ÷  2 =
11. 22 ÷ 11 =
12. 45 ÷ 9 =
13. 4 ÷ 4 =
14. 24 ÷  6
15. 81 ÷ 9 =
16. 88 ÷ 8 =
17. 30 ÷ 3 =
18. 12 ÷ 4 =
19. 33 ÷ 3 =
20. 66 ÷ 11 =
21. 20 ÷ 5 =

Answers to Exercise 2

1. 12
2. 6
3. 3
4. 8
5. 3
6. 10
7. 3
8. 10
9. 6
10. 4
11. 2
12. 5
13. 1
14. 4
15. 9
16. 11
17. 10
18. 3
19. 11
20. 6
21. 4

Exercise 3

Check your division facts by quickly doing this exercise. Check your work using the answer key at the end of the exercise.

1. 90 ÷ 10 =
2. 70 ÷ 7 =
3. 28 ÷ 7 =
4. 32 ÷ 8 =
5. 24 ÷ 3 =
6. 36 ÷ 12 =
7. 84 ÷ 7 =
8. 10 ÷ 2 =
9. 64 ÷ 8 =
10. 6 ÷ 6 =
11. 60 ÷ 12 =
12. 48 ÷ 4 =
13. 72 ÷ 9 =
14. 20 ÷ 10 =
15. 49 ÷ 7 =
16. 48 ÷ 6 =
17. 36 ÷ 9 =
18. 21 ÷ 3 =

Answers to Exercise 3

1. 9
2. 10
3. 4
4. 4
5. 8
6. 3
7. 12
8. 5
9. 8
10. 1
11. 5
12. 12
13. 8
14. 2
15. 7
16. 8
17. 4
18. 7

Exercise 4

Check your division facts by quickly doing this exercise. Check your work using the answer key at the end of the exercise.

1. 12 ÷ 6 =
2. 27 ÷ 9 =
3. 56 ÷ 7 =
4. 3 ÷ 1 =
5. 20 ÷ 2 =
6. 9 ÷ 3 =
7. 55 ÷ 5 =
8. 14 ÷ 7 =
9. 42 ÷ 6 =
10. 18 ÷ 3 =
11. 88 ÷ 11 =
12. 63 ÷ 9 =
13. 28 ÷ 4 =
14. 6 ÷ 1 =
15. 30 ÷ 5 =
16. 4 ÷ 2 =
17. 7 ÷ 7 =
18. 48 ÷ 12 =

Answers to Exercise 4

1. 2
2. 3
3. 8
4. 3
5. 10
6. 3
7. 11
8. 2
9. 7
10. 6
11. 8
12. 7
13. 7
14. 6
15. 6
16. 2
17. 1
18. 4

Tip: Make a list of any errors that you made and the facts that you had to really think about. If you have any more than five facts on your list, ask your instructor for suggestions on learning and drilling the division facts.

Remainders

You have been practicing the division facts that always work out evenly – nothing is left over. Well, in the real world things are not usually so perfect! You have 7 candies to share among your 3 children. We call the left-over the remainder. For now, put R and the left over number after your quotient.

[latex]7\div3=2\text{ R}1[/latex]                            [latex]\begin{array}{r}2\text{ R}1\\3 \enclose{longdiv}{7}\hspace{1.3em}\end{array}[/latex]

Example A

Here are 22 cookies. Circle groups of 5. How many groups of 5 in 22? You should have 4 groups with 2 left over.

[latex]22\div5=4\text{ R}2[/latex]                            [latex]\begin{array}{r}4\text{ R}2\\5 \enclose{longdiv}{22}\hspace{1.3em}\end{array}[/latex]

The remainder must not be the same size or bigger than the divisor. If it is bigger, it means another group could be made.

Example B

Here are 66 suns. Make groups of 9. How many groups of 9 in 66? How many groups? 7 How many left over? 3

[latex]66\div9=7\text{ R}3[/latex]                            [latex]\begin{array}{r}7\text{ R}3\\9 \enclose{longdiv}{66}\hspace{1.3em}\end{array}[/latex]

Tip: The remainder must not be the same size or bigger than the divisor. Why not? It would make another group.

Exercise 5

Draw pictures to find the quotient and the remainder. Write each question using the other division sign as well. Have your instructor check your work.

1. [latex]23\div10=2\text{ R}3[/latex]         [latex]\begin{array}{r}2\text{ R}3\\10 \enclose{longdiv}{23}\hspace{1.3em}\end{array}[/latex]

2. 24 ÷ 7 =
3. 19 ÷ 3 =
4. 39 ÷ 12 =

You cannot always draw pictures, so how should you find the quotients?

Example C

29 ÷ 3 = Use multiplication tables or the division facts to find a trial quotient. What can you multiply by 3 to find a number close to 29?

• 3 × 9 = 27
• 3 × 10 = 30

Use 9 as the trial quotient. Do not use 10 because 3 × 10 = 30, which is more than the dividend 29.

1. Divide. [latex]\begin{array}{r}9\\3 \enclose{longdiv}{29}\end{array}[/latex]
2. Multiply. 9 × 3 = 27. Write the product under the 29. [latex]\begin{array}{r}9\\3 \enclose{longdiv}{29}\\27\end{array}[/latex]
3. Subtract 27 from 29 to find the remainder. [latex]\begin{array}{r}9\\3 \enclose{longdiv}{29}\\-27\\\hline2\end{array}[/latex]
4. Check (compare) to be sure the remainder is less then (<) the divisor. 2 < 3

29 ÷ 3 = 9 R2

Example D

60 ÷ 7 = Think what can be multiplied by 7 to find a number close to 60.

• 7 × 8 = 56 (good)
• 7 × 9 = 63 (too big)

Use 8 as the trial quotient.

1. Divide. [latex]\begin{array}{r}8\\7 \enclose{longdiv}{60}\end{array}[/latex]
2. Multiply. [latex]\begin{array}{r}8\\7 \enclose{longdiv}{60}\\56\end{array}[/latex]
3. Subtract. [latex]\begin{array}{r}8\\7 \enclose{longdiv}{60}\\-56\\\hline4\end{array}[/latex]
4. Compare to be sure the remainder is less than the divisor. 4 < 7

60 ÷ 7 = 8 R4

Exercise 6

Find the quotients and remainders (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.

1. [latex]5\enclose{longdiv}{28}[/latex]
2. [latex]4\enclose{longdiv}{15}[/latex]
3. [latex]6\enclose{longdiv}{47}[/latex]
4. [latex]9\enclose{longdiv}{37}[/latex]
5. [latex]2\enclose{longdiv}{13}[/latex]
6. [latex]6\enclose{longdiv}{25}[/latex]
7. [latex]8\enclose{longdiv}{75}[/latex]
8. [latex]3\enclose{longdiv}{19}[/latex]
9. [latex]7\enclose{longdiv}{32}[/latex]
10. [latex]4\enclose{longdiv}{9}[/latex]
11. [latex]9\enclose{longdiv}{55}[/latex]
12. [latex]10\enclose{longdiv}{98}[/latex]
13. [latex]3\enclose{longdiv}{26}[/latex]
14. [latex]8\enclose{longdiv}{47}[/latex]
15. [latex]9\enclose{longdiv}{46}[/latex]
16. [latex]6\enclose{longdiv}{43}[/latex]
17. [latex]5\enclose{longdiv}{49}[/latex]
18. [latex]4\enclose{longdiv}{38}[/latex]
19. [latex]2\enclose{longdiv}{19}[/latex]
20. [latex]7\enclose{longdiv}{61}[/latex]
21. [latex]3\enclose{longdiv}{23}[/latex]
22. [latex]8\enclose{longdiv}{78}[/latex]
23. [latex]9\enclose{longdiv}{67}[/latex]
24. [latex]6\enclose{longdiv}{45}[/latex]

Answers to Exercise 6

1. 5 R3
2. 3 R3
3. 7 R5
4. 4 R1
5. 6 R1
6. 4 R1
7. 9 R3
8. 6 R1
9. 4 R4
10. 2 R1
11. 6 R1
12. 9 R8
13. 8 R2
14. 5 R7
15. 5 R1
16. 7 R1
17. 9 R4
18. 9 R2
19. 9 R1
20. 8 R5
21. 7 R2
22. 9 R6
23. 7 R4
24. 7 R3

Exercise 7

Find the quotients and remainders (divide, multiply, subtract, compare.) Check your work using the answer key at the end of the exercise. Example 59 ÷ 7 = Rewrite: [latex]7\enclose{longdiv}{59}[/latex] Then solve: [latex]\begin{array}{r}8\\7 \enclose{longdiv}{59}\\-56\\\hline3\end{array}[/latex] Answer: 8 R3

1. 27 ÷ 5 =
2. 13 ÷ 2 =
3. 46 ÷ 9 =
4. 38 ÷ 6 =
5. 61 ÷ 7 =
6. 14 ÷ 5 =
7. 49 ÷ 8 =
8. 28 ÷ 3 =
9. 78 ÷ 8 =
10. 37 ÷ 4 =
11. 67 ÷ 9 =
12. 52 ÷ 6 =
13. 45 ÷ 8 =
14. 25 ÷ 7 =
15. 11 ÷ 3 =
16. 53 ÷ 9 =
17. 19 ÷ 4 =
18. 77 ÷ 8 =
19. 20 ÷ 3 =
20. 11 ÷ 2 =
21. 23 ÷ 5 =
22. 54 ÷ 7 =
23. 87 ÷ 9 =
24. 9 ÷ 4 =

Answers for Exercise 7

1. 5 R2
2. 6 R1
3. 5 R1
4. 6 R2
5. 8 R5
6. 2 R4
7. 6 R1
8. 9 R1
9. 9 R6
10. 9 R1
11. 7 R4
12. 8 R4
13. 5 R5
14. 3 R4
15. 3 R2
16. 5 R8
17. 4 R3
18. 9 R5
19. 6 R2
20. 5 R1
21. 4 R3
22. 7 R5
23. 9 R6
24. 2 R1

Topic A: Self-Test

Mark /12          Aim 9/12

1. Give the answer. (6 marks)
   1. 63 ÷ 9 =
   2. 21 ÷ 7 =
   3. 72 ÷ 8 =
   4. 36 ÷ 4 =
   5. 32 ÷ 4 =
   6. 48 ÷ 6 =
2. Find the quotient. (6 marks)
   1. [latex]6\enclose{longdiv}{59}[/latex]
   2. [latex]9\enclose{longdiv}{87}[/latex]
   3. [latex]7\enclose{longdiv}{51}[/latex]
   4. [latex]8\enclose{longdiv}{76}[/latex]
   5. [latex]5\enclose{longdiv}{49}[/latex]
   6. [latex]3\enclose{longdiv}{26}[/latex]

Answers to Topic A Self-Test

1. Give the answer.
   1. 7
   2. 3
   3. 9
   4. 9
   5. 8
   6. 8
2. Find the quotient.
   1. 9 R5
   2. 9 R6
   3. 7 R2
   4. 9 R4
   5. 9 R4
   6. 8 R2

]]> 1078 1076 2 0 https://opentextbc.ca/alfm3/chapter/divisibility/ Tue, 10 Jan 2023 21:52:38 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1132 Divisibility by 2 A number is divisible by 2 if it ends in 0, 2, 4, 6 or 8.

Example A

438, 540, 256, 12, and 154 are all divisible by 2 because each number ends in a 0, 2, 4, 6, or 8.

Example B

351, 945, 849, 347, and 193 are not divisible by 2 because each number does not end in a 0, 2, 4, 6 or 8.

Exercise 1

Circle the numbers that are divisible by 2. Check your work using the answer key at the end of the exercise.

1. 22
2. 35
3. 17
4. 10
5. 274
6. 345
7. 639
8. 456
9. 2437
10. 7548
11. 6754
12. 5543

Answers to Exercise 1 The following numbers are divisible by 2: a, d, e, h, j, k.

Divisibility by 3

A number is divisible by 3 if the sum (total) of the digits is divisible by 3.

Example C

63 6 + 3 = 9 9 is divisible by three, so 63 is divisible by three.

Example D

148 1 + 4 + 8 = 13 13 is not divisible by three, so 148 is not divisible by 3.

Example E

5892 5 + 8 + 9 + 2 = 24 Add again: 2 + 4 = 6 6 is divisible by 3, so 5892 is divisible by 3.

Exercise 2

Circle the numbers that are divisible by 3. Check your work using the answer key at the end of the exercise.

1. 27
2. 35
3. 81
4. 94
5. 274
6. 581
7. 564
8. 316
9. 3175
10. 1458
11. 1890
12. 3934

Answers to Exercise 2 The following numbers are divisible by 3: a, c, g, j, k.

Divisibility by 5

A number is divisible by 5 if the number ends in 0 or 5.

Example F

290 is divisible by 5 because it ends in 0.

Example G

132 is not divisible by 5 because it does not end in 0 or 5.

Exercise 3

Circle the numbers that are divisible by 5. Check your work using the answer key at the end of the exercise.

1. 45
2. 84
3. 72
4. 90
5. 800
6. 753
7. 672
8. 355
9. 6009
10. 6375
11. 7020
12. 1704

Answers to Exercise 3 The following numbers are divisible by 5: a, d, e, h, j, k.

Exercise 4

For each number, identify if it is divisible by 2, 3, and 5. Check your work using the answer key at the end of the exercise.

Number	Divisible by 2	Divisible by 3	Divisible by 5
474	Yes	Yes	No
615
412
865
300
831
525
350
710
429
906
634
430
275

Answers to Exercise 4

Number	Divisible by 2	Divisible by 3	Divisible by 5
474	Yes	Yes	No
615	No	Yes	Yes
412	Yes	No	No
865	No	No	Yes
300	Yes	Yes	Yes
831	No	Yes	No
525	No	Yes	Yes
350	Yes	No	Yes
710	Yes	No	Yes
429	No	Yes	No
906	Yes	Yes	No
634	Yes	No	No
430	Yes	No	Yes
275	No	No	Yes

Exercise 5

For each number, identify if it is divisible by 2, 3, and 5. Check your work using the answer key at the end of the exercise.

Number	Divisible by 2	Divisible by 3	Divisible by 5
3585
7548
5890
6318
3905
5280
1760
8007
6752
7375
5523
2625
8956
9150

Answers to Exercise 5

Number	Divisible by 2	Divisible by 3	Divisible by 5
3585	No	Yes	Yes
7548	Yes	Yes	No
5890	Yes	No	Yes
6318	Yes	Yes	No
3905	No	No	Yes
5280	Yes	Yes	Yes
1760	Yes	No	Yes
8007	No	Yes	No
6752	Yes	No	No
7375	No	No	Yes
5523	No	Yes	No
2625	No	Yes	Yes
8956	Yes	No	No
9150	Yes	Yes	Yes

Divisibility by 9

A number is divisible by 9 if the sum (total) of the digits is divisible by 9.

Example H

135 1 + 3 + 5 = 9 9 is divisible by 9, so 135 is divisible by 9.

Example I

7578 7 + 5 + 7 + 8 = 27 27 is divisible by 9, so 7578 is divisible by 9.

Example J

57896 5 + 7 + 8 + 9 + 6 = 35 35 is not divisible by 9, so 57896 is not divisible by 9.

Exercise 6

Circle the numbers that are divisible by 9. Check your work using the answer key at the end of the exercise.

1. 538
2. 783
3. 954
4. 762
5. 6213
6. 5742
7. 7083
8. 5738
9. 34937
10. 39402
11. 74124
12. 45683

Answers to Exercise 6 The following numbers are divisible by 9: b, c, f, g, j, k

Exercise 7

For each number, identify if it is divisible by 2, 3, 5, and 9. Check your work using the answer key at the end of the exercise.

Number	Divisible by 2	Divisible by 3	Divisible by 5	Divisible by 9
453
320
216
726
712
425
630
375
990
210

Answers to Exercise 7

Number	Divisible by 2	Divisible by 3	Divisible by 5	Divisible by 9
453	No	Yes	No	No
320	Yes	No	Yes	No
216	Yes	Yes	No	Yes
726	Yes	Yes	No	No
712	Yes	No	No	No
425	No	No	Yes	No
630	Yes	Yes	Yes	Yes
375	No	Yes	Yes	No
990	Yes	Yes	Yes	Yes
210	Yes	Yes	Yes	No

Exercise 8

For each number, identify if it is divisible by 2, 3, 5, and 9. Check your work using the answer key at the end of the exercise.

Number	Divisible by 2	Divisible by 3	Divisible by 5	Divisible by 9
837
360
648
981
465
1002
3520
6435
8022
7425

Answers to Exercise 8

Number	Divisible by 2	Divisible by 3	Divisible by 5	Divisible by 9
837	No	Yes	No	Yes
360	Yes	Yes	Yes	Yes
648	Yes	Yes	No	Yes
981	No	Yes	No	Yes
465	No	Yes	Yes	No
1002	Yes	Yes	No	No
3520	Yes	No	Yes	No
6435	No	Yes	Yes	Yes
8022	Yes	Yes	No	No
7425	No	Yes	Yes	Yes

Exercise 9

For each number, identify if it is divisible by 2, 3, 5, and 9. Check your work using the answer key at the end of the exercise

Number	Divisible by 2	Divisible by 3	Divisible by 5	Divisible by 9
1200
7164
3681
8205
2745
4320
7350
4000
1368
6720

Answers to Exercise 9

Number	Divisible by 2	Divisible by3	Divisible by 5	Divisible by 9
1200	Yes	Yes	Yes	No
7164	Yes	Yes	No	Yes
3681	No	Yes	No	Yes
8205	No	Yes	Yes	No
2745	No	Yes	Yes	Yes
4320	Yes	Yes	Yes	Yes
7350	Yes	Yes	Yes	No
4000	Yes	No	Yes	No
1368	Yes	Yes	No	Yes
6720	Yes	Yes	Yes	No

Topic B: Self-Test

Mark /12          Aim 9/12

1. From the list of numbers, write the numbers that are divisible by the specified number. 48, 925, 1467, 2645, 5534, 7512, 31183, 52361
   1. Which numbers are divisible by 2?
   2. Which numbers are divisible by 3?
   3. Which numbers are divisible by 5?
   4. Which numbers are divisible by 9?
2. For each number, identify if it is divisible by 2, 3, 5, and 9.

   Number	Divisible by 2	Divisible by 3	Divisible by 5	Divisible by 9
   1200
   7164
   3681
   8205
   2745

Answers to Topic B Self-Test

1. From the list of numbers, write the numbers that are divisible by the specified number.
   1. 48, 7512, 5534
   2. 48, 1467, 7512
   3. 925, 2645
   4. 1467
2. For each number, identify if it is divisible by 2, 3, 5, and 9.

   Number	Divisible by 2	Divisible by 3	Divisible by 5	Divisible by 9
   1200	Yes	Yes	Yes	No
   7164	Yes	Yes	No	Yes
   3681	No	Yes	No	Yes
   8205	No	Yes	Yes	No
   2745	No	Yes	Yes	Yes

]]> 1132 1076 3 0 https://opentextbc.ca/alfm3/chapter/dividing-larger-numbers-by-one-digit-divisors/ Tue, 10 Jan 2023 23:10:10 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1139 One-Digit Divisors without Remainders Division has four steps which are repeated until the dividend is completely divided. Work through the three examples which show these steps.

1. Divide.
2. Multiply
3. Subtract and compare the remainder to the divisor.
4. Bring down the next digit in the dividend and repeat.

Example A

294 ÷ 7 = Rewrite as [latex]7\enclose{longdiv}{294}[/latex] Step 1: Divide.

1. Find a trial quotient using multiplication tables or division facts.
2. Look at the dividend one digit at a time.
   1. The first digit is a 2, which is really 2 hundreds.
   2. Will 7 go into 2? Can you divide 2 by 7? No.
   3. Look at the first 2 digits, 29, which is really 29 tens.
   4. Will 7 go into 29? Yes. 4 × 7 = 28.
3. The first number in the quotient is 4. Place the 4 in the quotient directly above the 9 tens. The 4 is 4 tens in the quotient.

[latex]\begin{array}{r}4\hspace{0.8em}\\7 \enclose{longdiv}{294}\end{array}[/latex]

Step 2: Multiply.

1. Multiply 4 × 7  = 28.
2. Write the 28 under the 29. Draw a line.

[latex]\begin{array}{r}4\hspace{0.8em}\\7 \enclose{longdiv}{294}\\28\hspace{0.8em}\\\hline\end{array}[/latex]

Step 3: Subtract.

1. Subtract 29 − 28 = 1 (ten).
2. Check 1 < 7.

[latex]\begin{array}{r}4\hspace{0.8em}\\7 \enclose{longdiv}{294}\\-28\hspace{0.8em}\\\hline1\hspace{0.8em}\end{array}[/latex]

Step 4: Bring down the next number in the dividend.

1. Bring down the next number in the dividend (4), and put it beside the result of the subtraction you just completed (1).
2. Together, they make 14. This 14 is the number that you must now divide.

[latex]\begin{array}{r}4\hspace{0.8em}\\7 \enclose{longdiv}{294}\\-28\hspace{0.8em}\\\hline14\end{array}[/latex]

Repeat Step 1: Divide.

1. Divide 14 ÷ 7 = 2
2. Put the 2 in the quotient right after the 4 in the ones place.

[latex]\begin{array}{r}42\\7 \enclose{longdiv}{294}\\-28\hspace{0.8em}\\\hline14\end{array}[/latex]

Repeat Step 2: Multiply.

1. Multiply 2 × 7 = 14.
2. Write the 14 under the 14. Draw a line.

[latex]\begin{array}{r}42\\7 \enclose{longdiv}{294}\\-28\hspace{0.8em}\\\hline14\\14\\\hline\end{array}[/latex]

Repeat Step 3: Subtract.

1. Subtract 14 − 14 = 0. There is 0 remainder.
2. Check 0 < 7.

[latex]\begin{array}{r}42\\7 \enclose{longdiv}{294}\\-28\hspace{0.8em}\\\hline14\\-14\\\hline0\end{array}[/latex]

There are no more numbers in the dividend to bring down, so you are done.

294 ÷ 7 = 42

Example B

128 ÷ 2 =

[latex]\begin{array}{r}64\\2 \enclose{longdiv}{128}\\-12\hspace{0.8em}\\\hline08\\-8\\\hline0\end{array}[/latex]

Step 1: Divide.

1. Can 2 go into 1? No.
2. Can 2 go into 12? Yes.
3. How many times?
   • 2 × 6 = 12; 12 ÷ 2 = 6
4. The first number in the trial quotient is 6. Put the 6 in the quotient directly above the 2 tens dividend.

Step 2: Multiply.

1. 6 × 2 = 12.
2. Write the 12 under the 12. Draw a line.

Step 3: Subtract.

1. 12 − 12 = 0
2. Check 0 < 12

Step 4: Bring down the next number in the dividend.

1. Bring down the next number in the dividend (8), and put it beside the result of the subtraction you just completed (0).
2. 8 is now the number to be divided.

Repeat

1. Divide: 8 ÷ 2 = 4
2. Multiple: 4 × 2 = 8
3. Subtract: 8 − 8 = 0
   1. Check 0 < 2
4. Bring down the next digit. There are no more digits in the dividend.

128 ÷ 2 = 64

Exercise 1

Find the quotients (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.

1. [latex]4\enclose{longdiv}{364}[/latex]
2. [latex]2\enclose{longdiv}{144}[/latex]
3. [latex]5\enclose{longdiv}{455}[/latex]
4. [latex]7\enclose{longdiv}{651}[/latex]
5. [latex]8\enclose{longdiv}{144}[/latex]
6. [latex]2\enclose{longdiv}{166}[/latex]
7. [latex]7\enclose{longdiv}{588}[/latex]
8. [latex]2\enclose{longdiv}{196}[/latex]
9. [latex]5\enclose{longdiv}{230}[/latex]
10. [latex]8\enclose{longdiv}{584}[/latex]
11. [latex]6\enclose{longdiv}{366}[/latex]
12. [latex]4\enclose{longdiv}{244}[/latex]
13. [latex]5\enclose{longdiv}{375}[/latex]
14. [latex]8\enclose{longdiv}{200}[/latex]
15. [latex]2\enclose{longdiv}{628}[/latex]
16. [latex]7\enclose{longdiv}{357}[/latex]
17. [latex]9\enclose{longdiv}{837}[/latex]
18. [latex]8\enclose{longdiv}{248}[/latex]
19. [latex]8\enclose{longdiv}{312}[/latex]
20. [latex]7\enclose{longdiv}{462}[/latex]
21. [latex]5\enclose{longdiv}{295}[/latex]
22. [latex]6\enclose{longdiv}{384}[/latex]
23. [latex]2\enclose{longdiv}{276}[/latex]
24. [latex]4\enclose{longdiv}{372}[/latex]

Answers to Exercise 1

1. 91
2. 72
3. 91
4. 93
5. 18
6. 83
7. 84
8. 98
9. 46
10. 73
11. 61
12. 61
13. 75
14. 25
15. 314
16. 51
17. 93
18. 31
19. 39
20. 66
21. 59
22. 64
23. 138
24. 93

Example C

856 ÷ 8 = [latex]8\enclose{longdiv}{856}[/latex] Divide Does 8 go into 8? Yes. 8 ÷ 8 = 1.

