Unit 3: Subtraction

# Topic B: Subtraction of Larger Numbers

You can find the difference between two large numbers using the subtraction facts you have been practicing. Always take away or subtract the number after the minus sign.

Use these steps to complete each subtraction question.

• Step 1: Subtract the ones from the ones.
• Step 2: Subtract the tens from the tens.
• Step 3: Subtract the hundreds from the hundreds.
• Step 4: Subtract the thousands from the thousands.
• Step 5: Subtract the ten thousands from the ten thousands and so on.

Example A: 57 − 26

Step 1: Subtract the ones from the ones. 7 ones − 6 ones = 1 one, write the answer in line with the ones in the question.

$\begin{array}[t]{rr}&57\\-&26\\ \hline &1\end{array}$

Step 2: Subtract the tens from the tens. 5 tens − 2 tens = 3 tens

The difference between 57 and 26 is 31.

$\begin{array}[t]{rr}&57\\-&26\\ \hline &31\end{array}$

Exercise One

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

1. $\begin{array}[t]{rr}&36\\-&13\\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&72\\-&42\\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}&48\\-&22\\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}&55\\-&31\\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&93\\-&40\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&76\\-&71\\ \hline \\ \end{array}$
7. $\begin{array}[t]{rr}&95\\-&62\\ \hline \\ \end{array}$
8. $\begin{array}[t]{rr}&39\\-&26\\ \hline \\ \end{array}$
9. $\begin{array}[t]{rr}&64\\-&21\\ \hline \\ \end{array}$
10. $\begin{array}[t]{rr}&85\\-&64\\ \hline \\ \end{array}$
11. $\begin{array}[t]{rr}&98\\-&73\\ \hline \\ \end{array}$
12. $\begin{array}[t]{rr}&76\\-&64\\ \hline \\ \end{array}$
13. $\begin{array}[t]{rr}&86\\-&50\\ \hline \\ \end{array}$
14. $\begin{array}[t]{rr}&95\\-&35\\ \hline \\ \end{array}$
15. $\begin{array}[t]{rr}&28\\-&17\\ \hline \\ \end{array}$
16. $\begin{array}[t]{rr}&69\\-&52\\ \hline \\ \end{array}$
17. $\begin{array}[t]{rr}&84\\-&40\\ \hline \\ \end{array}$
18. $\begin{array}[t]{rr}&74\\-&53\\ \hline \\ \end{array}$
19. $\begin{array}[t]{rr}&97\\-&83\\ \hline \\ \end{array}$
20. $\begin{array}[t]{rr}&89\\-&80\\ \hline \\ \end{array}$
21. $\begin{array}[t]{rr}&79\\-&29\\ \hline \\ \end{array}$
22. $\begin{array}[t]{rr}&89\\-&80\\ \hline \\ \end{array}$
23. $\begin{array}[t]{rr}&67\\-&61\\ \hline \\ \end{array}$
24. $\begin{array}[t]{rr}&48\\-&40\\ \hline \\ \end{array}$

1. 23
2. 30
3. 26
4. 24
5. 53
6. 5
7. 33
8. 13
9. 43
10. 21
11. 25
12. 12
13. 36
14. 60
15. 11
16. 17
17. 44
18. 21
19. 14
20. 9
21. 50
22. 9
23. 6
24. 8

# Checking Subtraction

You can check your subtraction. Add the answer (the difference) to the number you took away (the second number). If your subtracting was correct, the result of the adding will be the number you started with (the top number) in the subtraction question.

Example B

The difference is $\begin{array}[t]{rr}&928\\-&416\\ \hline&512\end{array}$

To check, add 512 to 416.

$\begin{array}[t]{rr}&512\\+&416\\ \hline&928\end{array}$

Exercise Two

Find the differences. Check your work by adding and then by using the answer key at the end of the exercise.