[latex]\begin{array}{r}1\hspace{1.2em}\\8 \enclose{longdiv}{856}\end{array}[/latex]

Multiply 1 × 8 = 8

[latex]\begin{array}{r}1\hspace{1.2em}\\8 \enclose{longdiv}{856}\\8\hspace{1.2em}\end{array}[/latex]

Subtract 8 − 8 = 0. Check 0 < 8.

[latex]\begin{array}{r}1\hspace{1.2em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline0\hspace{1.2em}\end{array}[/latex]

Bring down the next digit  5 is now the number to be divided.

[latex]\begin{array}{r}1\hspace{1.2em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\end{array}[/latex]

Now repeat. Divide Does 8 go into 5? No.

You must put a zero to hold the place in the quotient. If a digit is brought down, a digit must be placed in the quotient.

Multiply 0 × 8 = 0

[latex]\begin{array}{r}10\hspace{0.8em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\end{array}[/latex]

Subtract 5 − 0 = 5. Check 5 < 8.

[latex]\begin{array}{r}10\hspace{0.8em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline5\hspace{0.8em}\end{array}[/latex]

Bring down the next digit 56 is now the number to be divided.

[latex]\begin{array}{r}10\hspace{0.8em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline56\end{array}[/latex]

Now repeat. Divide Does 8 go into 56? Yes. 56 ÷ 8 = 7. Write 7 in the quotient in the ones place above the 6 in the dividend.

[latex]\begin{array}{r}107\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline56\end{array}[/latex]

Multiply 7 × 8 = 56

[latex]\begin{array}{r}107\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline56\\56\end{array}[/latex]

Subtract 56 − 56 = 0. Check 0 < 8.

[latex]\begin{array}{r}107\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline56\\-56\\\hline0\end{array}[/latex]

Bring down the next digit. No more digits.

856 ÷ 8 = 107

Exercise 2

Find the quotients (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.

1. [latex]7\enclose{longdiv}{721}[/latex]
2. [latex]9\enclose{longdiv}{954}[/latex]
3. [latex]3\enclose{longdiv}{927}[/latex]
4. [latex]3\enclose{longdiv}{621}[/latex]
5. [latex]4\enclose{longdiv}{824}[/latex]
6. [latex]9\enclose{longdiv}{972}[/latex]
7. [latex]7\enclose{longdiv}{714}[/latex]
8. [latex]2\enclose{longdiv}{416}[/latex]
9. [latex]5\enclose{longdiv}{540}[/latex]
10. [latex]6\enclose{longdiv}{654}[/latex]
11. [latex]8\enclose{longdiv}{832}[/latex]
12. [latex]4\enclose{longdiv}{436}[/latex]
13. [latex]5\enclose{longdiv}{515}[/latex]
14. [latex]2\enclose{longdiv}{814}[/latex]
15. [latex]6\enclose{longdiv}{648}[/latex]
16. [latex]8\enclose{longdiv}{856}[/latex]
17. [latex]5\enclose{longdiv}{525}[/latex]
18. [latex]7\enclose{longdiv}{763}[/latex]
19. [latex]9\enclose{longdiv}{945}[/latex]
20. [latex]3\enclose{longdiv}{315}[/latex]
21. [latex]8\enclose{longdiv}{872}[/latex]
22. [latex]4\enclose{longdiv}{416}[/latex]
23. [latex]6\enclose{longdiv}{618}[/latex]
24. [latex]2\enclose{longdiv}{612}[/latex]

Answers to Exercise 2

1. 103
2. 106
3. 309
4. 207
5. 206
6. 108
7. 102
8. 208
9. 108
10. 109
11. 104
12. 109
13. 103
14. 407
15. 108
16. 107
17. 105
18. 109
19. 105
20. 105
21. 109
22. 104
23. 103
24. 306

One-Digit Divisors with Remainders

Do the division exactly the same way that you have been learning. Often there is a remainder after the last subtraction. Write it with the quotient as you already know how to do.

Example D

259 ÷ 8 =

[latex]\begin{array}{l}\hspace{1.5em}32\text{ R}3\\8 \enclose{longdiv}{259}\\\hspace{0.3em}-24\\\hline\hspace{1.7em}19\\\hspace{1em}-16\\\hline\hspace{2.3em}3\end{array}[/latex]

259 ÷ 8 = 32 R3

Exercise 3

Divide and show any remainders. Check your work using the answer key at the end of the exercise.

1. [latex]20\enclose{longdiv}{93}[/latex]
2. [latex]3\enclose{longdiv}{52}[/latex]
3. [latex]5\enclose{longdiv}{94}[/latex]
4. [latex]7\enclose{longdiv}{74}[/latex]
5. [latex]4\enclose{longdiv}{95}[/latex]
6. [latex]9\enclose{longdiv}{96}[/latex]
7. [latex]6\enclose{longdiv}{97}[/latex]
8. [latex]8\enclose{longdiv}{99}[/latex]
9. [latex]9\enclose{longdiv}{98}[/latex]
10. [latex]4\enclose{longdiv}{59}[/latex]
11. [latex]6\enclose{longdiv}{76}[/latex]
12. [latex]3\enclose{longdiv}{79}[/latex]
13. [latex]7\enclose{longdiv}{96}[/latex]
14. [latex]5\enclose{longdiv}{57}[/latex]
15. [latex]2\enclose{longdiv}{47}[/latex]
16. [latex]8\enclose{longdiv}{91}[/latex]
17. [latex]7\enclose{longdiv}{89}[/latex]
18. [latex]6\enclose{longdiv}{82}[/latex]
19. [latex]5\enclose{longdiv}{67}[/latex]
20. [latex]2\enclose{longdiv}{85}[/latex]
21. [latex]4\enclose{longdiv}{71}[/latex]
22. [latex]3\enclose{longdiv}{65}[/latex]
23. [latex]9\enclose{longdiv}{92}[/latex]
24. [latex]8\enclose{longdiv}{94}[/latex]

Answers to Exercise 3

1. 46 R1
2. 17 R1
3. 18 R4
4. 10 R4
5. 23 R3
6. 10 R6
7. 16 R1
8. 12 R3
9. 10 R8
10. 14 R3
11. 12 R4
12. 26 R1
13. 13 R5
14. 11 R2
15. 23 R1
16. 11 R3
17. 12 R5
18. 13 R4
19. 13 R2
20. 42 R1
21. 17 R3
22. 21 R2
23. 10 R2
24. 11 R6

Check Division by Multiplying

To check your division, do this:

1. Multiply the quotient by the divisor.
2. Add on any remainder.

The product will equal the dividend if your arithmetic is correct.

Example E

[latex]\begin{array}{l}\hspace{1.5em}52\text{ R}1\\9 \enclose{longdiv}{469}\\\hspace{0.3em}-45\\\hline\hspace{1.7em}19\\\hspace{1em}-18\\\hline\hspace{2.3em}1\end{array}[/latex]                 [latex]\begin{array}{rr}&52\\\times&9\\\hline&468\end{array}[/latex]                 [latex]468+1=469[/latex]

Exercise 4

Divide and check your answer by multiplying. Check your work using the answer key at the end of the exercise.

1. [latex]7\enclose{longdiv}{709}[/latex]
2. [latex]2\enclose{longdiv}{423}[/latex]
3. [latex]5\enclose{longdiv}{538}[/latex]
4. [latex]4\enclose{longdiv}{609}[/latex]
5. [latex]9\enclose{longdiv}{406}[/latex]
6. [latex]6\enclose{longdiv}{125}[/latex]
7. [latex]3\enclose{longdiv}{605}[/latex]
8. [latex]9\enclose{longdiv}{928}[/latex]
9. [latex]3\enclose{longdiv}{962}[/latex]
10. [latex]4\enclose{longdiv}{805}[/latex]
11. [latex]8\enclose{longdiv}{301}[/latex]
12. [latex]2\enclose{longdiv}{807}[/latex]
13. [latex]6\enclose{longdiv}{725}[/latex]
14. [latex]7\enclose{longdiv}{320}[/latex]
15. [latex]9\enclose{longdiv}{140}[/latex]
16. [latex]8\enclose{longdiv}{483}[/latex]
17. [latex]2\enclose{longdiv}{197}[/latex]
18. [latex]6\enclose{longdiv}{307}[/latex]
19. [latex]5\enclose{longdiv}{504}[/latex]
20. [latex]8\enclose{longdiv}{709}[/latex]
21. [latex]7\enclose{longdiv}{876}[/latex]
22. [latex]4\enclose{longdiv}{101}[/latex]
23. [latex]3\enclose{longdiv}{269}[/latex]
24. [latex]5\enclose{longdiv}{473}[/latex]

Answers to Exercise 4

1. 101 R2
2. 211 R1
3. 107 R3
4. 152 R1
5. 45 R1
6. 20 R5
7. 201 R2
8. 103 R1
9. 320 R2
10. 201 R1
11. 37 R5
12. 403 R1
13. 120 R5
14. 45 R5
15. 15 R5
16. 60 R3
17. 98 R1
18. 51 R1
19. 100 R4
20. 88 R5
21. 125 R1
22. 25 R1
23. 89 R2
24. 94 R3

Topic C: Self-Test

Mark  /24   Aim  19/24

1. Find the quotient. (6 marks)
   1. [latex]6\enclose{longdiv}{96}[/latex]
   2. [latex]4\enclose{longdiv}{92}[/latex]
   3. [latex]7\enclose{longdiv}{91}[/latex]
   4. [latex]2\enclose{longdiv}{93}[/latex]
   5. [latex]5\enclose{longdiv}{94}[/latex]
   6. [latex]3\enclose{longdiv}{52}[/latex]
2. Divide. (6 marks)
   1. [latex]7\enclose{longdiv}{182}[/latex]
   2. [latex]8\enclose{longdiv}{736}[/latex]
   3. [latex]6\enclose{longdiv}{162}[/latex]
   4. [latex]5\enclose{longdiv}{295}[/latex]
   5. [latex]4\enclose{longdiv}{184}[/latex]
   6. [latex]9\enclose{longdiv}{576}[/latex]
3. Divide and show your check for each answer (12 marks - 1 mark for question, 1 mark for check).
   1. [latex]9\enclose{longdiv}{705}[/latex]
   2. [latex]4\enclose{longdiv}{257}[/latex]
   3. [latex]7\enclose{longdiv}{899}[/latex]
   4. [latex]5\enclose{longdiv}{538}[/latex]
   5. [latex]8\enclose{longdiv}{876}[/latex]
   6. [latex]6\enclose{longdiv}{628}[/latex]

Answers to Topic C Self-Test

1. Find the quotient.
   1. 16
   2. 23
   3. 13
   4. 46 R1
   5. 18 R4
   6. 17 R1
2. Divide.
   1. 26
   2. 92
   3. 27
   4. 59
   5. 46
   6. 64
3. Divide and show your check for each answer.
   1. 78 R3
   2. 64 R1
   3. 128 R3
   4. 107 R3
   5. 109 R4
   6. 104 R4

]]> 1139 1076 4 0 https://opentextbc.ca/alfm3/chapter/dividing-by-two-and-three-digit-divisors/ Mon, 16 Jan 2023 23:23:39 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1148 Finding Trial Quotients When dividing by 2-digit numbers, you will need to estimate the quotient. This guess is called a trial quotient.

Example A

[latex]624 \div 24[/latex] Rewrite as [latex]24\enclose{longdiv}{624}[/latex]

Step 1: Divide

1. Think: [latex]2\enclose{longdiv}{6}[/latex] is [latex]3[/latex]. So [latex]24\enclose{longdiv}{62}[/latex] is about [latex]3[/latex].

Step 2: Multiply and subtract. 

1. [latex]\begin{array}{r}3 \ \ \ \\ 24\enclose{longdiv}{624}\\72 \ \ \ \\ \hline \end{array}[/latex]
2. Since 72 > 62, 3 is too large.

Step 3: Try a smaller number, multiply and subtract.

1. [latex]\begin{array}{r}2\ \ \ \\ 24\enclose{longdiv}{624}\\48 \ \ \ \\ \hline 14 \ \ \ \end{array}[/latex]
2. Since 14 < 24, 2 is correct.

Step 4: Finish the problem.

Example B

[latex]630 \div 15[/latex] Rewrite as [latex]15\enclose{longdiv}{630}[/latex]

Step 1: Divide

1. 15 rounds to 20. Think: [latex]2\enclose{longdiv}{6}[/latex] is [latex]3[/latex]. So [latex]15\enclose{longdiv}{63}[/latex] is about [latex]3[/latex].

Step 2: Multiply and subtract. 

1. [latex]\begin{array}{r}3 \ \ \ \\ 15\enclose{longdiv}{630}\\45 \ \ \ \\ \hline 18 \ \ \ \end{array}[/latex]
2. Since 18 > 15, 3 is too small.

Step 3: Try a larger number, multiply and subtract.

1. [latex]\begin{array}{r}4 \ \ \ \\ 24\enclose{longdiv}{630}\\60 \ \ \\ \hline 3 \ \ \end{array}[/latex]
2. Since 3 < 15, 4 is correct.

Step 4: Finish the problem.

Exercise 1

In each question, the trial quotient is either too large or too small. Multiply. Write too large or too small on the line. Then, write the correct trial quotient beside. Check your work using the answer key at the end of the exercise.

1. [latex]\begin{array}{r}2 \ \ \ \\ 25\enclose{longdiv}{475}\end{array}[/latex]
2. [latex]\begin{array}{r}3 \ \ \ \\ 15\enclose{longdiv}{682}\end{array}[/latex]
3. [latex]\begin{array}{r}5 \ \ \ \\ 18\enclose{longdiv}{813}\end{array}[/latex]
4. [latex]\begin{array}{r}2\ \ \ \\ 25\enclose{longdiv}{810}\end{array}[/latex]
5. [latex]\begin{array}{r}3\ \ \ \\ 33\enclose{longdiv}{891}\end{array}[/latex]
6. [latex]\begin{array}{r}3\ \ \ \\ 18\enclose{longdiv}{819}\end{array}[/latex]
7. [latex]\begin{array}{r}3\ \ \ \\ 27\enclose{longdiv}{727}\end{array}[/latex]
8. [latex]\begin{array}{r}2 \ \ \ \\ 35\enclose{longdiv}{652}\end{array}[/latex]
9. [latex]\begin{array}{r}3\ \ \ \\ 25\enclose{longdiv}{650}\end{array}[/latex]
10. [latex]\begin{array}{r}4\ \ \ \\34\enclose{longdiv}{176}\end{array}[/latex]
11. [latex]\begin{array}{r}4\ \ \ \\ 12\enclose{longdiv}{420}\end{array}[/latex]
12. [latex]\begin{array}{r}2\ \ \ \\ 43\enclose{longdiv}{801}\end{array}[/latex]
13. [latex]\begin{array}{r}3\ \ \ \\ 31\enclose{longdiv}{899}\end{array}[/latex]
14. [latex]\begin{array}{r}4\ \ \ \\ 18\enclose{longdiv}{648}\end{array}[/latex]
15. [latex]\begin{array}{r}4\ \ \ \\ 27\enclose{longdiv}{946}\end{array}[/latex]
16. [latex]\begin{array}{r}3\ \ \ \\ 23\enclose{longdiv}{943}\end{array}[/latex]
17. [latex]\begin{array}{r}3\ \ \ \\ 24\enclose{longdiv}{578}\end{array}[/latex]
18. [latex]\begin{array}{r}2\ \ \ \\ 29\enclose{longdiv}{406}\end{array}[/latex]
19. [latex]\begin{array}{r}2\ \ \ \\ 48\enclose{longdiv}{892}\end{array}[/latex]
20. [latex]\begin{array}{r}2\ \ \ \\ 28\enclose{longdiv}{534}\end{array}[/latex]
21. [latex]\begin{array}{r}3\ \ \ \\ 37\enclose{longdiv}{939}\end{array}[/latex]
22. [latex]\begin{array}{r}2\ \ \ \\ 28\enclose{longdiv}{854}\end{array}[/latex]

Answers to Exercise 1

1. too large, 1
2. too small, 4
3. too large, 4
4. too small, 3
5. too large, 2
6. too small, 4
7. too large, 2
8. too large 1
9. too large, 2
10. too small, 5
11. too large, 3
12. too large, 1
13. too. large 2
14. too large, 3
15. too large, 3
16. too small, 4
17. too large, 2
18. too large, 1
19. too large, 1
20. too large 1
21. too large, 2
22. too small, 3

Example C

[latex]78\enclose{longdiv}{2706}[/latex]

Since 78 rounds to 80, think [latex]8\enclose{longdiv}{27}[/latex]. 8 goes into 27 ≈ 3. 3 would be a good trial quotient.

[latex]\begin{array}{r}3\ \ \ \\ 78\enclose{longdiv}{2706}\\234\ \ \ \\ \hline 36\ \ \ \end{array}[/latex]

Since 36 < 78, 3 is a good trial quotient.

Example D

[latex]27\enclose{longdiv}{2205}[/latex] Since 27 rounds to 30, think [latex]3\enclose{longdiv}{22}[/latex] . 3 goes into 22 ≈ 7. 7 would be a good trial quotient.

[latex]\begin{array}{r}7\ \ \ \\ 27\enclose{longdiv}{2205}\\189\ \ \ \\ \hline 31\ \ \ \end{array}[/latex]

Since 31 > 27, so 7 is too small.  A better trial quotient would be 8. 

Exercise 2

Find the first digit in the trial quotient.  Check your work using the answer key at the end of the exercise.

1. [latex]43\enclose{longdiv}{1772}[/latex] [latex]\begin{array}{r}4\\ 4\enclose{longdiv}{17}\\16\\ \hline 1\end{array}[/latex]. 1 < 4
2. [latex]64\enclose{longdiv}{3276}[/latex]
3. [latex]28\enclose{longdiv}{6008}[/latex]
4. [latex]33\enclose{longdiv}{2731}[/latex]
5. [latex]59\enclose{longdiv}{4164}[/latex]
6. [latex]75\enclose{longdiv}{2420}[/latex]
7. [latex]54\enclose{longdiv}{3316}[/latex]
8. [latex]38\enclose{longdiv}{2759}[/latex]
9. [latex]46\enclose{longdiv}{387}[/latex]
10. [latex]35\enclose{longdiv}{3316}[/latex]
11. [latex]83\enclose{longdiv}{7237}[/latex]
12. [latex]77\enclose{longdiv}{6763}[/latex]
13. [latex]93\enclose{longdiv}{3724}[/latex]
14. [latex]52\enclose{longdiv}{4690}[/latex]
15. [latex]86\enclose{longdiv}{2089}[/latex]
16. [latex]26\enclose{longdiv}{1417}[/latex]
17. [latex]72\enclose{longdiv}{1462}[/latex]
18. [latex]27\enclose{longdiv}{6939}[/latex]
19. [latex]32\enclose{longdiv}{7840}[/latex]
20. [latex]24\enclose{longdiv}{7605}[/latex]
21. [latex]16\enclose{longdiv}{8640}[/latex]
22. [latex]45\enclose{longdiv}{3060}[/latex]
23. [latex]38\enclose{longdiv}{2158}[/latex]
24. [latex]42\enclose{longdiv}{1491}[/latex]

Answers to Exercise 2

1. 4
2. 5
3. 2
4. 8
5. 7
6. 3
7. 6
8. 7
9. 8
10. 9
11. 8
12. 8
13. 4
14. 9
15. 2
16. 5
17. 2
18. 2
19. 2
20. 3
21. 5
22. 6
23. 5
24. 3

Two Digit Divisors

Dividing by large divisors is a challenge! You must estimate how many times one number will divide into another. Use pencil and have an eraser close by when you do these questions. You will use the same steps that you already know.

Example E

[latex]964 \div 75 =[/latex]

Step 1: Divide

1. Does 75 go into 9?  NO
2. Does 75 go into 96?  YES
3. Estimate
   1. Round 75 to 80 – think “8”
   2. Round 96 to 100 – think “10”
   3. How many 8’s in 10?  (8 1 = 8, 10  8  =  1)
   4. The estimate for the first digit in the trial quotient is 1.
4. Write 1 in the quotient above the 6 tens.

[latex]\begin{array}{r}1\ \ \ \\ 75\enclose{longdiv}{964}\end{array}[/latex]

Step 2:   Multiply 

[latex]1 \times 75 = 75[/latex]

1. Write 75 under 96.

  [latex]\begin{array}{r}1\ \ \ \\ 75\enclose{longdiv}{964}\\75 \ \ \\ \hline \end{array}[/latex]

Step 3:   Subtract              

[latex]96 - 75 = 21[/latex]

1. Check 21 < 75? YES!

  [latex]\begin{array}{r}1\ \ \ \\ 75\enclose{longdiv}{964}\\75\ \ \\ \hline 21 \ \ \end{array}[/latex]

Step 4: Bring down the next digit in the dividend. 214 is now the number to be divided.

  [latex]\begin{array}{r}1\ \ \ \\ 75\enclose{longdiv}{964}\\75 \downarrow \\ \hline 214\end{array}[/latex]

REPEAT   Step 1:   Divide

1. Does 75 go into 214?  YES
2. Estimate 75 as 80 – think “8”
   1. Estimate 214 as 200 – think “20”
   2. 8 goes into 20 2 times ( 8 2 = 16, so 20  8 2)
3. The estimate for the second digit in the trial quotient is 2. Write 2 in the quotient above the 4 in the dividend.

  [latex]\begin{array}{r}12\\ 75\enclose{longdiv}{964}\\75 \downarrow \\ \hline 214\end{array}[/latex]

Step 2:   Multiply

[latex]2 \times 75 = 150[/latex]

1. Write 150 under the 214.

  [latex]\begin{array}{r}12\\ 75\enclose{longdiv}{964}\\75 \downarrow \\ \hline 214 \\ 150 \\ \hline\end{array}[/latex]

Step 3:   Subtract and check that the remainder is less than the divisor.

  [latex]\begin{array}{r}12\\ 75\enclose{longdiv}{964}\\75 \downarrow \\ \hline 214 \\ 150 \\ \hline 64\end{array}[/latex]

  Step 4:   Bring down – no more digits in dividend. To check your answer

[latex]\begin{array}{rrr}&75\\\times&12\\\hline&150 \\ &750 \\ \hline &900 \\ + &64* \\ \hline &964\end{array}[/latex]

*Don’t forget to add the remainder when you check.

Exercise 3

Carefully divide these questions.  Be careful to keep the hundreds in line with the hundreds, the tens with the tens, and so on. You might want to use squared paper for long division. Check your work using the answer key at the end of the exercise. If you are having any difficulty, ask your instructor to watch you doing a few questions to be sure you are using a correct method.

1. [latex]10\enclose{longdiv}{720}[/latex]
2. [latex]12\enclose{longdiv}{564}[/latex]
3. [latex]21\enclose{longdiv}{882}[/latex]
4. [latex]22\enclose{longdiv}{946}[/latex]
5. [latex]32\enclose{longdiv}{1632}[/latex]
6. [latex]23\enclose{longdiv}{943}[/latex]
7. [latex]62\enclose{longdiv}{2528}[/latex]
8. [latex]71\enclose{longdiv}{2414}[/latex]
9. [latex]24\enclose{longdiv}{7578}[/latex]
10. [latex]82\enclose{longdiv}{2958}[/latex]
11. [latex]18\enclose{longdiv}{6250}[/latex]
12. [latex]25\enclose{longdiv}{1550}[/latex]
13. [latex]19\enclose{longdiv}{9595}[/latex]
14. [latex]47\enclose{longdiv}{3854}[/latex]
15. [latex]58\enclose{longdiv}{6500}[/latex]
16. [latex]24\enclose{longdiv}{9648}[/latex]
17. [latex]49\enclose{longdiv}{1312}[/latex]
18. [latex]67\enclose{longdiv}{7683}[/latex]

Answers to Exercise 3

1. 72
2. 47
3. 42
4. 43
5. 51
6. 41
7. 40 R48
8. 34
9. 315 R18
10. 36 R6
11. 347 R4
12. 62
13. 505
14. 82
15. 112 R4
16. 402
17. 26 R38
18. 114 R45

If the estimate for your trial quotient is too large, the result of the multiplication will be larger than the numbers in the dividend. Take, for example, the following division question:

[latex]23\enclose{longdiv}{784}[/latex]

When you divide, the trial estimate is 4:

[latex]\begin{array}{r}4\ \ \ \\ 23\enclose{longdiv}{784}\end{array}[/latex]

When you multiply:

1. [latex]4 \times 23 = 92[/latex]
2. 92 is larger than 78, so 4 is too large an estimate. Erase it. Try 3. [latex]3 \times 23 = 69[/latex]
3. 3 is the correct estimate and you can complete the division, as seen below:

[latex]\begin{array}{l}\hspace{2.3em}34\text{ R}2\\23 \enclose{longdiv}{784}\\\hspace{1.5em}69 \downarrow\\\hline\hspace{2.3em}94\\\hspace{2.3em}92\\\hline\hspace{2.8em}2\end{array}[/latex]

If the estimate is too small, the result of the subtraction will be larger than the divisor. Take this division question as an example:

[latex]72\enclose{longdiv}{4487}[/latex]

Say your trial quotient is 5. When you multiply, you get [latex]5 \times 72 = 360[/latex]. Since 360 is smaller than 448, you can go on to subtract:

[latex]448 - 360=88[/latex]

Is 88 less than 72? NO, 88 is greater than 72. This means that 5 is too small for the trial quotient. Use the larger number 6. Multiply [latex]6 \times 72 = 432[/latex]. Subtract [latex]448 - 432 = 16[/latex]. Since 16 is less than 72, you can continue the division. See the full division process below:

[latex]\begin{array}{l}\hspace{1.1cm}62\text{ R}23\\72 \enclose{longdiv}{4487}\\\hspace{1.45em}432 \downarrow\\\hline\hspace{2.1em}167\\\hspace{2.1em}144\\\hline\hspace{2.55em}23\end{array}[/latex]

Exercise 4

Divide and check your work by multiplying.  Check your work using the answer key at the end of the exercise.

1. [latex]18\enclose{longdiv}{648}[/latex]
2. [latex]26\enclose{longdiv}{6766}[/latex]
3. [latex]52\enclose{longdiv}{1968}[/latex]
4. [latex]84\enclose{longdiv}{8640}[/latex]
5. [latex]72\enclose{longdiv}{2883}[/latex]
6. [latex]94\enclose{longdiv}{8126}[/latex]
7. [latex]20\enclose{longdiv}{4060}[/latex]
8. [latex]47\enclose{longdiv}{1728}[/latex]
9. [latex]33\enclose{longdiv}{1886}[/latex]
10. [latex]25\enclose{longdiv}{5750}[/latex]
11. [latex]79\enclose{longdiv}{2765}[/latex]
12. [latex]42\enclose{longdiv}{8442}[/latex]
13. [latex]57\enclose{longdiv}{9144}[/latex]
14. [latex]96\enclose{longdiv}{20160}[/latex]
15. [latex]75\enclose{longdiv}{23550}[/latex]

Answers to Exercise 4

1. 36
2. 260 R6
3. 37 R44
4. 102 R72
5. 40 R3
6. 86 R42
7. 203
8. 36 R36
9. 57 R5
10. 230
11. 35
12. 201
13. 160 R24
14. 210
15. 314

Dividing by 10, 100, 1000...

What is the pattern?  When you divide by 10

1.   The ones digit in the dividend becomes the remainder.

[latex]10\enclose{longdiv}{324} = 32 R4[/latex]

2. The other numbers in the dividend stay the same, but each digit is one place value less.

• • the hundreds become tens
  • the tens become ones
  • the ones become the remainder

Exercise 5

Find the quotients. Look for the pattern. Check your work using the answer key at the end of the exercise.

1. [latex]10\enclose{longdiv}{46}[/latex]
2. [latex]10\enclose{longdiv}{75}[/latex]
3. [latex]10\enclose{longdiv}{136}[/latex]
4. [latex]10\enclose{longdiv}{832}[/latex]
5. [latex]10\enclose{longdiv}{674}[/latex]
6. [latex]10\enclose{longdiv}{952}[/latex]
7. [latex]10\enclose{longdiv}{2457}[/latex]
8. [latex]10\enclose{longdiv}{3685}[/latex]

Answers to Exercise 5

1. 4 R6
2. 7 R5
3. 13 R6
4. 83 R2
5. 67 R4
6. 95 R2
7. 245 R7
8. 368 R5

When you divide by 100

1.  The ones and tens digits in the dividend become the remainder.
2. The other digits in the dividend stay the same but each digit is two places less.
   • the thousands become tens

• • the hundreds become ones
  • the tens and ones become the remainder

Exercise 6

Find these quotients. Look for the pattern when you divide. Check your work using the answer key at the end of the exercise

1. [latex]100\enclose{longdiv}{386}[/latex]
2. [latex]100\enclose{longdiv}{995}[/latex]
3. [latex]100\enclose{longdiv}{269}[/latex]
4. [latex]100\enclose{longdiv}{175}[/latex]
5. [latex]100\enclose{longdiv}{2948}[/latex]
6. [latex]100\enclose{longdiv}{4671}[/latex]
7. [latex]100\enclose{longdiv}{92045}[/latex]
8. [latex]100\enclose{longdiv}{43821}[/latex]

Answers to Exercise 6

1. 3 R86
2. 9 R95
3. 2 R69
4. 1 R75
5. 29 R48
6. 46 R71
7. 920 R45
8. 438 R21

When you divide by 1000

1. The ones, tens, and hundreds digits become the remainder.
2.   The other digits stay the same but are three place values less.
   • thousands become ones
   • ten thousands become tens
   • hundred thousands become hundreds

Exercise 7

Try these. Check your work using the answer key at the end of the exercise.

1. [latex]1000\enclose{longdiv}{2398}[/latex]
2. [latex]1000\enclose{longdiv}{6475}[/latex]
3. [latex]1000\enclose{longdiv}{4835}[/latex]
4. [latex]1000\enclose{longdiv}{63291}[/latex]
5. [latex]1000\enclose{longdiv}{82405}[/latex]
6. [latex]1000\enclose{longdiv}{293591}[/latex]

Answers to Exercise 7

1. 2 R398
2. 6 R475
3. 4 R835
4. 63 R291
5. 82 R405
6. 293 R591

Three-Digit Divisors

If the divisor has three digits, use the method you know for two-digit divisors, but estimate the divisor to the nearest hundred to find the trial quotient. Be very careful to put the first digit in the quotient in the correct place.

Example F

17902 ÷ 381 = Step 1: Divide

1. Does 381 go into 1? NO
2. Does 381 go into 17?  NO
3. Does 381 go into 179? NO
4. Does 381 go into 1790? YES
5. Estimate 381 as 400. Think 4.
6. Estimate 1790 as 1800. Think 18.
7. 4 goes into 18 ≈ 4 times ([latex]4\times 4 = 16[/latex])
8. Your estimate is 4. Write 4 in the quotient above the 0 in the dividend.

[latex]\begin{array}{r}4 \ \ \ \\ 381\enclose{longdiv}{17902} \end{array}[/latex]

Step 2: Multiply

1. 4 × 381 = 1524

[latex]\begin{array}{r}4 \ \ \ \\ 381\enclose{longdiv}{17902} \\ 1524 \ \ \ \\ \hline \end{array}[/latex]

Step 3: Subtract

1. 1790 − 1524 = 266
2. Check 266 < 381? YES!

[latex]\begin{array}{r}4 \ \ \ \\ 381\enclose{longdiv}{17902} \\ 1524 \ \ \ \\ \hline 266 \ \ \ \end{array}[/latex]

Step 4:  Bring down the 2. 2662 is now the number to be divided

[latex]\begin{array}{r}4 \ \ \ \\ 381\enclose{longdiv}{17902} \\ 1524 \downarrow \\ \hline 2662 \end{array}[/latex]

REPEAT   Step 1: Divide [latex]2662 \div 381 = [/latex]

1. Estimate 381 as 400. Think of 4.
2. Estimate 2662 as 2700. Think 27.
3. 4 goes into 27 ≈ 6 times ([latex]4 \times 6 = 24[/latex]).
4. Place this estimate in the quotient above the 2

[latex]\begin{array}{r}4 \ \ \ \\ 381\enclose{longdiv}{17902} \\ 1524 \downarrow \\ \hline 2662 \end{array}[/latex]

Step 2: Multiply

1. [latex]6\times381 = 2286[/latex]

[latex]\begin{array}{r}46 \ \ \ \\ 381\enclose{longdiv}{17902} \\ 1524 \downarrow \\ \hline 2662 \\ 2286 \\ \hline \end{array}[/latex]

Step 3: Subtract

1. 2662 − 2286 = 376
2. Check 376 < 381? YES!

[latex]\begin{array}{r}46 \ \ \ \\ 381\enclose{longdiv}{17902} \\ 1524 \downarrow \\ \hline 2662 \\ 2286 \\ \hline 376 \end{array}[/latex]

Step 4: No more digits to bring down.

17902 ÷ 381 = 46 R376

Exercise 8

Divide and check your answers. These questions are hard work! Check your work using the answer key at the end of the exercise.

1. [latex]115\enclose{longdiv}{8682}[/latex]
2. [latex]205\enclose{longdiv}{2384}[/latex]
3. [latex]325\enclose{longdiv}{66321}[/latex]
4. [latex]241\enclose{longdiv}{13284}[/latex]
5. [latex]860\enclose{longdiv}{262412}[/latex]
6. [latex]659\enclose{longdiv}{270190}[/latex]

Answers to Exercise 8

1. 75 R57
2. 11 R129
3. 204 R21
4. 55 R29
5. 305 R112
6. 410

Topic D: Self-Test

Mark  /12   Aim  10/12

1. Divide and check your work for questions b and f using multiplication. (12 marks)
   1. [latex]185 \div 10 = [/latex]
   2. [latex]4\enclose{longdiv}{92}[/latex]
   3. [latex]408 \div 50 =[/latex]
   4. [latex]72\enclose{longdiv}{6768}[/latex]
   5. [latex]67\enclose{longdiv}{5963}[/latex]
   6. [latex]53\enclose{longdiv}{4856}[/latex]
   7. [latex]91\enclose{longdiv}{8736}[/latex]
   8. [latex]265\enclose{longdiv}{133624}[/latex]
   9. [latex]606\enclose{longdiv}{26094}[/latex]
   10. [latex]1000\enclose{longdiv}{83652}[/latex]

Answers to Topic D Self-Test

1. Divide and check your work for questions b and f using multiplication.
   1. 18 R5
   2. 23
   3. 8 R8
   4. 94
   5. 89
   6. 91 R33
   7. 96
   8. 504 R64
   9. 43 R36
   10. 83 R652

]]> 1148 1076 5 0 https://opentextbc.ca/alfm3/chapter/estimating-quotients/ Tue, 17 Jan 2023 21:24:33 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1170 Divide Numbers That Both End With Zeros In Unit 1 you learned a shortcut for multiplying numbers that end with zeros. Now you will learn a short way to divide numbers that both end with zeros. First do this exercise and notice the pattern in the quotients.

Exercise 1

Divide. Check your work using the answer key at the end of the exercise.

1. [latex]2 \enclose{longdiv}{6}[/latex]
2. [latex]20 \enclose{longdiv}{60}[/latex]
3. [latex]200 \enclose{longdiv}{600}[/latex]
4. [latex]2000 \enclose{longdiv}{6000}[/latex]
5. [latex]5 \enclose{longdiv}{25}[/latex]
6. [latex]50 \enclose{longdiv}{250}[/latex]
7. [latex]500 \enclose{longdiv}{2500}[/latex]
8. [latex]5000 \enclose{longdiv}{25000}[/latex]
9. [latex]14 \enclose{longdiv}{28}[/latex]
10. [latex]140 \enclose{longdiv}{280}[/latex]
11. [latex]1400 \enclose{longdiv}{2800}[/latex]
12. [latex]14000 \enclose{longdiv}{28000}[/latex]

Answers to Exercise 1

1. 3
2. 3
3. 3
4. 3
5. 5
6. 5
7. 5
8. 5
9. 2
10. 2
11. 2
12. 2

Here is the shortcut: When dividing numbers that both end with zeros, cross off the same number of zeros from the end of the divisor and the dividend. This is sometimes called cancelling zeros.

Example A

[latex]4800 \div 60 = 480\cancel{0} \div 6\cancel{0}[/latex]

[latex]\begin{array}{r}80\\ 6\enclose{longdiv}{480}\end{array}[/latex]

Example B

[latex]23000 \div 500 = 230\cancel{00} \div 5\cancel{00}[/latex]

[latex]\begin{array}{r}46\\ 5\enclose{longdiv}{230} \\ 20 \downarrow \\ \hline 30 \\ 30 \\ \hline 0\end{array}[/latex]

Example C

[latex]2\cancel{000}\enclose{longdiv}{680\cancel{000}}[/latex]

[latex]\begin{array}{r}340 \\ 2\enclose{longdiv}{680}\\ 6\downarrow \ \\\hline 08 \ \ \ \\ 8 \downarrow \\ \hline 00 \\ 0 \\ \hline 0\end{array}[/latex]

If you are interested in the facts of arithmetic that make this shortcut work, ask your instructor for an explanation.

Exercise 2

Quickly  find the quotients. Remember to cancel  the same number of zeros in both the divisor and dividend in each question. Check your work using the answer key at the end of the exercise.

1. [latex]30\enclose{longdiv}{90}[/latex]
2. [latex]40\enclose{longdiv}{1600}[/latex]
3. [latex]300\enclose{longdiv}{1200}[/latex]
4. [latex]400\enclose{longdiv}{20000}[/latex]
5. [latex]500\enclose{longdiv}{35000}[/latex]
6. [latex]700\enclose{longdiv}{42000}[/latex]
7. [latex]60000\enclose{longdiv}{2400000}[/latex]
8. [latex]800000\enclose{longdiv}{400000000}[/latex]

Answers to Exercise 2

1. 3
2. 40
3. 4
4. 50
5. 70
6. 60
7. 40
8. 500

Rounding Division Questions to Estimate

We round numbers and estimate to get a quick answer. In division, round the divisor and dividend before you divide.

1. If the divisor only has one digit, do not round it,
2. Round the dividend to make the arithmetic easier for yourself.

Example D

Look at the two ways of rounding this question.

[latex]1796 \div 32 = [/latex]

The divisor (32) will round to 30. This dividend (1796) can be rounded to 1800 or to 2000. Let's try each: Round to 1800.

[latex]\begin{array}{r}60\ \ \ \ \\ 3\cancel{0}\enclose{longdiv}{180\cancel{0}}\end{array}[/latex]

Round to 2000.

[latex]\begin{array}{l}\hspace{2.5em}66\text{ R}2\\3\cancel{0}\enclose{longdiv}{200\cancel{0}} \\\hspace{2em}18\downarrow \\\hline\hspace{2.5em}20\\\hspace{2.5em}18\\\hline\hspace{1.5cm}2\end{array}[/latex]

Rounding 1796 to 1800 is easier arithmetic because [latex]18 \div 3[/latex] works out evenly, so [latex]180 \div 3[/latex] works out evenly. Both estimates are correct.

Example E

2688 ÷ 28 =

1. Round the divisor (28) to 30.
2. Round the dividend (2688) to 2700 or to 3000.

Round to 2700	[latex]\begin{array}{r}90\ \ \ \ \\\ 3\cancel{0}\enclose{longdiv}{270\cancel{0}}\end{array}[/latex]
Round to 3000	[latex]\begin{array}{r}100\ \ \ \ \ \\ 3\cancel{0}\enclose{longdiv}{300\cancel{0}}\end{array}[/latex]

Both estimates are correct and both are easy to do.

Example F

2893 ÷ 47 =

1. Round the divisor (47) to 50.
2. Round the dividend (2893) to 2900 or 3000.
3. Which rounded dividend will be easier to divide by 50?
   1. Answer: The 3000 because 5 goes evenly into 30.

[latex]\begin{array}{r}60\ \ \ \ \ \\5\cancel{0} \enclose{longdiv}{300\cancel{0}}\end{array}[/latex]

Exercise 3

Give an estimated quotient.  Show your rounding. Check your work using the answer key at the end of the exercise.

1. [latex]365\enclose{longdiv}{27692}[/latex]
2. [latex]23\enclose{longdiv}{34459}[/latex]
3. [latex]45\enclose{longdiv}{4590}[/latex]
4. [latex]16\enclose{longdiv}{6729}[/latex]
5. [latex]56\enclose{longdiv}{4792}[/latex]
6. [latex]75\enclose{longdiv}{7648}[/latex]
7. [latex]81\enclose{longdiv}{4049}[/latex]
8. [latex]68\enclose{longdiv}{5636}[/latex]
9. [latex]19\enclose{longdiv}{1672}[/latex]
10. [latex]200\enclose{longdiv}{20000}[/latex]
11. [latex]557\enclose{longdiv}{41680}[/latex]

Answers to Exercise 3

1. 28000 ÷ 400 = 70
2. 34000 ÷ 20 =1700
3. 5000 ÷ 50 =100
4. 7000 ÷ 20 = 350
5. 4800 ÷ 60 = 80
6. 8000 ÷ 80 = 100
7. 4000 ÷ 80 = 50
8. 5600 ÷ 70 = 80
9. 2000 ÷ 20 = 100
10. 20000 ÷ 200 = 100
11. 42000 ÷ 600 = 70

Topic E: Self-Test

Mark  /6   Aim  5/6

1. Give an estimated quotient. Show your work. (6 marks)
   1. [latex]98\enclose{longdiv}{8541}[/latex]
   2. [latex]27\enclose{longdiv}{2963}[/latex]
   3. [latex]241\enclose{longdiv}{26348}[/latex]
   4. [latex]55\enclose{longdiv}{3276}[/latex]
   5. [latex]24\enclose{longdiv}{1776}[/latex]
   6. [latex]59\enclose{longdiv}{11830}[/latex]

Answers to Topic E Self-Test

1. Give an estimated quotient. Show your work.
   1. 8500 ÷ 100 = 85
   2. 3000 ÷ 30 = 100
   3. 26000 ÷ 200 = 130
   4. 3000 ÷ 60 = 50
   5. 2000 ÷ 20 = 100
   6. 12000 ÷ 60 = 200

]]> 1170 1076 6 0 https://opentextbc.ca/alfm3/chapter/division-problems/ Tue, 17 Jan 2023 23:02:32 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1176 Review Topic F: Problem Solving in Adult Literacy Fundamentals Mathematics: Book 2. One common type of division problem gives a total amount for several things and asks you to find what the amount would be for one.

Problems may tell you…	and ask you to find…
kilometres driven in 8 hours (h)	km driven in 1 h
cost for 15 kg (or litres, etc.)	cost for one kg
pay for 40 hours	pay for one hour
rent for one year (12 months)	rent for one month
work done in eight hours	work done in one hour
kilometres driven on 55 L of gas	km driven on 1 L of gas

The word per is a Latin word meaning “for each”. For example, “Find the kilometres per hour” may be used to mean, “Find the kilometres driven in one hour.” A slash (/ ) also means per  e.g. km/h.

“Find the average” is another way of asking you to find the amount for one.

It may be difficult to decide which number is the dividend and which is the divisor. These suggestions should help:

•  Look at the question in the problem. What do you have to find out? Look for the words “per” and “for one.”
• How will the answer be written? That is your clue. If the answer is km/h then the division equation will be total km ÷ h.  Study these examples:
  • [latex]\text{total of kilometres} \div \text{number of hours} = \text{km/h}[/latex]
  • [latex]\text{total of kilometres} \div \text{number of litres} = \text{km/L}[/latex]
  • [latex]\text{total cost} \div \text{unit} = \text{cost per unit}[/latex]
  • [latex]\text{total pay} \div \text{hours (or days, etc.)} = \text{pay per hour}[/latex]
  • [latex]\text{total rent}\div \text{number of months} = \text{rent/month}[/latex]
  • [latex]\text{total things done} \div \text{total time} = \text{number done/unit of time}[/latex]
• Do a quick estimate.
• Look at your estimate and re-read the problem. Does your answer make sense?

To find the average, divide the total amount by the number of items that make up the total. You may first have to add the different items together to find the total.

Average = The sum of all values given ÷ the number of values added up

Example A

You bowled 5 games with scores of 124, 187, 164, 205, 130. What was your average score?

1. Find the total by adding [latex]124 + 187 + 164 + 205 + 130 = 810[/latex]
2. Divide the total by number of items [latex]810 \div 5 \text{ games} = 162 \text{ per game}[/latex]

Example B

Joan and Rick have been keeping track of their household costs. They want to plan a monthly budget. Their grocery bills for six months were $428, $605, $397, $530, $590, and $474. What is their average monthly grocery cost?

1. Find the total amount.

$428 + $605 + $397 + $530 + $590 + $474 = $3024

2. Divide total amount by number of items.

$3024 ÷ 6 = $504 average cost per month

Some details to remember:

• 1 minute = 60 seconds
• 1 hour = 60 minutes
• 1 year = 365 days
• 1 year = 12 months
• 1 year = 52 weeks

Key words that point to division:

• Find the average
• Separated
• Find the ____ per ____
• Split
• Find the unit price
• Shared

Exercise 1

Solve these problems.  Use the five problem solving steps. Be sure to write down an estimate and check that the estimate makes sense before you find the actual solution. Check your work using the answer key at the end of the exercise.

1. A machine shop can stamp out 360 car parts in an 8-hour working day. How many parts is that per hour?
2. Izyan paid $560 for 4 tires. How much did each tire cost?
3. Bjork earned $8840 in 4 months.
   1. How much did he earn each month?
   2. How much did he earn per week? (4 months is 17 weeks)
4. Theron used 9 L of gasoline to drive 207 km. How many kilometres did he drive per litre?
5. The total cost of the car Elena bought is $14880 including taxes and interest. She will pay for it in 24 equal payments. How much will each payment be?
6. Diego worked 8 hours a day for five days and earned $360. How much was he paid per hour? (This is a 2-step problem — you must first find the total number of hours Diego worked.)
7. Dae-Hyun and Mi-Ok can afford no more than a total of $14940 per year for rent, electricity, and phone. How much can they pay per month?

Answers to Exercise 1

1. 45 parts per hour
2. $140 per tire
3. 1. $2210 per month
   2. $520 per week
4. 23 km/L
5. $620 per payment
6. $9 per hour
7. $1245 per month

A second type of division problem gives the total amount and the size of each group. You will find the number of groups. You will notice that both numbers have the same units. The answer to the problem will give another unit. This other unit will be asked for in the problem.

Example C

One necklace uses 125 beads. How many necklaces can Susan make for the craft fair if she has 6250 beads?  Find how many groups of 125 there are in 6520.

6250 ÷ 125 =

[latex]\begin{array}{r}50\\125\enclose{longdiv}{6250}\\625 \\ \hline 0 \end{array}[/latex]

She can make 50 necklaces.

Example D

If you drive an average speed of 80 km an hour, how many hours will it take you to drive 560 km? Find how many groups of 80 km there are in 560 km.

[latex]56\cancel{0} \div 8\cancel{0} = 7[/latex]

The 560 km trip will take 7 hours.

Exercise 2

Pay attention to wording and situations as you solve these problems. Use the five problem solving steps. Be sure to write down an estimate and check that the estimate makes sense before you find the actual solution. Check your work using the answer key at the end of the exercise.

1. A train travels 90 km per hour. How many hours will it take the train to go 540 km?
2. A car gets 16 km per litre of gasoline. How many litres will the car need to go 128 km?
3. About 8 m is needed for one parking space. How many parking spaces can be made along a street that is 232 m long?
4. If you spend an average of 8 minutes on one math problem, how many problems can you finish in one hour? Will you have any time left?  How much?
5. The Skating Club members decided to sell home-made candy to raise money. The boxes they bought will hold 45 pieces of candy. If everyone makes a double batch of fudge they will have 2590 pieces of How many boxes can they fill? How many pieces of fudge are left-over for them to eat?
6. A class of 334 students is going to Victoria by bus. Each bus holds 43 passengers. How many buses do they need? Will there be any empty seats? (Be careful with this one!)

Answers to Exercise 2

1. 6 hours
2. 8 L
3. 29 parking spaces
4. 7 problems, yes, 4 min
5. 57 boxes, 25 pieces left over
6. 8 buses, 10 empty seats

Unit Pricing

A unit price is the price for one of something. To find unit price, divide the total cost by the number of things bought.

Example E

5 shirts cost $60 To find the cost per shirt, [latex]$60 \div 5 =[/latex]

[latex]\begin{array}{r}12\\5\enclose{longdiv}{60}\end{array}[/latex]

The unit price is $12.

Example F

6 L of oil for $18 To find the cost per L, [latex]$18 \div 6 =[/latex]

[latex]\begin{array}{r}3\\6\enclose{longdiv}{18}\end{array}[/latex]

The unit price is $3.

Exercise 3

Solve the cost per unit price. Check your work using the answer key at the end of the exercise.

1. 2 CDs for $26
2. 3 cans of dog food for $6
3. 4 air fresheners for $8
4. 2 cat treats for $4
5. 2 pizzas for $22
6. 2 cans of peanuts for $8
7. 2 ice cream for $12
8. 4 boxes of chocolate bars for $48
9. 2 WD-40 for $6
10. 3 paint rollers for $9
11. 4 tie downs for $20
12. 3 boxes of diapers for $51
13. 3 work shirts for $45
14. 8 pairs of socks for $64

Answers to Exercise 3

1. $13
2. $2
3. $2
4. $2
5. $11
6. $4
7. $6
8. $12
9. $3
10. $3
11. $5
12. $17
13. $15
14. $8

Best Buy

The best buy is the lowest unit price.

Example G

You can buy 4 L of canola oil for $8 or 10 L of canola oil for $30. Which is the best buy? [latex]$8\div4=[/latex] can be rewritten and solved: [latex]\begin{array}{r}2\\4\enclose{longdiv}{8}\end{array}[/latex] [latex]$30 \div 10 =[/latex] can be rewritten and solved: [latex]\begin{array}{r}3\\10\enclose{longdiv}{30}\end{array}[/latex] 4 L of canola oil for $8 is a better buy since the unit price is $2 per L, while 10 L for $30 has a unit price of $3 per L.