1. $\begin{array}[t]{rr}&87\\-&36\\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&29\\-&21\\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}&48\\-&40\\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}&99\\-&63\\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&75\\-&45\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&73\\-&20\\ \hline \\ \end{array}$
7. $\begin{array}[t]{rr}&92\\-&21\\ \hline \\ \end{array}$
8. $\begin{array}[t]{rr}&58\\-&27\\ \hline \\ \end{array}$
9. $\begin{array}[t]{rr}&84\\-&23\\ \hline \\ \end{array}$
10. $\begin{array}[t]{rr}&69\\-&38\\ \hline \\ \end{array}$
11. $\begin{array}[t]{rr}&45\\-&23\\ \hline \\ \end{array}$
12. $\begin{array}[t]{rr}&49\\-&19\\ \hline \\ \end{array}$
13. $\begin{array}[t]{rr}&59\\-&14\\ \hline \\ \end{array}$
14. $\begin{array}[t]{rr}&89\\-&63\\ \hline \\ \end{array}$
15. $\begin{array}[t]{rr}&88\\-&15\\ \hline \\ \end{array}$
16. $\begin{array}[t]{rr}&56\\-&44\\ \hline \\ \end{array}$
17. $\begin{array}[t]{rr}&96\\-&75\\ \hline \\ \end{array}$
18. $\begin{array}[t]{rr}&37\\-&17\\ \hline \\ \end{array}$
19. $\begin{array}[t]{rr}&70\\-&50\\ \hline \\ \end{array}$
20. $\begin{array}[t]{rr}&38\\-&24\\ \hline \\ \end{array}$
21. $\begin{array}[t]{rr}&31\\-&10\\ \hline \\ \end{array}$
22. $\begin{array}[t]{rr}&27\\-&12\\ \hline \\ \end{array}$
23. $\begin{array}[t]{rr}&74\\-&53\\ \hline \\ \end{array}$
24. $\begin{array}[t]{rr}&45\\-&20\\ \hline \\ \end{array}$

1. 51
2. 8
3. 8
4. 36
5. 30
6. 53
7. 71
8. 31
9. 61
10. 31
11. 22
12. 30
13. 45
14. 24
15. 73
16. 12
17. 21
18. 20
19. 20
20. 14
21. 21
22. 15
23. 21
24. 25

Example C: 696 − 251 =

Use these steps to complete each subtraction question.

Step 1: Subtract the ones from the ones. 6 ones − 1 one = 5 ones

$\begin{array}[t]{rr}&696\\-&251\\ \hline &5 \end{array}$

Step 2: Subtract the tens from the tens. 9 tens − 5 tens = 4 tens

$\begin{array}[t]{rr}& 696\\-&251\\ \hline &45 \end{array}$

Step 3: Subtract the hundreds from the hundreds.

6 hundreds − 2 hundreds = 4 hundreds

$\begin{array}[t]{rr}& 696\\-&251\\ \hline &445 \end{array}$

The difference between 696 and 251 is 445.

Exercise Three

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

1. $\begin{array}[t]{rr}&995\\-&452\\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&877\\-&342\\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}&788\\-&615\\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}&987\\-&243\\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&549\\-&131\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&806\\-&204\\ \hline \\ \end{array}$
7. $\begin{array}[t]{rr}&953\\-&603\\ \hline \\ \end{array}$
8. $\begin{array}[t]{rr}&569\\-&403\\ \hline \\ \end{array}$
9. $\begin{array}[t]{rr}&874\\-&650\\ \hline \\ \end{array}$
10. $\begin{array}[t]{rr}&269\\-&159\\ \hline \\ \end{array}$
11. $\begin{array}[t]{rr}&485\\-&203\\ \hline \\ \end{array}$
12. $\begin{array}[t]{rr}&381\\-&270\\ \hline \\ \end{array}$
13. $\begin{array}[t]{rr}&796\\-&172\\ \hline \\ \end{array}$
14. $\begin{array}[t]{rr}&864\\-&531\\ \hline \\ \end{array}$
15. $\begin{array}[t]{rr}&963\\-&810\\ \hline \\ \end{array}$
16. $\begin{array}[t]{rr}&957\\-&342\\ \hline \\ \end{array}$
17. $\begin{array}[t]{rr}&837\\-&410\\ \hline \\ \end{array}$
18. $\begin{array}[t]{rr}&528\\-&208\\ \hline \\ \end{array}$
19. $\begin{array}[t]{rr}&549\\-&120\\ \hline \\ \end{array}$
20. $\begin{array}[t]{rr}&627\\-&523\\ \hline \\ \end{array}$
21. $\begin{array}[t]{rr}&849\\-&246\\ \hline \\ \end{array}$
22. $\begin{array}[t]{rr}&175\\-&163\\ \hline \\ \end{array}$
23. $\begin{array}[t]{rr}&937\\-&224\\ \hline \\ \end{array}$
24. $\begin{array}[t]{rr}&875\\-&252\\ \hline \\ \end{array}$