Exercise 4

Solve the unit price and then underline the best buy.  Check your work using the answer key at the end of the exercise.

1. 2 L of engine oil for $8 or 5 L of engine oil for $15
2. 4 tires for $240 or 2 tires for $110
3. 6 jars of salad dressing for $24 or 3 jars of salad dressing for $15
4. 7 kg of dog food for $21or 16 kg of dog food for $32
5. 3 DVDs for $54 or 7 DVDs for $119
6. 3 L of laundry soap for $6 or 17 L of laundry soap for $68

Answers to Exercise 4

1. $4, $3, 5 L for $15 is the best buy.
2. $60, $55, 2 tires for $110 is the best buy.
3. $4, $5, 6 salad dressing for $24 is the best buy.
4. $3, $2, 16 kg for $32 is the best buy.
5. $18, $17, 7 DVDs for $119 is the best buy.
6. $2, $4, 3 L for $6 is the best buy.

Topic F: Self Test

Mark  /12   Aim  10/12

1. Solve these problems. (12 marks) 2 marks each – 1 for correct method, 1 for correct solution.
   1. Enrique drove the 1 920 km from Dease Lake to Creston in 24 hours. What was his average speed in kilometres per hour?
   2. The Evergreen Company employs 26 people. Its total payroll for last month was $84 162.  What was the average monthly pay cheque per person?
   3. The proud gardener grew a total crop of 135 cucumbers on 15 plants. What was the average crop per plant?
   4. In a recent truckload sale, electric stoves were sold for $432. The gross income from the stove sale was $42336.  How many stoves were sold?
   5. The 39 farmers in Jones Valley had a total income last year of $2905500. What was their average income?
   6. A store has an inventory (stock on hand) of chairs with a total value of $1738. Each chair is to be sold at $79.  How many of these chairs are there?

Answers to Topic E Self-Test

1. Give an estimated quotient. Show your work.
   1. 80 km/h
   2. $3237 per month
   3. 9 cucumbers per plant
   4. 98 stoves
   5. $74500
   6. 22 chairs

]]> 1176 1076 7 0 https://opentextbc.ca/alfm3/chapter/mixed-problems/ Wed, 18 Jan 2023 18:39:05 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1186 Topic F: Problem Solving in Adult Literacy Fundamentals Mathematics: Book 2, or ask your instructor for a copy of those pages. Read the problems to help you get a feel for the wording and problem situations you can expect for addition, subtraction, multiplication, and division problems. Ask your instructor for a list of key words that will point to the operation you should choose.

Exercise 1

Solve these problems using the five problem solving steps. Show your estimation and actual work. Write a sentence answer remembering to use the units. Check your work using the answer key at the end of the exercise.

1. Saika gave her students cinnamon hearts on Valentine’s Day. She bought a box of 1120 cinnamon hearts and gave each student 35 candies, using up the whole box. How many students does she have?
2. Each stamp cost 57 cents. Dolores bought 100 stamps. How much money did she spend on stamps (before taxes)?
3. Etienne planted 30 tomato plants in rows of 5 plants.  How many rows did he plant?
4. There are 8 servings per large economy-size can of fruit. The restaurant ordered 5 cases with 24 cans per case. How many servings of fruit can the restaurant get from this order? (This is a two step problem – first find the total number of cans. Then find the number of servings.)
5. A train traveled 2250 km at a speed of 75 km per hour. How many hours did the trip take?
6. The regular mountain bike costs $499 and the fancy model is $675. How much more do you pay for the fancy mountain bike?
7. The members of the Shiny Wheels Bicycle Club ride at an average speed of 16 km/h. On their weekend trip they rode 2 hours Friday night, 7 hours on Saturday, spent two hours soaking their aching bones at the Hot Springs, and then rode a final five hours on Sunday.  How many kilometres did they ride on this weekend trip?  (2 steps)
8. Last week Mrs. Sanderson drove 29 km on Monday, 42 km on Tuesday, 5 km on Wednesday, and 21 km on Friday.  How far did she drive last week?

Answers to Exercise 1

1. 32 students
2. $57.00
3. 6 rows
4. 960 servings
5. 30 hours
6. $176 more
7. 224 km
8. 97 km

]]> 1186 1076 8 0 https://opentextbc.ca/alfm3/chapter/review-division/ Wed, 18 Jan 2023 20:54:06 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1201

Complete this chart

	Multiplication	Division	Division	"Say"
a)	[latex]5\times3=15[/latex] [latex]3\times5=15[/latex]	[latex]15\div3=5[/latex] [latex]15\div5=3[/latex]	[latex]\begin{array}{r}5\\3\enclose{longdiv}{15} \end{array}[/latex] [latex]\begin{array}{r}3\\5\enclose{longdiv}{15} \end{array}[/latex]	"15 divided by 3 is 5." "15 divided by 5 is 3."
b)	[latex]3\times6=18[/latex]
c)	[latex]3\times7=21[/latex]
d)	[latex]5\times9=45[/latex]

Give the answer.

1. [latex]56\div7=[/latex]
2. [latex]40\div8=[/latex]
3. [latex]54\div9=[/latex]
4. [latex]6\enclose{longdiv}{42}[/latex]
5. [latex]9\enclose{longdiv}{72}[/latex]
6. [latex]8\enclose{longdiv}{32}[/latex]

Find the quotients.

1. [latex]7\enclose{longdiv}{68}[/latex]
2. [latex]4\enclose{longdiv}{29}[/latex]
3. [latex]5\enclose{longdiv}{24}[/latex]
4. [latex]6\enclose{longdiv}{53}[/latex]

For each number, identify if it is divisible by 2, 3, 5, and, 9.

#	Number	2	3	5	9
a)	135
b)	384
c)	4614
d)	495
e)	648
f)	745

Find the quotients.

1. [latex]8\enclose{longdiv}{296}[/latex]
2. [latex]6\enclose{longdiv}{252}[/latex]
3. [latex]4\enclose{longdiv}{732}[/latex]
4. [latex]5\enclose{longdiv}{175}[/latex]

Find the quotients.

1. [latex]3\enclose{longdiv}{86}[/latex]
2. [latex]4\enclose{longdiv}{97}[/latex]
3. [latex]2\enclose{longdiv}{71}[/latex]
4. [latex]5\enclose{longdiv}{59}[/latex]

Find the quotients.

1. [latex]7\enclose{longdiv}{615}[/latex]
2. [latex]2\enclose{longdiv}{647}[/latex]
3. [latex]3\enclose{longdiv}{781}[/latex]
4. [latex]9\enclose{longdiv}{839}[/latex]

Find the quotients.

1. [latex]8956\div42=[/latex]
2. [latex]32\enclose{longdiv}{832}[/latex]
3. [latex]69140\div56=[/latex]
4. [latex]312\enclose{longdiv}{9984}[/latex]
5. [latex]41082\div334=[/latex]
6. [latex]781\enclose{longdiv}{39752}[/latex]
7. [latex]275\enclose{longdiv}{55661}[/latex]
8. [latex]307\enclose{longdiv}{91838}[/latex]

Find the quotients.

1. [latex]1000\enclose{longdiv}{38645}[/latex]
2. [latex]18592\div100=[/latex]
3. [latex]4923\div10=[/latex]
4. [latex]100\enclose{longdiv}{17342}[/latex]

Quickly find the quotients. Remember to cancel the same number of zeros in both the divisor and dividend in each question.

1. [latex]200\enclose{longdiv}{50000}[/latex]
2. [latex]6000\enclose{longdiv}{360000}[/latex]
3. [latex]40000\enclose{longdiv}{1600000}[/latex]
4. [latex]70000\enclose{longdiv}{6300000}[/latex]

Give an estimated quotient. Show your rounding.

1. [latex]37\enclose{longdiv}{15725}[/latex]
2. [latex]54\enclose{longdiv}{8478}[/latex]
3. [latex]768\enclose{longdiv}{63721}[/latex]
4. [latex]6267\enclose{longdiv}{536497}[/latex]

Word Problems

1. At the Kaizen Factory, 14325 cars were put together in 5 days. Each day the same number of cars were built. How many cars were built each day?
2. The Blaster Rubber Company needs to make 6912 hockey pucks. Mr. Frost, the foreman, says that their machines can make the pucks in 12 hours. How many pucks would be made in one hour?
3. The distance between Fort St. John and Kimberley is 1092 km. What was your average speed if the trip took 12 hours?
4. The new stadium has 15981 seats divided evenly into 76 sections. Estimate how many seats are in each section?

Solve the cost per unit price.

1. 4 rolls of hockey tape for $8
2. 4 cans of butane fuel for $12

Solve the unit price and then underline the best buy.

1. 2 L of antifreeze for $6 or 5 L of antifreeze for $10
2. 8 kilograms of bird seed for $16 or 4 kilograms of bird seed for $12

Word Problems.

1. The bakery uses 43 kilograms of butter in each batch of shortbread cookies. How many batches of shortbread can be made from 3569 kilograms of butter?
2. Each crate that the men unloaded weighed 175 kilograms. If they unloaded 232 crates, how many kilograms did they unload?
3. The parts factory produced 4173 less parts this month than last month. The factory produced 49736 parts this month. How many parts did the factory produce last month?
4. Three Eastjet jets were flown 24826 kilometres, 9423 kilometres and 56015 kilometres. What is the total kilometres the three jets were flown?

Answers to Unit 2 Review

1. Complete this chart

   #	Multiplication	Division	Division	"Say"
   a)	[latex]5\times3=15[/latex] [latex]3\times5=15[/latex]	[latex]15\div3=5[/latex] [latex]15\div5=3[/latex]	[latex]\begin{array}{r}5\\3\enclose{longdiv}{15} \end{array}[/latex] [latex]\begin{array}{r}3\\5\enclose{longdiv}{15} \end{array}[/latex]	15 divided by 3 is 5. 15 divided by 5 is 3.
   b)	[latex]3\times6=18[/latex] [latex]6\times3=18[/latex]	[latex]18\div6=3[/latex] [latex]18\div3=6[/latex]	[latex]\begin{array}{r}3\\6\enclose{longdiv}{18} \end{array}[/latex] [latex]\begin{array}{r}6\\3\enclose{longdiv}{18} \end{array}[/latex]	18 divided by 6 is 3. 18 divided by 3 is 6.
   c)	[latex]3\times7=21[/latex] [latex]7\times3=21[/latex]	[latex]21\div7=3[/latex] [latex]21\div3=7[/latex]	[latex]\begin{array}{r}3\\7\enclose{longdiv}{21} \end{array}[/latex] [latex]\begin{array}{r}7\\3\enclose{longdiv}{21} \end{array}[/latex]	21 divided by 7 is 3. 21 divided by 3 is 7.
   d)	[latex]5\times9=45[/latex] [latex]9\times5=45[/latex]	[latex]45\div9=5[/latex] [latex]45\div5=9[/latex]	[latex]\begin{array}{r}5\\9\enclose{longdiv}{45} \end{array}[/latex] [latex]\begin{array}{r}9\\5\enclose{longdiv}{45} \end{array}[/latex]	45 divided by 9 is 5. 45 divided by 5 is 9.

2. Give the answer.
   1. 8
   2. 5
   3. 6
   4. 7
   5. 8
   6. 4
3. Find the quotients.
   1. 9 R5
   2. 7 R1
   3. 4 R4
   4. 8 R5
4. For each number, identify if it is divisible by 2, 3, 5, and, 9.

   	Number	2	3	5	9
   a)	135	No	Yes	Yes	Yes
   b)	384	Yes	Yes	No	No
   c)	4614	Yes	Yes	No	No
   d)	495	No	Yes	Yes	Yes
   e)	648	Yes	Yes	No	Yes
   f)	745	No	No	Yes	No

5. Find the quotients.
   1. 37
   2. 42
   3. 183
   4. 35
6. Find the quotients.
   1. 28 R2
   2. 24 R1
   3. 35 R1
   4. 11 R4
7. Find the quotients.
   1. 87 R6
   2. 323 R1
   3. 260 R1
   4. 93 R2
8. Find the quotients.
   1. 213 R10
   2. 26
   3. 1234 R36
   4. 32
   5. 123
   6. 50 R702
   7. 202 R111
   8. 299 R45
9. Find the quotients.
   1. 38 R645
   2. 185 R92
   3. 492 R3
   4. 173 R42
10. Quickly find the quotients. Remember to cancel the same number of zeros in both the divisor and dividend in each question.
    1. 250
    2. 60
    3. 40
    4. 90
11. Give an estimated quotient. Show your rounding.
    1. [latex]1600 \div 40=400[/latex]
    2. [latex]8500\div50=170[/latex]
    3. [latex]64000\div800=80[/latex]
    4. [latex]540000\div6000=90[/latex]
12. Word Problems
    1. 2865 cars per day
    2. 576 pucks per hour
    3. 91 km per hour
    4. [latex]16000\div80=200[/latex] 200 seats per section
13. Solve the cost per unit price.
    1. $2
    2. $3
14. Solve the unit price and then underline the best buy.
    1. $3, $2, 5 L of antifreeze for $10 is the best buy
    2. $2, $3, 8 kilograms of bird seed for $16 is the best buy
15. Word Problems.
    1. 83 batches
    2. 40600 kilograms
    3. 53909 parts
    4. 90264 kilometres

]]> 1201 1076 9 0 https://opentextbc.ca/alfm3/chapter/acounting-to-make-change/ Wed, 18 Jan 2023 20:59:06 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1205 Practice your counting by filling in the counting chart. Have your instructor check your chart when you are done.

0	1	2	3	4	5	6	7	8	9
10

Use your counting chart and start at 0.  Count two and write down that number.

0	2	4

If you had a pile of toonies or two dollar coins and wanted to know how much money you have, you would count by 2’s. Use your counting chart and start at 0.  Count five and write down that number.

0	5	10

If you had a pile of nickels or five dollar bills and wanted to know how much money you have, you would count by 5’s.

Use your counting chart and start at 0.  Count ten and write down that number.

0	10	20

If you had a pile of dimes or ten dollar bills and wanted to know how much money you have, you would count by 10’s. Use your counting chart and start at 0.  Count twenty and write down that number.

0

20

40

If you had a pile of twenty dollar bills and wanted to know how much money you have, you would count by 20’s. Use your counting chart and start at 0.  Count twenty-five and write down that number.

0

25

If you had a pile of quarters and wanted to know how much money you have, you would count by 25’s.

Exercise 1

Write the missing numerals. Check your work using the answer key at the end of the exercise.

1. Count by 5’s.

   0		10		20		30		40
   50		60		70		80		90

2. Count by 5’s.

   0	5		15		25		35		45
   	55		65		75		85		95

3. Count by 5's.

   0

4. Count by 10’s.

   0

   10

   30

   50

   70

   90

5. Count by 10’s.

   0

   20

   40

   60

   80

   100

6. Count by 10’s.

   0

7. Count by 20’s

   0

   40

   80

8. Count by 20’s

   0

9. Count by 25’s.

   0

   25

   75

10. Count by 25’s.

    0

    50

    100

11. Count by 25’s.

    0

Answers to Exercise 1

1. Count by 5’s.

   0	5	10	15	20	25	30	35	40	45
   50	55	60	65	70	75	80	85	90	95

2. Count by 5’s.

   0	5	10	15	20	25	30	35	40	45
   50	55	60	65	70	75	80	85	90	95

3. Count by 5's.

   0	5	10	15	20	25	30	35	40	45
   50	55	60	65	70	75	80	85	90	95

4. Count by 10’s.

   0

   10

   20

   30

   40

   50

   60

   70

   80

   90

   100

5. Count by 10’s.

   0

   10

   20

   30

   40

   50

   60

   70

   80

   90

   100

6. Count by 10’s.

   0

   10

   20

   30

   40

   50

   60

   70

   80

   90

   100

7. Count by 20’s

   0

   20

   40

   60

   80

   100

8. Count by 20’s

   0

   20

   40

   60

   80

   100

9. Count by 25’s.

   0

   25

   50

   75

   100

10. Count by 25’s.

    0

    25

    50

    75

    100

11. Count by 25’s.

    0

    25

    50

    75

    100

]]> 1205 1203 1 0 https://opentextbc.ca/alfm3/back-matter/acknowledgements-1st-edition/ Thu, 26 Jan 2023 21:56:32 +0000 https://opentextbc.ca/alfm3/?post_type=back-matter&p=1416 Curriculum Writers

• Liz Girard, North Island College
• Wendy Tagami, Selkirk College

Advisory Committee Members

• Jill Auchinachie, Camosun College
• Leanne Caillier-Smith, College of the Rockies
• Mercedes de la Nuez, Coast Mountain College
• Barbara Stirsky, University of the Fraser Valley
• Jan Weiten, Vancouver Community College

The Deans and Directors of Developmental Education

• Stephanie Jewell, Vancouver Community
• College Vivian Hermansen, North Island College
• Lyle Olsen, Selkirk College
• Allison Alder, Selkirk College

Also

• The Adult Literacy Fundamental Working Group
• Cheryl Porter, North Island College
• Stephen & Jennifer Marks, Layout editors

]]> 1416 0 3 0 https://opentextbc.ca/alfm3/back-matter/review/ Fri, 27 Jan 2023 16:48:24 +0000 https://opentextbc.ca/alfm3/?post_type=back-matter&p=1422 If you can’t remember how to do a question, go back to the lesson on this topic to refresh your memory. The unit and topic for each question is listed.

Example:  1-B means Unit 1, Topic B

Book 3 Review Questions

1-A

1. Find the products.

   1. [latex]\begin{array}{rr}&4\\\times&9\\\hline\end{array}[/latex]

   2. [latex]\begin{array}{rr}&7\\\times&8\\\hline\end{array}[/latex]
   3. [latex]\begin{array}{rr}&2\\\times&6\\\hline\end{array}[/latex]
   4. [latex]\begin{array}{rr}&9\\\times&5\\\hline\end{array}[/latex]
   5. [latex]\begin{array}{rr}&6\\\times&10\\\hline\end{array}[/latex]
   6. [latex]\begin{array}{rr}&0\\\times&3\\\hline\end{array}[/latex]
   7. [latex]\begin{array}{rr}&8\\\times&4\\\hline\end{array}[/latex]
   8. [latex]\begin{array}{rr}&5\\\times&2\\\hline\end{array}[/latex]
   9. [latex]\begin{array}{rr}&10\\\times&10\\\hline\end{array}[/latex]

1-B

2. Find the products.
   1. [latex]\begin{array}{rr}&71\\\times&3\\\hline\end{array}[/latex]
   2. [latex]\begin{array}{rr}&623\\\times&3\\\hline\end{array}[/latex]
   3. [latex]\begin{array}{rr}&8431\\\times&2\\\hline\end{array}[/latex]
   4. [latex]\begin{array}{rr}&5231\\\times&3\\\hline\end{array}[/latex]
3. Find the products.
   1. [latex]\begin{array}{rr}&68\\\times&5\\\hline\end{array}[/latex]
   2. [latex]\begin{array}{rr}&457\\\times&6\\\hline\end{array}[/latex]
   3. [latex]\begin{array}{rr}&9346\\\times&7\\\hline\end{array}[/latex]
   4. [latex]\begin{array}{rr}&1329\\\times&4\\\hline\end{array}[/latex]

4. Find the products.
   1. [latex]\begin{array}{rr}&45\\\times&26\\\hline\end{array}[/latex]
   2. [latex]\begin{array}{rr}&542\\\times&38\\\hline\end{array}[/latex]
   3. [latex]\begin{array}{rr}&3829\\\times&52\\\hline\end{array}[/latex]
   4. [latex]\begin{array}{rr}&463\\\times&179\\\hline\end{array}[/latex]
   5. [latex]\begin{array}{rr}&6314\\\times&231\\\hline\end{array}[/latex]
   6. [latex]\begin{array}{rr}&1425\\\times&537\\\hline\end{array}[/latex]
5. Find the products. Use the shortcut.
   1. [latex]\begin{array}{rr}&1000\\\times&792\\\hline\end{array}[/latex]
   2. [latex]\begin{array}{rr}&9264\\\times&100\\\hline\end{array}[/latex]
   3. [latex]\begin{array}{rr}&1000\\\times&85\\\hline\end{array}[/latex]
   4. [latex]3609\times10=[/latex]
   5. [latex]100\times259=[/latex]
   6. [latex]10\times46=[/latex]
   7. [latex]5719\times1000=[/latex]

1-C

6. Find an estimated product.
   1. [latex]\begin{array}{rr}&72\\\times&38\\\hline\end{array}[/latex]
   2. [latex]\begin{array}{rr}&574\\\times&83\\\hline\end{array}[/latex]
   3. [latex]\begin{array}{rr}&5492\\\times&87\\\hline\end{array}[/latex]
   4. [latex]\begin{array}{rr}&792\\\times&901\\\hline\end{array}[/latex]
   5. [latex]\begin{array}{rr}&8560\\\times&193\\\hline\end{array}[/latex]
   6. [latex]\begin{array}{rr}&29492\\\times&585\\\hline\end{array}[/latex]

1-D

7. Word Problems.
   1. The Great Belt Suspension Bridge in Denmark is 1624 metres. How many metres will 24 trucks travel crossing the bridge?
   2. How many cans of peaches are needed to pack 300 boxes, if each box has 3 rows and each row has 6 cans? (2 step question)
   3. The Krubera Cave in Georgia is the deepest cave in the world at 2191 metres. Estimate how many metres 348 visitors will cover going down to the cave.

2-A

8. Complete this chart.

   	Multiplication	Division	Division	“Say”
   a)	[latex]3\times8 = 24[/latex] [latex]8\times3 = 24[/latex]	[latex]24 \div8 = 3[/latex] [latex]24\div3 = 8[/latex]	[latex]\begin{array}{r}3\\8\enclose{longdiv}{24}\end{array} [/latex] [latex]\begin{array}{r}8\\3\enclose{longdiv}{24}\end{array} [/latex]	"24 divided by 8 is 3" "24 divided by 3 is 8"
   b)	[latex]7\times5 = 35[/latex]
   c)	[latex]9\times3 = 27[/latex]

9. Give the answer.
   1. [latex]28 \div 4 =[/latex]
   2. [latex]18 \div 6 = [/latex]
   3. [latex]64 \div 8 =[/latex]
   4. [latex]9\enclose{longdiv}{81}[/latex]
   5. [latex]5\enclose{longdiv}{40}[/latex]
   6. [latex]3\enclose{longdiv}{32}[/latex]
10. Find the quotients.
    1. [latex]8\enclose{longdiv}{60}[/latex]
    2. [latex]5\enclose{longdiv}{49}[/latex]
    3. [latex]9\enclose{longdiv}{43}[/latex]
    4. [latex]3\enclose{longdiv}{19}[/latex]

2-B

11. Using the following list of numbers, answer questions a, b, c and d. 96, 345, 3816, 6815, 38433, 95373
    1. Which numbers are divisible by 2?
    2. Which numbers are divisible by 3?
    3. Which numbers are divisible by 5?
    4. Which numbers are divisible by 9?

2-C

12. Find the quotients.
    1. [latex]3\enclose{longdiv}{963}[/latex]
    2. [latex]2\enclose{longdiv}{682}[/latex]
    3. [latex]4\enclose{longdiv}{844}[/latex]
    4. [latex]5\enclose{longdiv}{550}[/latex]
13. Find the quotients.
    1. [latex]9\enclose{longdiv}{387}[/latex]
    2. [latex]6\enclose{longdiv}{492}[/latex]
    3. [latex]5\enclose{longdiv}{915}[/latex]
    4. [latex]7\enclose{longdiv}{469}[/latex]
14. Find the quotients.
    1. [latex]8\enclose{longdiv}{832}[/latex]
    2. [latex]4\enclose{longdiv}{836}[/latex]
    3. [latex]3\enclose{longdiv}{927}[/latex]
    4. [latex]2\enclose{longdiv}{416}[/latex]
15. Find the quotients.
    1. [latex]5\enclose{longdiv}{92}[/latex]
    2. [latex]7\enclose{longdiv}{86}[/latex]
    3. [latex]4\enclose{longdiv}{73}[/latex]
    4. [latex]6\enclose{longdiv}{91}[/latex]
16. Find the quotients.
    1. [latex]3\enclose{longdiv}{851}[/latex]
    2. [latex]8\enclose{longdiv}{509}[/latex]
    3. [latex]2\enclose{longdiv}{407}[/latex]
    4. [latex]7\enclose{longdiv}{954}[/latex]

2-D

17. Find the quotients.
    1. [latex]24\enclose{longdiv}{480}[/latex]
    2. [latex]58\enclose{longdiv}{928}[/latex]
    3. [latex]36\enclose{longdiv}{1944}[/latex]
    4. [latex]73\enclose{longdiv}{37668}[/latex]
18. Find the quotients.
    1. [latex]10\enclose{longdiv}{683}[/latex]
    2. [latex]1000\enclose{longdiv}{41839}[/latex]
    3. [latex]100\enclose{longdiv}{13041}[/latex]
    4. [latex]1000\enclose{longdiv}{63125}[/latex]
19. Find the quotients.
    1. [latex]348\enclose{longdiv}{8010}[/latex]
    2. [latex]483\enclose{longdiv}{27150}[/latex]
    3. [latex]753\enclose{longdiv}{619345}[/latex]
    4. [latex]73\enclose{longdiv}{37668}[/latex]

2-E

20. Give an estimated quotient. Show your rounding where needed.
    1. [latex]30\enclose{longdiv}{63000}[/latex]
    2. [latex]7000\enclose{longdiv}{8400000}[/latex]
    3. [latex]58\enclose{longdiv}{2894}[/latex]
    4. [latex]438\enclose{longdiv}{23689}[/latex]
    5. [latex]768\enclose{longdiv}{63875}[/latex]
    6. [latex]896\enclose{longdiv}{80986}[/latex]

2-F

21. Word problems.
    1. A satellite orbits the moon every 58 minutes. How many complete orbits does it make 6728 minutes?
    2. It takes 73 hours to make a snow blower. How many snow blowers can be made in 47815 hours?
    3. There were 10780 tickets sold at the game. There were 150 tickets in each roll. How many complete rolls of tickets were used? How many were sold from the next roll?
22. Solve the cost per unit price.
    1. 6 packages of rice for $12
    2. 2 tubs of yogurt for $8
23. Solve the unit price and then underline the best buy.
    1. Dog food 8 kilograms for $16 or 15 kilograms for $45
    2. Movies 9 movies for $162 or 3 movies for $48

3-B

24. Circle the number of coins or bills you would need to get from the first number to the second number. Make sure to use the least number of coins or bills.
    1. $58 to $60
    2. $41 to $50
    3. $78 to $90
25. State the number and kind of coins and bills you would need to get from the first number to the second number. Make sure you use the least number of coins and bills as possible.
    1. $38 to $40
    2. $21 to $40
    3. $76 to $100
26. State the number and kind of coins and bills you would need to get change from the second number. Make sure you use the least number of coins and bills as possible.

    1. $43 to $100

       Need	To get to

    2. $23 to $80

       Need	To get to

    3. $58.40 to $100

       Need	To get to

    4. $62.75 to $100

       Need	To get to

27. State the number and kind of coins and bills you would need to get change from $100.  Make sure you use the least number of coins and bills as possible.
    1. Bread maker for $61.60
    2. Shop vacuum cleaner for $84.45
    3. Mrs. Chui bought building blocks for $33.45.  How much change will she get from $100?

3-C

28. Circle the letter of the most reasonable measure.
    1. Depth of the ocean
       1. 3926 mm
       2. 3926 km
       3. 3926 m
    2. Thickness of string
       1. 5 mm
       2. 5 cm
       3. 5 m
    3. Distance from the earth to moon
       1. 3476 m
       2. 3476 mm
       3. 3476 km
    4. Length of a banana
       1. 15 km
       2. 15 mm
       3. 15 cm
29. Choose the most reasonable measure.
    1. A spoonful of medicine
       1. 5 L
       2. 5 mL
       3. 50 mL
    2. A bottle of orange juice
       1. 4 mL
       2. 4 L
       3. 40 L
    3. A tube of toothpaste holds 130         .
    4. The gas tank of a car holds 70         .
30. Choose the most reasonable measure.
    1. A sugar cube has a mass of
       1. 1 g
       2. 10 g
       3. 10 kg
    2. A cat weighs
       1. 7 mg
       2. 7 kg
       3. 7 g
    3. A headache pill has 375         of medicine
31. Write the base unit of measure and then the prefix if one is needed.

    	Item	Base	Prefix (if needed)
    a)	thickness of a rope
    b)	water in a bathtub
    c)	a bag of rice
    d)	length of a table

32. Find the area of each shape.
    1. 
    2. 
33. Find the perimeter and area of each shape.
    1. 
    2. 
    3. Tiananmen Square measures 880 metres by 500 metres. Find the perimeter and area of Tiananmen.
    4. Andrèe wants to build a square patio whose side is 13 m. Find the perimeter and area of her new patio.

Answers to Book 3 Review

1. 1. 36
   2. 56
   3. 12
   4. 45
   5. 60
   6. 0
   7. 32
   8. 10
   9. 100
2. 1. 213
   2. 1869
   3. 16862
   4. 15693
3. 1. 340
   2. 2742
   3. 65422
   4. 5316
4. 1. 1170
   2. 20596
   3. 199108
   4. 82877
   5. 1458534
   6. 765225
5. 1. 792000
   2. 926400
   3. 85000
   4. 36090
   5. 25900
   6. 460
   7. 5719000
6. 1. [latex]70 \times 40 = 2800[/latex]
   2. [latex]600\times80=48000[/latex]
   3. [latex]5000\times90=450000[/latex]
   4. [latex]800\times900=720000[/latex]
   5. [latex]9000\times 200=1800000[/latex]
   6. [latex]30000\times600=18000000[/latex]
7. 1. 38976 metres
   2. 5400 cans
   3. 600000 metres

8. 	Multiplication	Division	Division	“Say”
   a)	[latex]3 \times 8 = 24[/latex] [latex]8 \times 3 = 24[/latex]	[latex]24 \div 8= 3[/latex] [latex]24 \div 3= 8[/latex]	[latex]\begin{array}{r}3\\8\enclose{longdiv}{24}\end{array} [/latex][latex]\begin{array}{r}8\\3\enclose{longdiv}{24}\end{array} [/latex]	"24 divided by 8 is 3"  "24 divided by 3 is 8"
   b)	[latex]7 \times5 = 35[/latex] [latex]5 \times 7 = 35[/latex]	[latex]35 \div 5= 7[/latex] [latex]35 \div 7= 5[/latex]	[latex]\begin{array}{r}7\\5\enclose{longdiv}{35}\end{array} [/latex][latex]\begin{array}{r}5\\7\enclose{longdiv}{35}\end{array} [/latex]	"35 divided by 5 is 7" "35 divided by 7 is 5"
   c)	[latex]9 \times 3 = 27[/latex] [latex]3 \times  9 = 27[/latex]	[latex]27 \div  3 = 9[/latex] [latex]27 \div  9 = 3[/latex]	[latex]\begin{array}{r}9\\3\enclose{longdiv}{27}\end{array} [/latex][latex]\begin{array}{r}3\\9\enclose{longdiv}{27}\end{array} [/latex]	"27 divided by 3 is 9" "27 divided by 9 is 3"

9. 1. 7
   2. 3
   3. 8
   4. 9
   5. 8
   6. 10 R2
10. 1. 7 R4
    2. 9 R4
    3. 4 R7
    4. 6 R1
11. 1. 96, 3816
    2. 96, 345, 3816, 38433, 95373
    3. 345, 6815
    4. 3816, 95373

12. 1. 321
    2. 341
    3. 211
    4. 110
13. 1. 43
    2. 82
    3. 183
    4. 67
14. 1. 104
    2. 209
    3. 309
    4. 208
15. 1. 18 R2
    2. 12 R2
    3. 18 R1
    4. 15 R1
16. 1. 283 R2
    2. 63 R5
    3. 203 R1
    4. 136 R2
17. 1. 20
    2. 16
    3. 54
    4. 516
18. 1. 68 R3
    2. 418 R839
    3. 130 R41
    4. 63 R125
19. 1. 23 R6
    2. 56 R102
    3. 822 R379
    4. 516
20. 1. 2100
    2. 1200
    3. [latex]30000\div60=50[/latex]
    4. [latex]24000\div400=60[/latex]
    5. [latex]64000\div800=80[/latex]
    6. [latex]81000\div900=90[/latex]
21. 1. 116 orbits
    2. 655 snow blowers
    3. 71 full rolls, 130 tickets
22. 1. $2
    2. $4
23. 1. $2, $3, best buy is 8 kilograms for $16
    2. $18, $16, best buy is 3 movies for $48
24. 1. 1 toonie
    2. 2 toonies, 1 $5 bill
    3. 1 toonie, 1 $10 bill
25. 1. 1 toonie
    2. 2 toonies, 1 $5 bill, 1 $10 bill
    3. 2 toonies, 1 $20 bill

26. 1.  $43 to $100

       Need	To get to
       1 toonie	$45
       1 $5 bill	$50
       1 $10 bill	$60
       2 $20 bills	$100

    2. $23 to $80

       Need	To get to
       1 toonie	$25
       1 $5 bill	$30
       1 $10 bill	$40
       2 $20 bills	$80

    3. $58.40 to $100

       Need	To get to
       1 dime	$58.50
       2 quarters	$59.00
       1 loonie	$60.00
       2 $20 bills	$100.00

    4. $62.75 to $100

       Need	To get to
       1 quarter	$63.00
       1 toonie	$65.00
       1 $5 bill	$70.00
       1 $10 bill	$80.00
       1 $20 bill	$100.00

27. 1. 1 nickel, 1 dime, 1 quarter, 1 loonie, 1 toonie, 1 $5 bill, 1 $10 bill, 1 $20 bill
    2. 1 nickel, 2 quarters, 1 $5 bill, 1 $10 bill
    3. 1 nickel, 2 quarters, 1 loonie, 1 $5 bill, 3 $20 bill
28. 1. iii
    2. i
    3. iii
    4. iii
29. 1. ii
    2. ii
    3. mL
    4. L
30. 1. i
    2. ii
    3. mg

31. 	Item	Base	Prefix (if needed)
    a)	thickness of a rope	m	m
    b)	water in a bathtub	L
    c)	a bag of rice	g	k
    d)	length of a table	m	c

32. 1. [latex]1305 \text{ mm}^2[/latex]
    2. [latex]2916 \text{ cm}^2[/latex]
33. 1. [latex]P=294 \text{ m}[/latex], [latex]A = 5330 \text{ m}^2[/latex]
    2. [latex]P = 212 \text{ mm}[/latex], [latex]A = 2809 \text{ mm}^2[/latex]
    3. [latex]P = 2760 \text{ m}[/latex], [latex]A = 440000 \text{ m}^2[/latex]
    4. [latex]P = 52 \text{ m}[/latex], [latex]A = 169 \text{ m}^2[/latex]

]]> 1422 0 1 0 https://opentextbc.ca/alfm3/back-matter/versioning-history/ Tue, 31 Jan 2023 18:27:34 +0000 https://opentextbc.ca/alfm3/?post_type=back-matter&p=1503 Report an Error form.

Version	Date	Change	Details
1.00	October 3, 2014	Book published using Microsoft Word.
2.00		Book updated and republished in Pressbooks as a 2nd Edition.	Removed coverage of time in last unit Reduced the number of exercises per example. Created a “How to Deal with Math Anxiety” front matter section, which is now standardized across all ALF Math books. Deleted “Topic A: Emotions and Learning” since that content is now covered in the “How to Deal with Math Anxiety” front matter. Re-lettered all units and topics in unit 1. Moved content from Word into Pressbooks. Added textboxes to visually identify examples and exercises. Added some headings to give long chapters more structure.
2.01	June 12, 2024	Corrected answers.	In Topic B: Two- and Three-Digit Multipliers in Unit 1: Multiplication, the answers to many of the problems in Exercise 2 were corrected.
2.02	March 7, 2025	Corrected content and formatting.	Corrected content and formatting errors throughout the book, including wrong answers, misplaced formatting, and outdated references to pennies.
2.03	September 19, 2025	Corrected errors and formatting.	Corrected errors and added content in the following sections: Topic B: Two- and Three-Digit Multipliers in Unit 1 Topic D: Multiplication Problems in Unit 1 Topic A: Introduction and Division Facts in Unit 2 Topic D: Dividing by Two- and Three- Digit Divisors in Unit 2 Topic E: Estimating Quotients in Unit 2 Topic F: Division Problems in Unit 2 Unit 2 Review: Division Topic B: Making Change in Unit 3 Topic C: The Metric System in Unit 3 Unit 3 Review: Change and the Metric System Book 3 Review

]]> 1503 0 4 0 https://opentextbc.ca/alfm3/back-matter/glossary/ Tue, 31 Jan 2023 18:32:52 +0000 https://opentextbc.ca/alfm3/?post_type=back-matter&p=1636 1636 0 2 0 https://opentextbc.ca/alfm3/?attachment_id=1682 Wed, 01 Feb 2023 21:37:00 +0000 https://opentextbc.ca/alfm3/?attachment_id=1682 1682 16 0 0 https://opentextbc.ca/alfm3/?post_type=back-matter&p=1727 Thu, 18 Sep 2025 22:22:29 +0000 https://opentextbc.ca/alfm3/?post_type=back-matter&p=1727 Version Date Change Details 1.00 October 3, 2014 Book published using Microsoft Word. 2.00 Book updated and republished in Pressbooks as a 2nd Edition.

• Removed coverage of time in last unit
• Reduced the number of exercises per example.
• Created a “How to Deal with Math Anxiety” front matter section, which is now standardized across all ALF Math books.
• Deleted “Topic A: Emotions and Learning” since that content is now covered in the “How to Deal with Math Anxiety” front matter.
• Re-lettered all units and topics in unit 1.
• Moved content from Word into Pressbooks.
• Added textboxes to visually identify examples and exercises.
• Added some headings to give long chapters more structure.

2.01 June 12, 2024 Corrected answers. In Topic B: Two- and Three-Digit Multipliers in Unit 1: Multiplication, the answers to many of the problems in Exercise 2 were corrected. 2.02 March 7, 2025 Corrected content and formatting. Corrected content and formatting errors throughout the book, including wrong answers, misplaced formatting, and outdated references to pennies. 2.03 September 18, 2025 Corrected errors and formatting. Corrected errors and added content in the following sections:

• Topic B: Two- and Three-Digit Multipliers in Unit 1
• Topic D: Multiplication Problems in Unit 1
• Topic A: Introduction and Division Facts in Unit 2
• Topic D: Dividing by Two- and Three- Digit Divisors in Unit 2
• Topic E: Estimating Quotients in Unit 2
• Topic F: Division Problems in Unit 2
• Unit 2 Review: Division
• Topic B: Making Change in Unit 3
• Topic C: The Metric System in Unit 3
• Unit 3 Review: Change and the Metric System
• Book 3 Review

]]> 1727 0 5 0 https://opentextbc.ca/alfm3/front-matter/introduction/ Thu, 05 Jan 2023 23:03:03 +0000 https://opentextbc.ca/alfm3/?p=4 Adult Literacy Fundamental Mathematics: Book 3. You have the skills you need to be a strong student in this class. Your instructor knows this because you have passed the Adult Literacy Fundamental Mathematics Level 2 class, or you have been assessed into this level. Adult math learners have many skills. They have a lot of life experience. They also use math in their everyday lives. This means that adult math learners may already know some of what is being taught in this book. Use what you already know with confidence!

How to Use This Book

This textbook has:

• A Table of Contents listing the units, the major topics, and the subtopics.
• A Glossary giving definitions for mathematical vocabulary used in the course.
• A Grades Record to keep track of your marks.
• Many Exercises to practice what you learned. Some are quite short, but others have a great number of questions. You do not have to do every single question!
  • Do as many questions as you feel are necessary for you to be confident in your skill. It is best to do all the word problems.
  • If you leave out some questions, try doing every second or every third question. Always do some questions from the end of each exercise because the questions usually get harder at the end. You might use the skipped questions for review before a test.
  • If you are working on a difficult skill or concept, do half the exercise one day and finish the exercise the next day. That is a much better way to learn.
• Self-tests at the end of most topics have an "Aim" at the top. If you do not meet the aim, talk to your instructor, find what is causing the trouble, and do some more review before you go on.
• A Review and Extra Practice section is at the end of each unit. If there is an area of the unit that you need extra practice in, you can use this. Or, if you want, you can use the section for more review.
• A Practice Test is available for each unit. You may:
  • Write the practice test after you have studied the unit as a practice for the end-of-chapter test, OR
  • You might want to write it before you start the unit to find what you already know and which areas you need to work on.
• Unit Tests are written after each unit. Again, you must reach the Aim before you begin the next unit. If you do not reach the aim, the instructor will assist you in finding and practising the difficult areas. When you are ready, you can write a B test to show that you have mastered the skills.
• A Final Test is to be written when you have finished the book. This final test will assess your skills from the whole book. You have mastered the skills in each unit and then kept using many of them throughout the course. The test reviews all those skills.

Grades Record

You have also been given a sheet to write down your grades. After each test, you can write in the mark. This way you can keep track of your grades as you go through the course. This is a good idea to use in all your courses.

Grade Record - Book 3

Unit	Practice Test	Date of Test A	Test A	Date of Test B	Test B
Example		September 4, 2020	25/33	September 7, 2020	25/33
1
2
3
Final Test

]]> 4 0 4 0 https://opentextbc.ca/alfm3/chapter/making-change/ Wed, 18 Jan 2023 23:28:15 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1212

Example A

$4 to $5 To get from $4 to $5, you could use 1 loonie.

Example B

$23 to $25 To get from $23 to $25, you could use 1 toonie.

Example C

$55 to $60 To get from $55 to $60, you could use 1 five-dollar bill.

Exercise 1

Circle the number of coins or bills you would need to get from the first number to the second number. Make sure to use the least number of coins or bills. Check your work using the answer key at the end of the exercise.

1. $33 to $35
2. $48 to $50
3. $16 to $20
4. $68 to $70
5. $10 to $15
6. $35 to $40
7. $55 to $60
8. $85 to $90
9. $60 to $70
10. $90 to $100
11. $30 to $40
12. $40 to $50
13. $30 to $50
14. $70 to $80
15. $80 to $100
16. $45 to $50
17. $21 to $25
18. $55 to $60
19. $45 to $50
20. $40 to $50
21. $70 to $80

Answers to Exercise 1

1. 1 toonie
2. 1 toonie
3. 2 toonies
4. 1 toonie
5. 1 $5 bill
6. 1 $5 bill
7. 1 $5 bill
8. 1 $5 bill
9. 1 $10 bill
10. 1 $10 bill
11. 1 $10 bill
12. 1 $10 bill
13. 1 $20 bill
14. 1 $10 bill
15. 1 $20 bill
16. 1 $5 bill
17. 2 toonies
18. 1 $5 bill
19. 1 $5 bill
20. 1 $10 bill
21. 1 $10 bil

Exercise 2

State the number and kind of coins and bills you would need to get from the first number to the second number. Make sure you use the least number of coins and bills as possible. Check your work using the answer key at the end of the exercise. Example: $56 to $60. You require 2 toonies to get to $60.

1. $28 to $30
2. $35 to $40
3. $90 to $100
4. $32 to $50
5. $54 to $55
6. $30 to $50
7. $65 to $70
8. $45 to $50

Answers to Exercise 2

1. 1 toonie
2. 1 $5 bill
3. 1 $10 bill
4. 1 $10 bill, 1 $5 bill, 1 toonie, and 1 loonie
5. 1 loonie
6. 1 $20 bill
7. 1 $5 bill
8. 1 $5 bill

Example D

$28 to $50

Need	To get to
1 toonie	$30
1 $20 bill	$50

Example E

$36 to $50

Need	To get to
2 toonies	$40
1 $10 bill	$50

Example F

$63 to $80

Need	To get to
1 toonie	$65
1 $5 bill	$70
1 $10 bill	$80

Exercise 3

State the number and kind of coins and bills you would need to get from the first number to the second number. Make sure you use the least number of coins and bills as possible. Check your work using the answer key at the end of the exercise. Example:

$67 to $80

Need	To get to
1 loonie	$68
1 toonie	$70
1 $10 bill	$80

1. $26 to $40

   Need	To get to

2. $47 to $60

   Need	To get to

3. $69 to $80

   Need	To get to

4. $18 to $20

   Need	To get to

5. $36 to $50

   Need	To get to

6. $51 to $60

   Need	To get to

7. $78 to $100

   Need	To get to

8. $82 to $100

   Need	To get to

9. $93 to $100

   Need	To get to

10. $3 to $10

    Need	To get to

Answers to Exercise 3

1. $26 to $40

   Need	To get to
   2 toonies	$30
   1 $10 bill	$40

2. $47 to $60

   Need	To get to
   1 loonie	$48
   1 toonie	$50
   1 $10	$60

3. $69 to $80

   Need	To get to
   1 loonie	$70
   1 $10 bill	$80

4. $18 to $20

   Need	To get to
   1 toonie	$20

5. $36 to $50

   Need	To get to
   2 toonies	$40
   1 $10 bill	$50

6. $51 to $60

   Need	To get to
   2 toonies	$55
   1 $5 bill	$60

7. $78 to $100

   Need	To get to
   1 toonie	$80
   1 $20 bill	$100

8. $82 to $100

   Need	To get to
   1 loonie	$83
   1 toonie	$85
   1 $5 bill	$90
   1 $10 bill	$100

9. $93 to $100

   Need	To get to
   1 toonie	$95
   1 $5 bill	$100

10. $3 to $10

    Need	To get to
    1 toonie	$5
    1 $5 bill	$10

Exercise 4

State the number and kind of coins and bills you would need to get change from $100. Make sure you use the least number of coins and bills as possible. Check your work using the answer key at the end of the exercise. Example: $67 to $100

Need	To get to
1 loonie	$68
1 toonie	$70
1 $10 bill	$80
1 $20 bill	$100

1. $26

   Need	To get to

2. $13

   Need	To get to

3. $57

   Need	To get to

4. $49

   Need	To get to

5. $38

   Need	To get to

6. $74

   Need	To get to

Answers to Exercise 4

1. $26

   Need	To get to
   2 toonies	$30
   1 $10 bill	$40
   3 $20 bills	$100

2. $13

   Need	To get to
   1 toonie	$15
   1 $5 bill	$20
   4 $20 bills	$100

3. $57

   Need	To get to
   1 loonie	$58
   1 toonie	$60
   2 $20 bills	$100

4. $49

   Need	To get to
   1 loonie	$50
   1 $10 bill	$60
   2 $20 bills	$100

5. $38

   Need	To get to
   1 toonie	$40
   3 $20	$100

6. $74

   Need	To get to
   3 toonies	$80
   1 $20 bill	$100

Exercise 5

State the number and kind of coins and bills you would need to get from the first number to the second number. Make sure you use the least number of coins and bills as possible. Check your work using the answer key at the end of the exercise. Example A: $2.70 to $5.00

Need	To get to
1 nickel	$2.75
1 quarter	$3.00
1 toonie	$5.00

 Example B: $6.30 to $10.00

Need	To get to
2 dimes	$6.50
2 quarters	$7.00
1 loonie	$8.00
1 toonie	$10.00

 Example C: $12.50 to $20.00

Need	To get to
2 quarters	$13.00
1 toonie	$15.00
1 $5 bill	$20.00

1. $2.20 to $10.00

   Need	To get to

2. $6.50 to $20.00

   Need	To get to

3. $8.70 to $20.00

   Need	To get to

4. $3.35 to $10.00

   Need	To get to

5. $17.85 to $20.00

   Need	To get to

6. $50.25 to $60.00

   Need	To get to

7. $20.55 to $40.00

   Need	To get to

8. $37.75 to $50.00

   Need	To get to

9. $19.90 to $50.00

   Need	To get to

10. $4.40 to $5.00

    Need	To get to

11. $44.55 to $60.00

    Need	To get to

12. $29.15 to $40.00

    Need	To get to

13. $65.80 to $80.00

    Need	To get to

14. $42.00 to $60.00

    Need	To get to

15. $97.70 to $100.00

    Need	To get to

16. $32.05 to $35.00

    Need	To get to

17. $58.30 to $100.00

    Need	To get to

18. $61.15 to $80.00

    Need	To get to

19. $72.85 to $100.00

    Need	To get to

20. $83.95 to $100.00

    Need	To get to

21. $5.25 to $20.00

    Need	To get to

22. $19.60 to $40.00

    Need	To get to

Answers to Exercise 5

1. $2.20 to $10.00

   Need	To get to
   1 nickel	$2.25
   3 quarters	$3
   1 toonie	$5
   1 $5 bill	$10

2. $6.50 to $20.00

   Need	To get to
   2 quarters	$7
   1 loonie	$8
   1 toonie	$10
   1 $10 bill	$20

3. $8.70 to $20.00

   Need	To get to
   1 nickel	$8.75
   1 quarter	$9
   1 loonie	$10
   1 $10 bill	$20

4. $3.35 to $10.00

   Need	To get to
   1 nickel	$3.40
   1 dime	$3.50
   2 quarters	$4
   1 loonie	$5
   1 $5 bill	$10

5. $17.85 to $20.00

   Need	To get to
   1 nickel	$17.90
   1 dime	$18
   1 toonie	$20

6. $50.25 to $60.00

   Need	To get to
   3 quarters	$51
   2 toonies	$55
   1 $5 bill	$60

7. $20.55 to $40.00

   Need	To get to
   2 dimes	$20.75
   1 quarter	$21
   2 toonies	$25
   1 $5 bill	$30
   1 $10 bill	$40

8. $37.75 to $50.00

   Need	To get to
   1 quarter	$38
   1 toonie	$40
   1 $10 bill	$50

9. $19.90 to $50.00

   Need	To get to
   1 dime	$20
   1 $10 bill	$30
   1 $20 bill	$50

10. $4.40 to $5.00

    Need	To get to
    1 dime	$4.50
    2 quarters	$5

11. $44.55 to $60.00

    Need	To get to
    2 dimes	$44.75
    1 quarter	$45
    1 $5 bill	$50
    1 $10 bill	$60

12. $29.15 to $40.00

    Need	To get to
    1 dime	$29.25
    3 quarters	$30
    1 $10 bill	$40

13. $65.80 to $80.00

    Need	To get to
    2 dimes	$66
    2 toonies	$70
    1 $10 bill	$80

14. $42.00 to $60.00

    Need	To get to
    1 loonie	$43
    1 toonie	$45
    1 $5 bill	$50
    1 $10 bill	$60

15. $97.70 to $100.00

    Need	To get to
    1 nickel	$97.75
    1 quarter	$98
    1 toonie	$100

16. $32.05 to $35.00

    Need	To get to
    2 dimes	$32.25
    3 quarters	$33
    1 toonie	$35

17. $58.30 to $100.00

    Need	To get to
    2 dimes	$58.50
    2 quarters	$59
    1 loonie	$60
    2 $20 bills	$100

18. $61.15 to $80.00

    Need	To get to
    1 dime	$61.25
    3 quarters	$62
    1 loonie	$63
    1 toonie	$65
    1 $5 bill	$70
    1 $10 bill	$80

19. $72.85 to $100.00

    Need	To get to
    1 nickel	$72.90
    1 dime	$73
    1 toonie	$75
    1 $5 bill	$80
    1 $20 bill	$100

20. $83.95 to $100.00

    Need	To get to
    1 nickel	$84
    1 loonie	$85
    1 $5 bill	$90
    1 $10 bill	$100

21. $5.25 to $20.00

    Need	To get to
    3 quarters	$6
    2 toonies	$10
    1 $10 bill	$20

22. $19.60 to $40.00

    Need	To get to
    1 nickel	$19.65
    1 dime	$19.75
    1 quarter	$20
    1 $20 bill	$40

Exercise 6

State the number and kind of coins and bills you would need to get from the first number to the second number. Make sure you use the least number of coins and bills as possible. Check your work using the answer key at the end of the exercise.

1. $1.75 to $5.00
2. $54.05 to $60.00
3. $96.45 to $100.00
4. $28.20 to $30.00
5. $73.95 to $80.00
6. $32.85 to $50.00
7. $9.40 to $20.00
8. $85.25 to $100.00

Answers to Exercise 6

1. $1.75 to $5.00
   • 1 quarter
   • 1 loonie
   • 1 toonie
2. $54.05 to $60.00
   • 2 dimes
   • 3 quarters
   • 1 $5 bill
3. $96.45 to $100.00
   • 1 nickel
   • 2 quarters
   • 1 loonie
   • 1 toonie
4. $28.20 to $30.00
   • 1 nickel
   • 3 quarters
   • 1 loonie
5. $73.95 to $80.00
   • 1 nickel
   • 1 loonie
   • 1 $5 bill
6. $32.85 to $50.00
   • 1 nickel
   • 1 dime
   • 1 toonie
   • 1 $5 bill
   • 1 $10 bill
7. $9.40 to $20.00
   • 1 dime
   • 2 quarters
   • 1 $10 bill
8. $85.25 to $100.00
   • 3 quarters
   • 2 toonies
   • 1 $10 bill

Exercise 7

State the number and kind of coins and bills you would need to get change after making each purchase with a $100 bill. Make sure you use the least number of coins and bills as possible. Check your work using the answer key at the end of the exercise.

1. 1  kg of chicken for $24.60
2. DVD Player for $25.75
3. Metal shelf for $75.60
4. Heavy duty drill costs $89.90
5. Skates cost $67.50
6. Floor lamp costs $73.95
7. coffee maker costs $22.40
8. a package of toilet paper costs $6.75
9. a box of laundry detergent costs $13.45
10. a can of baby formula costs $30.25

Answers to Exercise 7

1. 1 nickel, 1 dime, 1 quarter, 1 $5 bill, 1 $10 bill, 3 $20 bills
2. 1 quarter, 2 toonies, 1 $10 bill, 3 $20 bills
3. 1 nickel, 1 dime, 1 quarter, 2 toonies, 1 $20 bill
4. 1 dime, 1 $10 bill
5. 2 quarters, 1 toonie, 1 $10 bill, 1 $20 bill
6. 1 nickel, 1 loonie, 1 $5 bill, 1 $20 bill
7. 1 dime, 2 quarters, 1 toonie, 1 $5 bill, 1 $10 bill, 3 $20 bills
8. 1 quarter, 1 loonie, 1 toonie, 1 $10 bill, 4 $20 bills
9. 1 nickel, 2 quarters, 1 loonie, 1 $5 bill, 4 $20 bills
10. 3 quarters, 2 toonies, 1 $5 bill, 3 $20 bills

Exercise 8

State the number and kind of coins and bills you would need to get change from $100. Make sure you use the least number of coins and bills as possible. Check your work using the answer key at the end of the exercise.

1. Mrs. Bhabra bought a food processor that cost $56.00. What change will she get from $100?
2. Pablo bought Lego for $30.25. What change will she get from $100?
3. A case of 6 bottles of motor oil costs $43.70. What change will you get from?
4. Shampoo costs $3.95 and conditioner costs $4.95. Together with taxes, they cost $9.35. What change will you get from $100?

Answers to Exercise 8

1. 2 toonies, 2 $20 bills
2. 3 quarters, 2 toonies, 1 $5 bill, 3 $20 bills
3. 1 nickel, 1 quarter, 1 loonie, 1 $5 bill, 1 $10 bill, 2 $20 bills
4. 1 nickel, 1 dime, 2 quarters, 1 $10 bill, 4 $20 bills

Topic B: Self-Test

Mark  /21   Aim  17/21

1. Circle the number of coins and bills needed to get from the first number to the second number.  Use the least number of coins. (4 marks)
   1. $76 to $80
   2. $22 to $25
   3. $40 to $50
   4. $55 to $60
2. State the number and kind of coins or bills are needed to get from the first number to the second number. (4 marks)
   1. $48 to $50
   2. $76 to $80
   3. $95 to $100
   4. $40 to $50
3. State the number and kind of coins and bills you would need to get from the first number to the second number. Make sure you use the least number of coins and bills as possible. (4 marks)
   1. $37 to $50
   2. $16 to $50
   3. $42 to $60
   4. $81 to $100
4. State the number and kind of coins and bills you would need to get change from $100. Make sure you use the least number of coins and bills as possible. (9 marks)
   1. $23
   2. $41
   3. $68
   4. $72
   5. groceries cost $89.65
   6. telephone bill was $51.10
   7. gas for the car cost $61.60
   8. Kristina bought a new vacuum cleaner for $86.35. What change will she get from $100?
   9. Uchida bought a new frying pan for $39.20. How much change will she get back from $100?

Answers to Topic B Self-Test

1. 1. 2 toonies
   2. 1 loonie, 1 toonie
   3. 1 $10 bill
   4. 1 $5 bill
2. 1. 1 toonie
   2. 2 toonies
   3. 1 $5 bill
   4. 1 $10 bill
3. 1. 1 loonie, 1 toonie, 1 $10 bill
   2. 2 toonies, 1 $10 bill, 1 $20 bill
   3. 1 loonie, 1 toonie, 1 $5 bill, 1 $10 bill
   4. 2 toonies, 1 $5 bill, 1 $10 bill
4. 1. 1 toonie, 1 $5 bill, 1 $10 bill, 3 $20 bill
   2. 2 toonies, 1 $5 bill, 1 $10 bill, 2 $20 bills
   3. 1 toonie, 1 $10 bill, 1 $20 bills
   4. 1 loonie, 1 toonie, 1 $5 bill, 1 $20 bill
   5. 1 dime, 1 quarter, 1 $10 bill
   6. 1 nickel, 1 dime, 3 quarters, 1 loonie, 1 toonie, 1 $5 bill, 2 $20 bills
   7. 1 nickel, 1 dime, 1 quarter, 1 loonie, 1 toonie, 1 $5 bill, 1 $10 bill, 1 $20 bill
   8. 1 nickel, 1 dime, 2 quarters, 1 loonie, 1 toonie, 1 $10 bill
   9. 1 nickel, 3 quarters, 3 $20 bills

]]> 1212 1203 2 0 https://opentextbc.ca/alfm3/chapter/the-metric-system/ Thu, 19 Jan 2023 22:08:01 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1249 comparing. Measurement is comparing something with a standard unit of measure. In the past, units of measure were based on things found in a community. Often, lengths of parts of the body were used to measure:

• Inch: the width of a thumb
• Span: the distance from tip of thumb to tip of little finger when the hand is spread out
• Foot: the distance from big toe to heel of foot
• Yard (becomes “rod): the distance from tip of nose to tip of thumb of an outstretched hand and arm
• Cubit: the distance from the tip of the middle finger to the elbow
• Fathom: the distance from the tip of one hand to the tip of the other with both arms stretched out
• Mile: 1000 military double steps in the Roman army (mile passuum means "1000 paces")

The problem with these units was the distances would be different based on the size of the person doing the measuring. The problem grew even more when trade was started between cities. Over a long period of time, people in different countries came up with different standard units of measure. The British came up with imperial units such as inch, foot, yard and mile. The French came up with metric units such as metre, centimetre, litre and gram. In Canada, we use both metric and imperial units.

Measuring Length

The basic unit of measure for length is the metre (abbreviation m). If you stretch your arm straight out beside you, a metre is about the distance from the tip of your nose to the tip of your middle finger.

Exercise 1

Consider the following distances. Answer yes or no if you would use a metre to measure. Check your work using the answer key at the end of the exercise. Example:

• The length of a table - Yes
• The width of your watchband - No

1. length of your classroom
2. thickness of a piece of paper
3. length of your pen or pencil
4. height of the door
5. distance from Prince George to Fort Nelson
6. the width of your baby finger
7. the size of a postage stamp
8. the thickness of a quarter
9. the length of the hallway outside your classroom
10. the distance from your home to college
11. the height of your coffee mug
12. the width of your book
13. the distance from your home to Moncton, New Brunswick
14. the length of a city bus

Answers to Exercise 1

1. yes
2. no
3. no
4. yes
5. no
6. no
7. no
8. no
9. yes
10. no
11. no
12. no
13. no
14. yes

Exercise 2

Estimate the length of each item. Remember a metre is about the distance from the tip of your nose to the tip of your middle finger when your arm is stretched out beside you. Be sure to include the unit of measure in your answer. Have your instructor check your work.

1. the height of the doorway
2. the height of your table
3. the width of the doorway
4. the length of your arm
5. the distance from the floor to hip
6. the distance from the floor to waist
7. the height of the ceiling
8. the width of the window
9. the length of your classroom
10. the width of your classroom

Exercise 3

Circle the most reasonable measure. Remember a metre is about the distance from the tip of your nose to the tip of your middle finger when your arm is stretched out beside you. Check your work using the answer key at the end of the exercise.

1. A person's height
   1. 2m
   2. 20m
   3. 200m
2. The height of a child
   1. 10 m
   2. 100 m
   3. 1 m
3. The length of a house
   1. 150 m
   2. 15 m
   3. 1 m
4. The length of a bed
   1. 200 m
   2. 2 m
   3. 20 m
5. The height of a building
   1. 1 m
   2. 100 m
   3. 10 m
6. The height of a refrigerator
   1. 20 m
   2. 200 m
   3. 2 m

Answers to Exercise 3

1. i
2. iii
3. ii
4. ii
5. ii
6. iii

Measuring Small Lengths and Long Distances

It is hard to measure small things using a metre.  To measure small things, you can use centimetre (cm) or millimetre (mm). A centimetre (cm) is about the width of your baby finger. Remember it is just a guide. A millimetre (mm) is about the thickness of your fingernail. It is hard to measure long distances using a metre. To measure long distances, you can use kilometre (km). A kilometre is 1000 metres.

Exercise 4

For each item, circle the unit of measure you would use. Check your work using the answer key at the end of the exercise

	Item	Unit of Measure
a)	the width of a room	m, cm, mm
b)	the thickness of a coin	m, cm, mm
c)	the length of your pencil	m, cm, mm
d)	the length of the hall	m, cm, mm
e)	the length of this page	m, cm, mm
f)	the length of a screw	m, cm, mm
g)	the height of your cup	m, cm, mm
h)	the length of a bus	m, cm, mm
i)	the thickness of a window pane	m, cm, mm
j)	the width of a chair	m, cm, mm

Answers to Exercise 4

1. m
2. mm
3. cm
4. m
5. cm
6. mm
7. cm
8. m
9. mm
10. cm

Exercise 5

For each item, circle the letter of the most reasonable unit of measure. Check your work using the answer key at the end of the exercise.

1. The width of a doorway
   1. 50 mm
   2. 1 m
   3. 50 m
2. The length of your pencil
   1. 20 m
   2. 20 mm
   3. 20 cm
3. The height of a tall building
   1. 1 m
   2. 100 m
   3. 10 m
4. The height of a refrigerator
   1. 20 m
   2. 200 m
   3. 2 m
5. The diameter of a quarter
   1. 24 mm
   2. 24 cm
   3. 24 m
6. The height of the kitchen counter
   1. 9 m
   2. 9 cm
   3. 90 cm
7. The distance around your wrist
   1. 15 mm
   2. 15 cm
   3. 15 m
8. The width of a small TV screen
   1. 28 mm
   2. 128 cm
   3. 28 m
9. The length of a car
   1. 5 m
   2. 5 cm
   3. 5 mm
10. The height of a bookcase
    1. 2 cm
    2. 2 mm
    3. 2 m

Answers to Exercise 5

1. ii
2. iii
3. ii
4. iii
5. i
6. iii
7. ii
8. ii
9. i
10. iii

Exercise 6

Fill in the blank with the most reasonable unit of measure. Check your work using the answer key at the end of the exercise

1. Most hand held calculators are about 15          long.
2. The CN Tower in Toronto is 555          tall.
3. Many young men have an 80          waist.
4. Computer monitor screens are 28          wide.
5. The handle of a hammer is 20          long.
6. A table is about 65          long.
7. The seat of a chair is about 30          above the floor.
8. The window is about 3          long.
9. A roll of tape is about 13          wide.
10. A rope is about 7          thick.

Answers to Exercise 6

1. cm
2. m
3. cm
4. cm
5. cm
6. cm
7. cm
8. m
9. mm
10. mm

Measuring Capacity (Volume)

Volume is a measure of how much space something takes up. The basic unit of measure for volume is the Litre (L). Can you think of two things that we buy in litres?  We buy gasoline and milk in litres. We use millilitres (mL) to measure small volumes. For example, a small cup of coffee is about 180 mL.  Can you think of two things we buy in mL?

Exercise 7

Write the unit of measure you would use to measure each item (L or mL). Check your work using the answer key at the end of the exercise.

1. Bottle of pop
2. Gasoline
3. Car window wash
4. Can of beans
5. Large bottle of juice
6. Liquid dish soap
7. Cough syrup
8. Mixing bowls
9. Ketchup
10. Shampoo
11. Vinegar
12. Bathtub
13. Ice cube tray
14. Paint

Answers to Exercise 7

1. mL
2. L
3. L
4. mL
5. L
6. mL or L
7. mL
8. L
9. mL or L
10. mL
11. L
12. L
13. mL
14. L

Exercise 8

Circle the letter of the most reasonable unit of measure. Check your work using the answer key at the end of the exercise.

1. A can of soup
   1. 3 L
   2. 30 mL
   3. 300 mL
2. A large container of ice cream
   1. 5 L
   2. 500 L
   3. 50L
3. A hot water heater
   1. 200 mL
   2. 50 L
   3. 200 L
4. A cup of tea
   1. 18 mL
   2. 180 mL
   3. 218 L
5. A garbage can
   1. 120 L
   2. 120 mL
   3. 12 L
6. A saucepan
   1. 2 L
   2. 20 L
   3. 2 mL
7. A dose of cough syrup
   1. 40 L
   2. 4 mL
   3. 40 mL
8. The gas tank of a car
   1. 500 mL
   2. 5 L
   3. 50 L
9. A jar of mustard
   1. 150 mL
   2. 15 L
   3. 15 mL
10. A large mixing bowl
    1. 6 mL
    2. 60 L
    3. 6 L

Answers to Exercise 8

1. iii
2. i
3. iii
4. ii
5. i
6. i
7. ii
8. iii
9. i
10. iii

Measuring Mass

Mass is a measure of matter in something. The basic unit of measure for mass is the gram (g).  We buy sliced meats, bulk food, spices and cereal in grams. We use kilogram (kg) to measure the mass of large things such as cars, people, flour and sugar.  Can you think of two things that we buy in kilograms? We use milligram (mg) to measure the mass of small things such as medicine or vitamins. A milligram is very small.  Can you think of two things that we buy in milligrams?

Exercise 9

Circle the unit of measure you would use to measure each item. Check your work using the answer key at the end of the exercise

	Item	Unit of Measure
a)	pasta	mg, g, kg
b)	vitamin C	mg, g, kg
c)	peanut butter	mg, g, kg
d)	flour	mg, g, kg
e)	nails	mg, g, kg
f)	dry dog food	mg, g, kg
g)	rice	mg, g, kg
h)	cookies	mg, g, kg
i)	apples	mg, g, kg
j)	spices	mg, g, kg
k)	cement	mg, g, kg
l)	medicine tablets	mg, g, kg
m)	the family pet	mg, g, kg
n)	a coin	mg, g, kg

Answers to Exercise 9

1. g or kg
2. mg
3. g or kg
4. kg
5. kg
6. kg
7. kg
8. g
9. kg
10. g
11. kg
12. mg
13. kg
14. g

Exercise 10

Circle the letter of the most reasonable unit of measure. Check your work using the answer key at the end of the exercise.

1. A nickel
   1. 5 kg
   2. 5 g
   3. 50 g
2. A small television
   1. 8 g
   2. 8 kg
   3. 80 g
3. A flashlight battery
   1. 8 g
   2. 8 kg
   3. 80 g
4. A baby
   1. 30 kg
   2. 3 kg
   3. 300 kg
5. A dinner fork
   1. 50 g
   2. 5 g
   3. 5 kg
6. A slice of bread
   1. 2 g
   2. 20 g
   3. 2 kg
7. A sugar cube
   1. 2 mg
   2. 20 g
   3. 2 g
8. A refrigerator
   1. 120 g
   2. 120 kg
   3. 12 kg
9. A bag of potatoes
   1. 5 g
   2. 5 kg
   3. 50 mg
10. A car
    1. 100 kg
    2. 1000 kg
    3. 10 kg
11. A chocolate bar
    1. 300 mg
    2. 300 mg
    3. 300 g
12. A back pack
    1. 12 kg
    2. 12 g
    3. 12 mg

Answers to Exercise 10

1. ii
2. ii
3. i
4. ii
5. i
6. ii
7. iii
8. ii
9. ii
10. ii
11. iii
12. i

Metric Prefixes

In the metric system a prefix is used to tell if something is large or small. A prefix is a part of a word that is added to the start of word to change the meaning.

The base units of measure in the metric system are the metre (m), litre (L) and gram (g).

If the prefix kilo is added to one of the base units of measures, such as kilometre or kilogram, you know that these are large amounts.

A kilometre is 1000 metres.

A kilogram is 1000 grams.

If the prefix centi or milli is added to one of the base units of measure, such as centimetre or milligram, you know that these are small amounts.

It takes 100 centimetres to make a metre. It takes 1000 milligrams to make a gram.

Measures	Large	Base	Small
length	kilometre (km)	metre (m)	centimetre (cm) millimetre (mm)
volume		litre (L)	millilitre (mL)
mass	kilogram (kg)	gram (g)	milligram (mg)

Exercise 11

Write large, small or base on the line.  Check your work using the answer key at the end of the exercise.

1. kilometre         .
2. millimetre         .
3. metre         .
4. gram         .
5. litre         .
6. millimetre         .
7. milligram         .
8. kilogram         .
9. centimetre         .

Answers to Exercise 11

1. large
2. small
3. base
4. base
5. base
6. small
7. small
8. large
9. small

Exercise 12

Write the base unit of measure and then the prefix if one is needed. Check your work using the answer key at the end of the exercise.

	Item	Base	Prefix (if needed)
a)	Height of a tree
b)	A bottle of vanilla
c)	A cold tablet
d)	Distance between Vancouver and Toronto
e)	Thickness of a piece of paper
f)	Length of your foot
g)	Length of a piece of lumber
h)	A bottle of hand lotion
i)	A granola bar
j)	Diameter of a DVD
k)	Mass of a book
l)	Water in a hot tub
m)	Distance around the Earth
n)	Gap in a spark plug

Answers to Exercise 12

	Item	Base	Prefix (if needed)
a)	Height of a tree	m
b)	A bottle of vanilla	L	milli
c)	A cold tablet	g	milli
d)	Distance between Vancouver and Toronto	m	kilo
e)	Thickness of a piece of paper	m	milli
f)	Length of your foot	m	centi
g)	Length of a piece of lumber	m
h)	A bottle of hand lotion	L	milli
i)	A granola bar	g
j)	Diameter of a DVD	m	centi
k)	Mass of a book	g
l)	Water in a hot tub	L
m)	Distance around the Earth	m	kilo
n)	Gap in a spark plug	m	milli

Exercise 13

Write the unit of measure you would use for each item below. Check your work using the answer key at the end of the exercise.

1. coffee in a cup - millilitres (mL)
2. bag of potatoes
3. gas for a car
4. length of the hall
5. vitamin C tablet
6. thickness of glass
7. width of a page
8. box of cereal
9. distance from Vancouver to Halifax
10. height of a child
11. can of soup
12. window wash for the car
13. dose of heart medicine
14. length of a machine bolt
15. cheese

Answers to Exercise 13

1. coffee in a cup - millilitres (mL)
2. bag of potatoes - kilogram (kg)
3. gas for a car - litre (L)
4. length of the hall - metre (m)
5. vitamin C tablet - milligram (mg)
6. thickness of glass - millimetre (mm)
7. width of a page - centimetre (cm)
8. box of cereal - gram (g)
9. distance from Vancouver to Halifax - kilometre (km)
10. height of a child - metre (m)
11. can of soup - millilitre (mL)
12. window wash for the car - litre (L)
13. dose of heart medicine - milligram (mg)
14. length of a machine bolt - millimetre (mm)
15. cheese - kilogram (kg) or gram (g)

Area of Rectangles and Squares

Area is the amount of surface within a figure. Area is described using square units. For example,

•  If the figure is a room, the area is the floor surface.
•  If the figure is a tabletop, the area is the top surface of the table.   If the figure is a roof, the area would be the shingled surface.
•  If the figure is property, the area is the ground within the property lines.
•  If the figure is this page, the area is the entire flat page that you are reading.

Example A

Find the area of this rectangle. The measurements of this rectangle are given in centimetres. To measure the area, we will use squares which are 1 cm by 1 cm ( a square centimetre). How many square centimetres will fit on the surface of this rectangle? Count the 1 cm squares drawn within the Example A rectangle. The area of this rectangle is           square centimetres. This is written as           cm² Square centimetres is usually written cm² which is said as "square centimetres" or "centimetres squared". The small number is called an exponent and if the exponent is 2, it means multiplied by itself, so cm² means [latex]\text{cm}\times \text{cm}[/latex]. Square kilometres are written km².  Square metres are written m².

Example B

This is a diagram of a large cattle ranch. The measurements of the ranch are shown as kilometres. What is the area of this ranch? The square units to measure will be square kilometres. The area of this ranch will be the number of units 1 km by 1 km (km²). The diagram shows how many square kilometres would fit in an area 16 km by 10 km. Count them. The area of the Lone Bar Ranch is           km². Did you find a quick method for counting the square units? Did you multiply the number  of rows by the number of square kilometres in each row? The quick method of finding the area of a rectangle is to multiply the length by the width. Use this formula to find the area of a rectangle:

[latex]\text{Area of a rectangle} = \text{length (}l\text{)} \times \text{width (}w\text{)}[/latex]

Length times width can also be expressed as lw,

so [latex]\text{A}_{\text{rectangle}}= lw[/latex]

The answer must be expressed in square units.

Example C

Give the area of a soccer field that is 100 m by 45 m.

A_rectangle = lw

[latex]\text{Area of the soccer field} = 100 \text{ m} \times 45 \text{ m} = 4500 \text{ m}^2[/latex]

Exercise 14

Find the area of the rectangles described below. The measures of the length (l) and the width (w) have been given. Draw and label a picture for each. Be sure to write the unit of measure for each answer. Check your work using the answer key at the end of the exercise.

1. [latex]l = 10 \text{ cm}[/latex], [latex]w = 6 \text{ cm}[/latex]
2. [latex]l = 100 \text{ km}[/latex], [latex]w = 70 \text{ km}[/latex]
3. [latex]l = 400 \text{ km}[/latex], [latex]w = 100 \text{ km}[/latex]
4. [latex]l = 975 \text{ cm}[/latex], [latex]w = 35 \text{ cm}[/latex]
5. [latex]l = 196 \text{ cm}[/latex], [latex]w = 28 \text{ cm}[/latex]
6. [latex]l = 82 \text{ km}[/latex], [latex]w = 12 \text{ km}[/latex]
7. [latex]l = 60 \text{ cm}[/latex], [latex]w = 250 \text{ cm}[/latex]
8. [latex]l = 90 \text{ cm}[/latex], [latex]w = 2 \text{ cm}[/latex]

Answers to Exercise 14

1. [latex]60 \text{ cm}^2[/latex]
2. [latex]7000 \text{ km}^2[/latex]
3. [latex]40000 \text{ km}^2[/latex]
4. [latex]34125 \text{ cm}^2[/latex]
5. [latex]5488 \text{ cm}^2[/latex]
6. [latex]984 \text{ km}^2[/latex]
7. [latex]1500 \text{ cm}^2[/latex]
8. [latex]180 \text{ cm}^2[/latex]

Squares are rectangles with all four sides congruent (the same length). So to find the area of a square you still use the same formula of multiplying the length times the width. But since the length and the width of a square are the same, you are multiplying the measure of the side (s) by itself. The formula for finding the area of a square is often written using an exponent.

A_square = s²

For example, to find the area of a square piece of property, multiply the length of one side by itself. If the measure of one side of a property is 75 m,

Area of this piece of property:  [latex]75^2 = 75\text{ m} \times75\text{ m} = 5625\text{ m}^2[/latex]

Exercise 15

Find the area of the squares. The measure of the side has been given. Draw and label a picture for each. Be sure to write the unit of measure for each answer. Check your work using the answer key at the end of the exercise.

1. A_square, if [latex] s = 5 \text{ cm}[/latex]
2. A_square, if [latex]s = 125 \text{ km}[/latex]
3. A_square, if [latex]s = 45 \text{ mm}[/latex]
4. A_square, if [latex]s = 100 \text{ m}[/latex]
5. A_square, if [latex]s = 14 \text{ km}[/latex]
6. A_square, if [latex]s = 25 \text{ cm}[/latex]

Answers to Exercise 15

1. [latex]25 \text{ cm}^2[/latex]
2. [latex]15625 \text{ km}^2[/latex]
3. [latex]2025 \text{ mm}^2[/latex]
4. [latex]10000 \text{ m}^2[/latex]
5. [latex]196 \text{ km}^2[/latex]
6. [latex]625 \text{ cm}^2[/latex]

Problems Using Area

Exercise 16

Do these problems by following the five problem-solving steps. Be sure to draw a picture. Check your work using the answer key at the end of the exercise.

1. A garden in the shape of a rectangle is 34 m long and 20 m wide. What is the area of the garden?
2. Mr. Pavelski has a lot in the shape of a square. If the side of his square lot is 50 m, what is the area of the lot?
3. A rectangular board is 58 cm wide and 64 cm long. How much area will this board cover?
4. Kyoko bought some curtain material that is 198 cm long and 40 cm wide. How many square centimetres of material did she buy?
5. The distance between bases of a baseball diamond (a square) is 27 m. What is the area of the baseball diamond?
6. The janitor waxed a floor that was 24 m long and 18 m wide. How many square metres of floor did he wax?

Answers to Exercise 16

1. [latex]680 \text{ m}^2[/latex]
2. [latex]2500 \text{ m}^2[/latex]
3. [latex]3712 \text{ cm}^2[/latex]
4. [latex]7920 \text{ cm}^2[/latex]
5. [latex]729 \text{ m}^2[/latex]
6. [latex]432 \text{ m}^2[/latex]

Perimeter and Area of Rectangles and Squares

Rectangle

Perimeter means distance around.  To find the perimeter of a rectangle, use the formula

[latex]P = 2 \times \text{length} + 2 \times \text{width}[/latex].

Example D

[latex]\begin{array}{l}P = 2 \times \text{length} + 2 \times \text{width} \\\hspace{1em} = 2\times 4 \text{ cm}+ 2 \times 2 \text{ cm}\\ \hspace{1em}= 8 \text{ cm}+4 \text{ cm}\\ \hspace{1em}=12 \text{ cm}\end{array}[/latex]

Remember:  Multiply first and then add.

Area means the amount of surface within a shape. To find the area of a rectangle, use the formula

[latex]A = \text{length} \times \text{width}[/latex]

Example E

[latex]\begin{array}{l}A = \text{length} \times \text{width} \\\hspace{1em} = 4 \text{ cm}\times 2 \text{ cm}\\\hspace{1em} = 8 \text{ cm}^2 \end{array}[/latex]

Exercise 17

For each rectangle, find both the perimeter (distance around) and the area (amount of surface within). Check your work using the answer key at the end of the exercise.

1. 
2. 
3. 
4. 
5. 
6. 
7. Raoul’s lot is shaped like a rectangle. If it is 55 m long and 15 m wide, what is the perimeter and area of his lot?
8. The playground is shaped like a rectangle. Its length is 140 m and its width is 60 What is the perimeter and area of the playground?

Answers to Exercise 17

1. P = 16 m, A = 12 m²
2. P = 38 cm, A= 84 cm²
3. P = 52 km, A = 153 km²
4. P = 40 mm, A 96 mm²
5. P = 94 m, A = 480 m²
6. P - 166 m, A = 1170 m²
7. P = 140 m, A = 825 m²
8. P = 400 m, A = 8400 m²

Square

Perimeter means distance around.  To find the perimeter of a square, use the formula

P = 4 × side or P_square = 4s

Example F

[latex]\begin{array}{l}P = 4\times \text{side} \\\hspace{1em} = 4 \times 9 \text{ cm}\\\hspace{1em} = 36 \text{ cm}\end{array}[/latex]

Area means the amount of surface within a shape. To find the area of a square, use the formula

A = side²   or  A_square  = s²

Example G

[latex]\begin{array}{l}A = \text{side}^2 \\\hspace{1em} = (4 \text{ cm})^2\\\hspace{1em} = 16 \text{ cm}^2\end{array}[/latex]

Exercise 18

For each square, find both the perimeter (distance around) and the area (amount of surface within). Check your work using the answer key at the end of the exercise.

1. 
2. 
3.  
4. 
5. 
6. 
7. Luisa bought a 115 cm square tablecloth. What is the perimeter and area of the tablecloth?
8. Liang bought a square tarp whose side was 31 m. What is the perimeter and area of the tarp?

Answers to Exercise 18

1. P = 20 m, A = 25 m²
2. P = 36 cm, A= 81 cm²
3. P = 60 cm, A = 255 cm²
4. P = 152 cm, A = 1444 cm²
5. P = 168 cm, A = 1764 cm²
6. P - 288 mm, A = 3249 mm²
7. P = 460 cm, A = 13225 cm²
8. P = 124 m, A = 961 m²

Topic C: Self Test

Mark  /38   Aim  30/38

1. For each item, circle the unit of measure you would use. (8 marks)

   	Item	Unit of Measure
   a)	Height of a doorknob above the floor	m, cm, mm, km
   b)	Thickness of a piece of wire	m, cm, mm, km
   c)	Length of a ski	m, cm, mm, km
   d)	Thickness of a piece of string	m, cm, mm, km
   e)	Height of a fence	m, cm, mm, km
   f)	Length of a finger	m, cm, mm, km
   g)	Length of a football field	m, cm, mm, km
   h)	How far you travelled on your holiday	m, cm, mm, km

2. Circle the letter of the most reasonable measure. (6 marks)
   1. Storage box
      1. 66 mL
      2. 66 L
      3. 6 L
   2. Baby Shampoo
      1. 593 mL
      2. 593 L
      3. 59 L
   3. Antifreeze
      1. 40 L
      2. 4 L
      3. 40 mL
   4. Wastebasket
      1. 42 mL
      2. 4 L
      3. 42 mL
   5. Deodorant
      1. 354 L
      2. 35 mL
      3. 354 mL
   6. Liquid laundry soap
      1. 975 mL
      2. 97 L
      3. 975 L
3. Circle the unit of measure you would use. (6 marks)

   	Item	Unit of Measure
   a)	can of peanuts	mg, g, kg
   b)	cat litter	mg, g, kg
   c)	an antacid tablet	mg, g, kg
   d)	bag of potato chips	mg, g, kg

4. Fill in the chart with the right metric prefix. (6 marks)

   Measure	Small	Base	Large

5. Find the perimeter and area for each shape. (12 marks)
   1. 
   2. 
   3.  
   4. 
   5. A double-size bed cover measures 135 cm wide and 190 cm What is the perimeter and area of the bed cover?
   6. An Olympic size swimming is 50 m long and 25 m wide. What is the perimeter and area of the swimming pool?

Answers to Topic D Self-Test

1. 1. cm
   2. mm
   3. cm
   4. mm
   5. m or cm
   6. cm
   7. m
   8. km
2. 1. ii
   2. i
   3. ii
   4. ii
   5. iii
   6. i
3. 1. g
   2. kg
   3. mg
   4. g

4. Measure	Small	Base	Large
   volume	milli	Litre
   length	milli	metre	kilo
   mass	milli	gram	kilo

5. 1. P = 20 cm, A = 21 cm²
   2. P = 24 km, A = 36 km²
   3. P = 392 m, A = 2208 m²
   4. P = 348 mm, A = 7569 mm²
   5. P = 650 cm, A = 25650 cm²
   6. P = 150 m, A = 1250 m²

]]> 1249 1203 3 0 https://opentextbc.ca/alfm3/chapter/review-change-and-the-metric-system/ Tue, 24 Jan 2023 20:08:30 +0000 https://opentextbc.ca/alfm3/?post_type=chapter&p=1309

Circle the number of coins or bills you would need to get from the first number to the second number. Make sure to use the least number of coins or bills.

1. $48 to $50
2. $59 to $60
3. $73 to $80
4. $33 to $40

State the number and kind of coins and bills you would need to get from the first number to the second number. Make sure you use the least number of coins and bills as possible.

1. $23 to $25
2. $31 to $35
3. $85 to $90
4. $70 to $90

State the number and kind of coins and bills you would need to get from the first number to the second number. Make sure you use the least number of coins and bills as possible.

1. $37 to $50

   Need	To get to

2. $53 to $60

   Need	To get to

3. $77 to $100

   Need	To get to

4. $21 to $50

   Need	To get to

State the number and kind of coins and bills you would need to get from the first number to the second number. Make sure you use the least number of coins and bills as possible.

1. $63.55 to $80

   Need	To get to

2. $32.65 to $50

   Need	To get to

3. $20.35 to $40

   Need	To get to

4. $72.20 to $100

   Need	To get to

State the number and kind of coins and bills you would need to get change from $100. Make sure you use the least number of coins and bills as possible.

1. printer for $78.40
2. cordless phone for $55.65
3. Mrs. Kono bought a new cordless kettle for $44.80. How much change will Mrs. Kono get from $100?

Circle the letter of the most reasonable measure.

1. Diameter of a hockey puck
   1. 76 mm
   2. 76 m
   3. 76 cm
2. Distance from the mall to home
   1. 10 km
   2. 10 m
   3. 10 cm
3. Thickness of a blanket
   1. 10 m
   2. 10 cm
   3. 10 mm
4. Height of a tree
   1. 28 mm
   2. 28 m
   3. 28 cm

Choose the most reasonable measure.

1. Carlos drinks
   1. 500 L of milk
   2. 500 mL of milk
   3. 5 mL of milk
2. A thermos holds
   1. 360 mL
   2. 360 L
   3. 36 L
3. A swimming pool holds 3758          of water
4. A tube of lotion is 50         .

Choose the most reasonable measure.

1. A dog weighs
   1. 17 g
   2. 17 kg
   3. 17 mg
2. A nickel has a mass of
   1. 5 g
   2. 5 mg
   3. 5 kg
3. A paper clip has mass of
   1. 1 kg
   2. 1 mg
   3. 1 g
4. Six math books have mass of
   1. 2 kg
   2. 2 mg
   3. 2 g

5. Elena took 400          of vitamin A
6. Suki bought 10          of potatoes

Write the base unit of measure and then the prefix if one is needed.

	Item	Base	Prefix (if needed)
a)	length of a garden hose
b)	a bottle of olive oil
c)	a child’s multivitamin
d)	distance between Jupiter and Mars
e)	thickness of a tissue

Write the unit of measure you would use for each item below.

1. Paint thinner
2. Cat litter
3. Deodorant
4. Length of the street
5. Aspirin

Find the area of each shape.

1. 
2. 
3. Red Square in Moscow measures 330 m long and 70 m wide. What is the area of Red Square?
4. Yoshiro is going to build a square patio whose side is 23 metres. What is the area of the patio?

Find the perimeter and area of each shape.

1. 
2. 
3. Nadal wants to fence his garden. It is 15 m wide and 26 m long. How much fencing does Nadal need?  How much space does Nadal have to plant a garden?
4. Yolanda would like to buy fencing and sod for her new lawn that is 54 m long and 42 m wide.  How much fencing does she need?  How much sod does she need?

Answers to Unit 3 Review

1. Circle the number of coins or bills you would need.
   1. 1 toonie
   2. 1 loonie
   3. 1 toonie, 1 $5 bill
   4. 1 toonie, 1 $5 bill
2. State the number and kind of coins and bills you would need.
   1. 1 toonie
   2. 2 toonies
   3. 1 $5 bill
   4. 1 $20 bill
3. State the number and kind of coins and bills you would need.

   1. $37 to $50

      Need	To get to
      1 loonie	$38
      1 toonie	$40
      1 $10 bill	$50

   2. $53 to $60

      Need	To get to
      1 toonie	$55
      1 $5 bill	$60

   3. $77 to $100

      Need	To get to
      1 loonie	$78
      1 toonie	$80
      1 $20 bill	$100

   4. $21 to $50

      Need	To get to
      2 toonies	$25
      1 $5 bill	$30
      1 $20 bill	$50

4. State the number and kind of coins and bills you would need.

   1. $63.55 to $80

      Need	To get to
      2 dimes	$63.75
      1 quarter	$64
      1 loonie	$65
      1 $5 bill	$70
      1 $10 bill	$80

   2. $32.65 to $50

      Need	To get to
      1 dime	$32.75
      1 quarter	$33
      1 toonie	$35
      1 $5 bill	$40
      1 $10 bill	$50

   3. $20.35 to $40

      Need	To get to
      1 nickel	$20.40
      1 dime	$20.50
      2 quarters	$21
      2 toonies	$25
      1 $5 bill	$30
      1 $10 bill	$40

   4. $72.20 to $100

      Need	To get to
      1 nickel	$72.25
      3 quarters	$73
      1 toonie	$75
      1 $5 bill	$80
      1 $20 bill	$100

5. State the number and kind of coins and bills you would need.
   1. 1 dime, 2 quarters, 1 loonie, 1 $20 bill
   2. 1 dime, 1 quarter, 2 toonies, 2 $20 bills
   3. 2 dimes, 1 $5 bill, 1 $10 bill, 2 $20 bills
6. Circle the letter of the most reasonable measure.
   1. i
   2. i
   3. iii
   4. ii
7. Choose the most reasonable measure.
   1. ii
   2. i
   3. L
   4. mL
8. Choose the most reasonable measure.
   1. ii
   2. i
   3. iii
   4. i
   5. mg
   6. kg
9. Write the base unit of measure and then the prefix if one is needed.

   	Item	Base	Prefix (if needed)
   a)	length of a garden hose	m
   b)	a bottle of olive oil	L	milli
   c)	a child’s multivitamin	g	milli
   d)	distance between Jupiter and Mars	m	kilo
   e)	thickness of a tissue	m	milli

10. Write the unit of measure you would use for each item below.
    1. L
    2. kg
    3. mL
    4. km
    5. mg
11. Find the area of each shape.
    1. [latex]A = 592 \text{ m}^2[/latex]
    2. [latex]A = 6724 \text{ cm}^2[/latex]
    3. [latex]A = 23100 \text{ m}^2[/latex]
    4. [latex]A = 529 \text{ m}^2[/latex]
12. Find the perimeter and area of each shape.
    1. [latex]P = 236 \text{ m}, A = 3312 \text{ m}^2[/latex]
    2. [latex]P = 156 \text{ mm}, A = 1521 \text{ mm}^2[/latex]
    3. [latex]P = 82 \text{ m}, A = 390 \text{ m}^2[/latex]
    4. [latex]P = 192 \text{ m}, A = 2268\text{ m}^2[/latex]

]]> 1309 1203 4 0 https://opentextbc.ca/alfm3/front-matter/how-to-deal-with-math-anxiety/ Wed, 25 Jan 2023 22:01:56 +0000 https://opentextbc.ca/alfm3/?post_type=front-matter&p=1371 Emotions and Learning Emotions, or what we feel about something, play a big part in how we learn. If we are calm, we learn well. If we are afraid or stressed, we do not learn as well. Many people are afraid of math. They fear making a mistake. “Math anxiety” is the fear of math. People who suffer from math anxiety may get headaches, sick stomachs, cold hands, or they may just sweat a lot or just feel scared. Math anxiety can happen for a few different reasons:

• Feeling anxious when writing tests
• Negative experiences in a past math class
• Embarrassment in a past math class
• Social pressures and expectations to not like math or not do well in math
• The want to get everything right
• Negative self-message (“I don’t know how to do it,” or “I hate math”)

Math anxiety is a learned habit. If it is learned, it can be unlearned. Most math anxiety comes from bad memories while learning math. It may be from doing badly on a test or asking a question then being made fun of. These bad memories can make learning math hard. Everyone can learn math. There is no special talent for math. There are some people who are better at math than others, but even these people had to learn to be good at math.

Do You Suffer from Math Anxiety?

Read the list below and put a check mark beside the ones you feel when thinking about or doing math.

• Are your palms moist?
• Is your stomach fluttering?
• Do you feel like you can’t think clearly?
• Do you feel like you would rather do anything else than learn math?
• Are you breathing faster than normal?
• Is your heart pounding?
• Do you feel cold?
• Do you feel sweaty?

If you answered yes to two or more of these items, you may have math anxiety. If you have math anxiety, a first step to understanding it is to look at where it all started. Make a list of your experiences with learning math. Think back to the first math experiences you had and write about them. Think about learning math in school from the younger grades to the higher grades and write about your experiences and feelings. Include this class and how you are feeling right now about learning math. Beside each experience, write if it was a positive or negative experience. Look at the examples below to give you an idea:

Positive or negative?	Math experience
Negative	My teacher in elementary school lined the whole class up in a row and made us play a multiplication game. I could see which question was mine, and I didn’t know the answer so I had to figure it out on my fingers before my turn came up. I got the answer right, but I was so nervous that I would be teased because I didn’t know the answer off the top of my head. I still don’t know my times tables.
Positive	In high school, I could use a calculator to figure out the simple multiplication problems, and then I could figure out the tougher problems without worrying about knowing my times tables.
Negative	Now that I am upgrading my math, I feel nervous every time I even think about opening the book. I want to get all the answers right, and I know that I won’t be able to. I really need everything to be right so that I know that I am getting it.

Once you have made a list of experiences, go over the stories with your instructor, or by yourself and try to find some common themes.

• Can you see when you felt anxiety?
• Can you see why you are now anxious about math?
• Is there any experience you could use now to help you feel calmer about math?

Hopefully by examining the beginnings of the anxiety, you can feel more in control of it.

How to Deal with Math Anxiety

Anyone can feel anxiety that will slow down learning. The key to learning is to be the “boss” of your anxiety. Here are an overview of some strategies that may help deal with your anxiety:

• Use breathing exercises
• Think positive math messages
• Know your textbook
• Understand test-taking anxiety

Remember, learning to deal with your math anxiety may take some time. It took you a long time to learn math anxiety, so it will take some time to overcome it.

Use Breathing Exercises

One way to be the “boss” is to relax. Try this breathing exercise.

Breathing Exercise

Start by breathing slowly to the count of four. It may help to close your eyes and count. Now hold your breath for four counts and then let your breath out slowly to the count of four. The counting is silent and should follow this pattern: “Breath in, two, three, four. Hold, two, three, four. Breath out, two, three, four. Wait, two, three, four.” With practice, the number of counts can be increased. This is an easy and good way to relax. Now, try this exercise quietly and repeat it five times slowly.

Each time you feel anxious about learning, use the breathing exercise to help calm yourself. Ask yourself if what you tried worked. Do you feel calmer?

Think Positive Math Messages

Another way to be the "boss" is to give yourself positive math messages. Read and think about the positive math messages listed below. Do you say any of those things to yourself?

• If the answer is yes, then great, keep doing that.
• If your answer is no, try to add this little mental trick to your day. The result will probably be that you start to see math as something you can do and that you may even like!

I like math.

I am good at math.

I understand math.

I can relax when I am studying math.

I am capable of learning math.

Math is my friend.

My math improves every day.

I am relaxed, calm and confident when I study math.

I understand math when I give myself a chance.

Math is creative.

Pick three statements that you like and say them to yourself as much as you can in each day. You can also write the statements out on paper and post them around your house so that you read them throughout the day.

Know Your Textbook

Look at the Table of Contents in the front of your textbook. It tells you what you will be learning. You may see some things that you already know, some things that you may have forgotten, and some things that are new to you. Flip the pages. You can see that the textbook is split into units. Each unit is something to learn. Each unit has exercises to do. Notice the answers are at the end of the exercise. You can check your answers as soon as you are done. You can also check your answer before moving on if are not sure if you are doing the question right. At the end of each unit is a self-test. It is a chance for you to see how well you have learned the skills in the unit. If you do well, you can move on. If you don’t do well, you can go back and practice those skills. Knowing your textbook gives you a good skill. If you get frustrated, you can use the Table of Contents to go back and find some help.

Understand Test-Taking Anxiety

There are four reasons people are anxious when writing tests. Any of the four reasons listed below might be the reason a person might feel anxious in a test-taking situation.

1. Not feeling prepared for the test
2. Not sure how to write the test in the best way
3. Feeling too much mental pressure
4. Poor health habits before writing a test

Here is an explanation of each reason and how to work your way out of the anxiety you may feel during tests.

1. Not feeling prepared for the test

Many students feel anxiety about taking math tests because they do not feel prepared for the test. To feel prepared, a student needs to have studied the work and know that they can do the problems they will be given. Get help from your classmates, friends, or your instructor to find out how you can improve your study habits. Getting ready for a test starts on the first day of class. Everything you do in class and at home is part of that getting ready.

• Always do as many exercises as you need to help you understand. Once you understand, do ten more questions, then you will know for sure that you really understand.
• Always correct your exercises. It is good to know that you are understanding and getting the questions right. It is also good to know if you are not understanding and need some help.
• Always do the self-tests. The self-tests can show things that you are not sure of.
• Always do the review. Review is part of this book. It is a chance to go over all the things you have learned in a unit before moving on. It prepares you for what will be on the test.
• Always do a practice test. A practice test gives you a chance to see how many questions and what kind of questions are on the test.

2. Not sure how to write the test in the best way

Here are some strategies students should know about how to write a test to do the best as possible on it:

• Before the Test
  1. Arrive early. Get out all the supplies you need to do the test (pencils, ruler, calculator, watch, etc.).
  2. Be comfortable, but alert. Choose a good spot in the room, and make sure you have enough space to work. Maintain a comfortable posture in your seat, but don’t “slouch.”
  3. Stay relaxed and confident. Keep a good attitude. If you find yourself anxious, take several slow, deep breaths to relax. Don’t talk about the test to other students just before entering the room: their anxiety can be contagious.
• During the test.
  1. Look over the test. Take a look at the whole test before starting. This takes very little time. Use a highlighter to highlight the questions that you know you can do easily, note key terms, mark the test with comments that come to mind. As you work, put a star beside any questions that you would like to go over again when you finish the test.
  2. Relax. Before starting the test, imagine yourself somewhere where you are calm and confident. Go there in your mind. Focus on how good you feel and how in control you are. If you become anxious during the test, in your mind go to the calming place. Focus on how calm you feel. Then go back to your test.
  3. Read the directions carefully. This may be obvious, but it will help you avoid careless errors.
  4. Answer questions in a strategic order.
     • Answer the easy questions first. This will help to build confidence and score points. It may also help you make connections with more difficult questions.
     • Then answer the difficult questions. Work on these harder questions with all the energy of the easier ones.
  5. Review your answers. Resist the urge to leave as soon as you are done writing. Spend as much time as you can going over your test to see if you:
     • Answered all the questions.
     • Wrote the answers in right.
     • Did not make simple mistakes.

3. Feeling too much mental pressure

There are many reasons why a student may feel mental pressure when writing a test. Listed below are a few main reasons:

• Negative beliefs about one’s math abilities
• Low self-esteem when it comes to math
• Too high expectations of success
• Fear that failure or low grades will affect the future
• Feelings of pressure of not wanting to let down family members

When students feel this kind of pressure, it is very hard to feel calm and relaxed about a test. The key to success in a math test is to keep the anxiety at a manageable level. You can do this in two ways:

1. Change negative self-talk. Any time a negative thought creeps into your head, it will make it harder to stay positive and relaxed about your test. If you have a negative thought like “I can’t do it”, try to replace it with a positive thought like “I can do this”.
2. Use relaxing and calming techniques. Use the calming breathing mentioned earlier in this section. This will help you keep calm. Also, do not study in the last half hour before the test. You will be calmer by spending time relaxing and breathing deeply in that last half hour.

4. Poor health habits before writing a test

When your body and mind are healthy, you will have a better chance of doing well on a test. Eat well, drink plenty of water and get daily exercise. The better you feel, the better you can perform (and a test is a performance!).

]]> 1371 0 5 0 https://opentextbc.ca/alfm3/glossary/addends/ Wed, 01 Sep 2021 01:11:38 +0000 https://opentextbc.ca/alfm3/glossary/addends/ 1506 0 1 0 https://opentextbc.ca/alfm3/glossary/axis/ Wed, 01 Sep 2021 01:12:09 +0000 https://opentextbc.ca/alfm3/glossary/axis/ 1508 0 2 0 https://opentextbc.ca/alfm3/glossary/balance/ Wed, 01 Sep 2021 01:12:25 +0000 https://opentextbc.ca/alfm3/glossary/balance/ 1510 0 3 0 https://opentextbc.ca/alfm3/glossary/cancelled-cheque/ Wed, 01 Sep 2021 01:12:43 +0000 https://opentextbc.ca/alfm3/glossary/cancelled-cheque/ 1512 0 4 0 https://opentextbc.ca/alfm3/glossary/circumference/ Wed, 01 Sep 2021 01:12:55 +0000 https://opentextbc.ca/alfm3/glossary/circumference/ 1514 0 5 0 https://opentextbc.ca/alfm3/glossary/commission/ Wed, 01 Sep 2021 01:13:13 +0000 https://opentextbc.ca/alfm3/glossary/commission/ 1516 0 6 0 https://opentextbc.ca/alfm3/glossary/common-fractions/ Wed, 01 Sep 2021 01:15:02 +0000 https://opentextbc.ca/alfm3/glossary/common-fractions/ 1518 0 7 0 https://opentextbc.ca/alfm3/glossary/cross-multiply/ Wed, 01 Sep 2021 01:16:09 +0000 https://opentextbc.ca/alfm3/glossary/cross-multiply/ 1520 0 8 0 https://opentextbc.ca/alfm3/glossary/denominator/ Wed, 01 Sep 2021 01:16:25 +0000 https://opentextbc.ca/alfm3/glossary/denominator/ 1522 0 9 0 https://opentextbc.ca/alfm3/glossary/diameter/ Wed, 01 Sep 2021 01:16:39 +0000 https://opentextbc.ca/alfm3/glossary/diameter/ 1524 0 10 0 https://opentextbc.ca/alfm3/glossary/difference/ Wed, 01 Sep 2021 01:16:51 +0000 https://opentextbc.ca/alfm3/glossary/difference/ 1526 0 11 0 https://opentextbc.ca/alfm3/glossary/digit/ Wed, 01 Sep 2021 01:17:08 +0000 https://opentextbc.ca/alfm3/glossary/digit/ 1528 0 12 0 https://opentextbc.ca/alfm3/front-matter/accessibility-statement/ Tue, 31 Jan 2023 18:55:08 +0000 https://opentextbc.ca/alfm3/?post_type=front-matter&p=1638 Accessibility of This Resource The web version of this resource has been designed to meet Web Content Accessibility Guidelines 2.0, level AA. In addition, it follows all guidelines in Appendix A: Checklist for Accessibility of the Accessibility Toolkit – 2nd Edition. It includes:

• Easy navigation. This resource has a linked table of contents and uses headings in each chapter to make navigation easy.
• Accessible math equations. Many of the equations in this resource have been written in LaTeX and rendered with MathJax, which makes them accessible to people using screen readers that are set up to read MathML. The rest of the equations are rendered as images with appropriate alternative text.
• Accessible images. All images in this resource that convey information have alternative text. Images that are decorative have empty alternative text.
• Accessible links. All links use descriptive link text.

Accessibility Checklist

Element	Requirements	Pass?
Headings	Content is organized under headings and subheadings that are used sequentially.	Yes
Images	Images that convey information include alternative text descriptions. These descriptions are provided in the alt text field, in the surrounding text, or linked to as a long description.	Yes
Images	Images and text do not rely on colour to convey information.	Yes
Images	Images that are purely decorative or are already described in the surrounding text contain empty alternative text descriptions. (Descriptive text is unnecessary if the image doesn’t convey contextual content information.)	Yes
Tables	Tables include row and/or column headers that have the correct scope assigned.	Yes
Tables	Tables include a title or caption.	No
Tables	Tables do not have merged or split cells.	Yes
Tables	Tables have adequate cell padding.	Yes
Links	The link text describes the destination of the link.	Yes
Links	Links do not open new windows or tabs. If they do, a textual reference is included in the link text.	Yes
Links	Links to files include the file type in the link text.	Yes
Audio	All audio content includes a transcript that includes all speech content and relevant descriptions of non-speech audio and speaker names/headings where necessary.	N/A
Video	All videos include high-quality (i.e., not machine generated) captions of all speech content and relevant non-speech content.	N/A
Video	All videos with contextual visuals (graphs, charts, etc.) are described audibly in the video.	N/A
H5P	All H5P activities have been tested for accessibility by the H5P team and have passed their testing.	N/A
H5P	All H5P activities that include images, videos, and/or audio content meet the accessibility requirements for those media types.	N/A
Formulas	Formulas have been created using LaTeX and are rendered with MathJax.	Yes
Formulas	If LaTeX is not an option, formulas are images with alternative text descriptions.	Yes
Font	Font size is 12 point or higher for body text.	Yes
Font	Font size is 9 point for footnotes or endnotes.	Yes
Font	Font size can be zoomed to 200% in the webbook or eBook formats.	Yes

Known Accessibility Issues and Areas for Improvement

This book is written in a way that is biased towards people with vision. So while the book technically meets accessibility guidelines, there are activities and concepts that are communicated in ways that will not be equally accessible to students with disabilities that affect their vision.

Let Us Know if You are Having Problems Accessing This Book

We are always looking for ways to make our resources more accessible. If you have problems accessing this resource, please contact us to let us know so we can fix the issue. Please include the following information:

• The name of the resource
• The location of the problem by providing a web address or page description.
• A description of the problem
• The computer, software, browser, and any assistive technology you are using that can help us diagnose and solve your issue (e.g., Windows 10, Google Chrome (Version 65.0.3325.181), NVDA screen reader)

You can contact us one of the following ways:

• Web form: BCcampus Open Ed Help
• Web form: Report an Error

This statement was last updated on January 31, 2023. The Accessibility Checklist table was adapted from one originally created by the Rebus Community and shared under a CC BY 4.0 licence.]]> 1638 0 1 0 https://opentextbc.ca/alfm3/front-matter/about-bccampus-open-education/ Tue, 31 Jan 2023 19:04:23 +0000 https://opentextbc.ca/alfm3/?post_type=front-matter&p=1642 Adult Literacy Fundamental Mathematics: Book 3 – 2nd Edition was funded by BCcampus Open Education. BCcampus Open Education began in 2012 as the B.C. Open Textbook Project with the goal of making post-secondary education in British Columbia more accessible by reducing students’ costs through the use of open textbooks and other OER. BCcampus supports the post-secondary institutions of British Columbia as they adapt and evolve their teaching and learning practices to enable powerful learning opportunities for the students of B.C. BCcampus Open Education is funded by the Ministry of Post-Secondary Education and Future Skills and the Hewlett Foundation. Open educational resources (OER) are teaching, learning, and research resources that, through permissions granted by the copyright holder, allow others to use, distribute, keep, or make changes to them. Our open textbooks are openly licensed using a Creative Commons licence and are offered in various eBook formats free of charge, or as printed books that are available at cost. For more information about open education in British Columbia, please visit the BCcampus Open Education website. If you are an instructor who is using this book for a course, please fill out our Adoption of an Open Textbook form.]]> 1642 0 3 0 https://opentextbc.ca/alfm3/front-matter/for-students-how-to-access-and-use-this-textbook/ Tue, 31 Jan 2023 19:05:57 +0000 https://opentextbc.ca/alfm3/?post_type=front-matter&p=1644

Online webbook. You can read this textbook online on a computer or mobile device in one of the following browsers: Chrome, Firefox, Edge, and Safari.

PDF. You can download this book as a PDF to read on a computer (Digital PDF) or print it out (Print PDF).

Mobile. If you want to read this textbook on your phone or tablet, you can use the EPUB (eReader) file.

HTML. An HTML file can be opened in a browser. It has very little style so it doesn't look very nice, but some people might find it useful.

For more information about the accessibility of this textbook, see the Accessibility Statement. You can access the online webbook and download any of the formats for free here: Adult Literacy Fundamental Mathematics: Book 3 – 2nd Edition. To download the book in a different format, look for the "Download this book" drop-down menu and select the file type you want.

How can I use the different formats?

Format	Internet required?	Device	Required apps	Accessibility Features	Screen reader compatible
Online webbook	Yes	Computer, tablet, phone	An Internet browser (Chrome, Firefox, Edge, or Safari)	WCAG 2.0 AA compliant, option to enlarge text, and compatible with browser text-to-speech tools	Yes
PDF	No	Computer, print copy	Adobe Reader (for reading on a computer) or a printer	Ability to highlight and annotate the text. If reading on the computer, you can zoom in.	Unsure
EPUB	No	Computer, tablet, phone	An eReader app	Option to enlarge text, change font style, size, and colour.	Unsure
HTML	No	Computer, tablet, phone	An Internet browser (Chrome, Firefox, Edge, or Safari)	WCAG 2.0 AA compliant and compatible with browser text-to-speech tools.	Yes

Tips for Using This Textbook

• Search the textbook.
  • If using the online webbook, you can use the search bar in the top right corner to search the entire book for a key word or phrase. To search a specific chapter, open that chapter and use your browser's search feature by hitting [Cntr] + [f] on your keyboard if using a Windows computer or [Command] + [f] if using a Mac computer.
  • The [Cntr] + [f] and [Command] + [f] keys will also allow you to search a PDF, HTML, and EPUB files if you are reading them on a computer.
  • If using an eBook app to read this textbook, the app should have a built-in search tool.
• Navigate the textbook.
  • This textbook has a table of contents to help you navigate through the book easier. If using the online webbook, you can find the full table of contents on the book's homepage or by selecting "Contents" from the top menu when you are in a chapter.
• Annotate the textbook.
  • If you like to highlight or write on your textbooks, you can do that by getting a print copy, using the Digital PDF in Adobe Reader, or using the highlighting tools in eReader apps.

]]> 1644 0 2 0 https://opentextbc.ca/alfm3/glossary/discount/ Wed, 01 Sep 2021 01:17:24 +0000 https://opentextbc.ca/alfm3/glossary/discount/ 1530 0 13 0 https://opentextbc.ca/alfm3/glossary/divide/ Wed, 01 Sep 2021 01:17:37 +0000 https://opentextbc.ca/alfm3/glossary/divide/ 1532 0 14 0 https://opentextbc.ca/alfm3/glossary/dividend/ Wed, 01 Sep 2021 01:17:49 +0000 https://opentextbc.ca/alfm3/glossary/dividend/ 1534 0 15 0 https://opentextbc.ca/alfm3/glossary/divisor/ Wed, 01 Sep 2021 01:18:02 +0000 https://opentextbc.ca/alfm3/glossary/divisor/ 1536 0 16 0 https://opentextbc.ca/alfm3/glossary/equal/ Wed, 01 Sep 2021 01:18:52 +0000 https://opentextbc.ca/alfm3/glossary/equal/ 1538 0 17 0 https://opentextbc.ca/alfm3/glossary/equation/ Wed, 01 Sep 2021 01:19:12 +0000 https://opentextbc.ca/alfm3/glossary/equation/ 1540 0 18 0 https://opentextbc.ca/alfm3/glossary/equivalent/ Wed, 01 Sep 2021 01:19:27 +0000 https://opentextbc.ca/alfm3/glossary/equivalent/ 1542 0 19 0 https://opentextbc.ca/alfm3/glossary/estimate/ Wed, 01 Sep 2021 01:20:09 +0000 https://opentextbc.ca/alfm3/glossary/estimate/ 1544 0 20 0 https://opentextbc.ca/alfm3/glossary/factors/ Wed, 01 Sep 2021 01:21:01 +0000 https://opentextbc.ca/alfm3/glossary/factors/ 1546 0 21 0 https://opentextbc.ca/alfm3/glossary/fraction/ Wed, 01 Sep 2021 01:23:45 +0000 https://opentextbc.ca/alfm3/glossary/fraction/ 1548 0 22 0 https://opentextbc.ca/alfm3/glossary/horizontal/ Wed, 01 Sep 2021 01:24:02 +0000 https://opentextbc.ca/alfm3/glossary/horizontal/ 1550 0 23 0 https://opentextbc.ca/alfm3/glossary/improper-fraction/ Wed, 01 Sep 2021 01:24:14 +0000 https://opentextbc.ca/alfm3/glossary/improper-fraction/ 1552 0 24 0 https://opentextbc.ca/alfm3/glossary/infinite/ Wed, 01 Sep 2021 01:24:25 +0000 https://opentextbc.ca/alfm3/glossary/infinite/ 1554 0 25 0 https://opentextbc.ca/alfm3/glossary/invert/ Wed, 01 Sep 2021 01:24:36 +0000 https://opentextbc.ca/alfm3/glossary/invert/ 1556 0 26 0 https://opentextbc.ca/alfm3/glossary/like-fractions/ Wed, 01 Sep 2021 01:24:46 +0000 https://opentextbc.ca/alfm3/glossary/like-fractions/ 1558 0 27 0 https://opentextbc.ca/alfm3/glossary/lowest-terms/ Wed, 01 Sep 2021 01:25:01 +0000 https://opentextbc.ca/alfm3/glossary/lowest-terms/ 1560 0 28 0 https://opentextbc.ca/alfm3/glossary/minuend/ Wed, 01 Sep 2021 01:25:14 +0000 https://opentextbc.ca/alfm3/glossary/minuend/ 1562 0 29 0 https://opentextbc.ca/alfm3/glossary/mixed-number/ Wed, 01 Sep 2021 01:25:52 +0000 https://opentextbc.ca/alfm3/glossary/mixed-number/ 1564 0 30 0 https://opentextbc.ca/alfm3/glossary/mixed-decimal/ Wed, 01 Sep 2021 01:28:54 +0000 https://opentextbc.ca/alfm3/glossary/mixed-decimal/ 1566 0 31 0 https://opentextbc.ca/alfm3/glossary/multiple/ Wed, 01 Sep 2021 01:29:16 +0000 https://opentextbc.ca/alfm3/glossary/multiple/ 1568 0 32 0 https://opentextbc.ca/alfm3/glossary/multiplicand/ Wed, 01 Sep 2021 01:29:30 +0000 https://opentextbc.ca/alfm3/glossary/multiplicand/ 1570 0 33 0 https://opentextbc.ca/alfm3/glossary/multiplier/ Wed, 01 Sep 2021 01:29:44 +0000 https://opentextbc.ca/alfm3/glossary/multiplier/ 1572 0 34 0 https://opentextbc.ca/alfm3/glossary/negotiable/ Wed, 01 Sep 2021 01:29:57 +0000 https://opentextbc.ca/alfm3/glossary/negotiable/ 1574 0 35 0 https://opentextbc.ca/alfm3/glossary/numbers/ Wed, 01 Sep 2021 01:30:15 +0000 https://opentextbc.ca/alfm3/glossary/numbers/ number is the idea of quantity or order.]]> 1576 0 36 0 https://opentextbc.ca/alfm3/glossary/numerals/ Wed, 01 Sep 2021 01:30:36 +0000 https://opentextbc.ca/alfm3/glossary/numerals/ 1578 0 37 0 https://opentextbc.ca/alfm3/glossary/numerator/ Wed, 01 Sep 2021 01:30:46 +0000 https://opentextbc.ca/alfm3/glossary/numerator/ 1580 0 38 0 https://opentextbc.ca/alfm3/glossary/overdrawn/ Wed, 01 Sep 2021 01:30:58 +0000 https://opentextbc.ca/alfm3/glossary/overdrawn/ 1582 0 39 0 https://opentextbc.ca/alfm3/glossary/parallel/ Wed, 01 Sep 2021 01:31:14 +0000 https://opentextbc.ca/alfm3/glossary/parallel/ 1584 0 40 0 https://opentextbc.ca/alfm3/glossary/percent/ Wed, 01 Sep 2021 01:31:58 +0000 https://opentextbc.ca/alfm3/glossary/percent/ 1586 0 41 0 https://opentextbc.ca/alfm3/glossary/perimeter/ Wed, 01 Sep 2021 01:32:11 +0000 https://opentextbc.ca/alfm3/glossary/perimeter/ 1588 0 42 0 https://opentextbc.ca/alfm3/glossary/place-value/ Wed, 01 Sep 2021 01:32:46 +0000 https://opentextbc.ca/alfm3/glossary/place-value/ decimal system. The place value is based on ten.]]> 1590 0 43 0 https://opentextbc.ca/alfm3/glossary/prime-number/ Wed, 01 Sep 2021 01:33:07 +0000 https://opentextbc.ca/alfm3/glossary/prime-number/ 1592 0 44 0 https://opentextbc.ca/alfm3/glossary/product/ Wed, 01 Sep 2021 01:33:17 +0000 https://opentextbc.ca/alfm3/glossary/product/ 1594 0 45 0 https://opentextbc.ca/alfm3/glossary/proper-fraction/ Wed, 01 Sep 2021 01:33:28 +0000 https://opentextbc.ca/alfm3/glossary/proper-fraction/ 1596 0 46 0 https://opentextbc.ca/alfm3/glossary/proportion/ Wed, 01 Sep 2021 01:33:51 +0000 https://opentextbc.ca/alfm3/glossary/proportion/ 1598 0 47 0 https://opentextbc.ca/alfm3/glossary/quotient/ Wed, 01 Sep 2021 01:34:08 +0000 https://opentextbc.ca/alfm3/glossary/quotient/ 1600 0 48 0 https://opentextbc.ca/alfm3/glossary/radius/ Wed, 01 Sep 2021 01:34:18 +0000 https://opentextbc.ca/alfm3/glossary/radius/ 1602 0 49 0 https://opentextbc.ca/alfm3/glossary/ratio/ Wed, 01 Sep 2021 01:35:12 +0000 https://opentextbc.ca/alfm3/glossary/ratio/ 1604 0 50 0 https://opentextbc.ca/alfm3/glossary/reciprocal/ Wed, 01 Sep 2021 01:36:05 +0000 https://opentextbc.ca/alfm3/glossary/reciprocal/ 1606 0 51 0 https://opentextbc.ca/alfm3/glossary/reduce/ Wed, 01 Sep 2021 01:36:28 +0000 https://opentextbc.ca/alfm3/glossary/reduce/ 1608 0 52 0 https://opentextbc.ca/alfm3/authors/ Thu, 05 Jan 2023 23:03:03 +0000 https://opentextbc.ca/alfm3/authors/ ]]> 7 0 0 0 https://opentextbc.ca/alfm3/ Thu, 05 Jan 2023 23:03:03 +0000 https://opentextbc.ca/alfm3/cover/ ]]> 8 0 0 0 https://opentextbc.ca/alfm3/table-of-contents/ Thu, 05 Jan 2023 23:03:03 +0000 https://opentextbc.ca/alfm3/table-of-contents/ ]]> 9 0 0 0 https://opentextbc.ca/alfm3/about/ Thu, 05 Jan 2023 23:03:03 +0000 https://opentextbc.ca/alfm3/about/ ]]> 10 0 0 0 https://opentextbc.ca/alfm3/buy/ Thu, 05 Jan 2023 23:03:03 +0000 https://opentextbc.ca/alfm3/buy/ ]]> 11 0 0 0 https://opentextbc.ca/alfm3/access-denied/ Thu, 05 Jan 2023 23:03:03 +0000 https://opentextbc.ca/alfm3/access-denied/ ]]> 12 0 0 0 https://opentextbc.ca/alfm3/?metadata=book-information Thu, 05 Jan 2023 23:03:03 +0000 https://opentextbc.ca/alfm3/?p=16 16 0 1 0 Adult Literacy Fundamentals Mathematics: Book 3 - 2nd Edition by Wendy Tagami and Liz Girard is used under a CC BY 4.0 licence.

Content edits to the 2nd Edition were made by Leanne Caillier-Smith. This book is based on the work of Leslie Tenta (1993), Marjorie E. Enns (1983), and Steve Ballantyne, Lynne Cannon, James Hooten, Kate Nonesuch (1994).

If you redistribute all or part of this book, it is recommended the following statement be added to the copyright page so readers can access the original book at no cost:

Download for free from the B.C. Open Collection.

Sample APA-style citation (7th Edition):

Tagami, W., & Girard, L. (2023). Adult literacy fundamentals mathematics: Book 3 (2nd ed). BCcampus. https://opentextbc.ca/alfm3/

Cover image attribution:

"Coloured Balls" by Ethelred The Unusual is licensed under a CC BY-NC-SA 2.0 licence.

Ebook ISBN: 978-1-77420-207-4 Print ISBN: 978-1-77420-206-7 Visit BCcampus Open Education to learn about open education in British Columbia.]]> https://opentextbc.ca/alfm3/glossary/remainder/ Wed, 01 Sep 2021 01:36:46 +0000 https://opentextbc.ca/alfm3/glossary/remainder/ 1610 0 53 0 https://opentextbc.ca/alfm3/glossary/sign/ Wed, 01 Sep 2021 01:39:41 +0000 https://opentextbc.ca/alfm3/glossary/sign/ + plus, means to add − minus, means to subtract × multiplied by, "times" ÷ divided by, division = equal, the same quantity as ≠ not equal ≈ approximately equal < less than > greater than ≤ less than or equal to ≥ greater than or equal to]]> 1612 0 54 0 https://opentextbc.ca/alfm3/glossary/simplify/ Wed, 01 Sep 2021 01:41:07 +0000 https://opentextbc.ca/alfm3/glossary/simplify/ reduce.]]> 1614 0 55 0 https://opentextbc.ca/alfm3/glossary/subtrahend/ Wed, 01 Sep 2021 01:41:24 +0000 https://opentextbc.ca/alfm3/glossary/subtrahend/ 1616 0 56 0 https://opentextbc.ca/alfm3/glossary/sum/ Wed, 01 Sep 2021 01:41:39 +0000 https://opentextbc.ca/alfm3/glossary/sum/ 1618 0 57 0 https://opentextbc.ca/alfm3/glossary/symbol/ Wed, 01 Sep 2021 01:41:50 +0000 https://opentextbc.ca/alfm3/glossary/symbol/ 1620 0 58 0 https://opentextbc.ca/alfm3/glossary/term/ Wed, 01 Sep 2021 01:42:26 +0000 https://opentextbc.ca/alfm3/glossary/term/ a) A definite period of time, such as a school term or the term of a loan. b) Conditions of a contract; the terms of the agreement. c) In mathematics, the quantities in a fraction and in a ratio are called the terms of the fraction or the terms of the ratio. In an algebra equation, the quantities connected by a + or − sign are also called terms.]]> 1622 0 59 0 https://opentextbc.ca/alfm3/glossary/total/ Wed, 01 Sep 2021 01:43:30 +0000 https://opentextbc.ca/alfm3/glossary/total/ 1624 0 60 0 https://opentextbc.ca/alfm3/glossary/transaction/ Wed, 01 Sep 2021 01:43:44 +0000 https://opentextbc.ca/alfm3/glossary/transaction/ 1626 0 61 0 https://opentextbc.ca/alfm3/glossary/unit/ Wed, 01 Sep 2021 01:44:01 +0000 https://opentextbc.ca/alfm3/glossary/unit/ 1628 0 62 0 https://opentextbc.ca/alfm3/glossary/unit-price/ Wed, 01 Sep 2021 01:44:15 +0000 https://opentextbc.ca/alfm3/glossary/unit-price/ 1630 0 63 0 https://opentextbc.ca/alfm3/glossary/unlike-fractions/ Wed, 01 Sep 2021 01:44:28 +0000 https://opentextbc.ca/alfm3/glossary/unlike-fractions/ 1632 0 64 0 https://opentextbc.ca/alfm3/glossary/vertical/ Wed, 01 Sep 2021 01:44:42 +0000 https://opentextbc.ca/alfm3/glossary/vertical/ 1634 0 65 0 https://opentextbc.ca/alfm3/h5p-listing/ Thu, 05 Jan 2023 23:03:05 +0000 https://opentextbc.ca/alfm3/h5p-listing/ ]]> 20 0 1 0 https://opentextbc.ca/alfm3/part/multiplication/ Thu, 05 Jan 2023 23:19:12 +0000 https://opentextbc.ca/alfm3/?post_type=part&p=1022 1022 0 1 0 https://opentextbc.ca/alfm3/part/unit-3-division/ Fri, 06 Jan 2023 23:35:03 +0000 https://opentextbc.ca/alfm3/?post_type=part&p=1076 1076 0 2 0 https://opentextbc.ca/alfm3/part/change-the-metric-system/ Wed, 18 Jan 2023 20:58:27 +0000 https://opentextbc.ca/alfm3/?post_type=part&p=1203 1203 0 3 0