1. 543
2. 535
3. 173
4. 744
5. 418
6. 602
7. 350
8. 166
9. 224
10. 110
11. 282
12. 111
13. 624
14. 333
15. 153
16. 615
17. 427
18. 320
19. 429
20. 104
21. 603
22. 12
23. 713
24. 623

Exercise Four

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

1. $\begin{array}[t]{rr}&543\\-&132\\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&752\\-&150\\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}& 328\\-&115\\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}& 758\\-&341\\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&587\\-&425\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&857\\-&143\\ \hline \\ \end{array}$
7. $\begin{array}[t]{rr}&545\\-&302\\ \hline \\ \end{array}$
8. $\begin{array}[t]{rr}&466\\-&115\\ \hline \\ \end{array}$
9. $\begin{array}[t]{rr}&964\\-&231\\ \hline \\ \end{array}$
10. $\begin{array}[t]{rr}&679\\-&424\\ \hline \\ \end{array}$
11. $\begin{array}[t]{rr}&757\\-&136\\ \hline \\ \end{array}$
12. $\begin{array}[t]{rr}&467\\-&132\\ \hline \\ \end{array}$

1. 411
2. 602
3. 213
4. 417
5. 162
6. 714
7. 243
8. 351
9. 733
10. 255
11. 621
12. 335

Use these steps to complete each subtraction question:

Example D: 4628 − 2604 =

Step 1: Subtract the ones from the ones. 8 ones − 4 ones = 4 ones

$\begin{array}[t]{rr}&4\, 628 \\− &2\, 604\\ \hline& 4 \end{array}$

Step 2: Subtract the tens from the tens. 2 tens − 0 tens = 2 tens

$\begin{array}[t]{rr}&4\, 628 \\−& 2\, 604\\ \hline &24 \end{array}$

Step 3: Subtract the hundreds from the hundreds.

6 hundreds − 6 hundreds = 0 hundreds

$\begin{array}[t]{rr}&4\, 628 \\−& 2\, 604\\ \hline &024 \end{array}$

The 0 must be placed in the answer to hold the hundreds place.

Step 4: Subtract the thousands from the thousands.

4 thousands − 2 thousands = 2 thousands

$\begin{array}[t]{rr}&4\, 628 \\−& 2\, 604\\ \hline &2\,024 \end{array}$

The difference between 4628 and 2604 is 2024.

Example E: 79486 − 42104 =

Step 1: Subtract the ones from the ones. 6 ones − 4 ones = 2 ones

$\begin{array}[t]{rr}&79\, 486 \\−& 42\, 104\\ \hline& 2 \end{array}$

Step 2: Subtract the tens from the tens. 8 tens − 0 tens = 8 tens

$\begin{array}[t]{rr}&79\, 486 \\− &42\, 104\\ \hline &82 \end{array}$

Step 3: Subtract the hundreds from the hundreds.

4 hundreds − 1 hundreds = 3 hundreds

$\begin{array}[t]{rr}&79\, 486 \\− &42\, 104\\ \hline &382 \end{array}$

Step 4: Subtract the thousands from the thousands.

9 thousands − 2 thousands = 7 thousands

$\begin{array}[t]{rr}&79\, 486 \\− &42\, 104\\ \hline& 7\,382 \end{array}$

Step 5: Subtract the ten thousands from the ten thousands.

7 ten thousands − 4 ten thousands = 3 ten thousands

$\begin{array}[t]{rr}&79\, 486 \\− &42\, 104\\ \hline &37\,382 \end{array}$

The difference between 79486 and 42104 is 37382.

Exercise Five

1. $\begin{array}[t]{rr}&8\, 646 \\-& 542\\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&7\, 295 \\-& 231\\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}&9\, 738 \\-& 215\\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}&6\, 498 \\-& 253\\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&3\, 674 \\-& 2\, 503\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&3 \,219 \\-& 2\, 116\\ \hline \\ \end{array}$
7. $\begin{array}[t]{rr}&6\, 456 \\-& 5\,\ 234\\ \hline \\ \end{array}$
8. $\begin{array}[t]{rr}&1\, 758 \\-& 1\, 431\\ \hline \\ \end{array}$
9. $\begin{array}[t]{rr}&8\, 954 \\-& 2\, 151\\ \hline \\ \end{array}$
10. $\begin{array}[t]{rr}&8\, 975 \\-& 4\, 732\\ \hline \\ \end{array}$
11. $\begin{array}[t]{rr}&7\, 296 \\-& 5\, 081\\ \hline \\ \end{array}$
12. $\begin{array}[t]{rr}&9\, 678 \\-& 4\, 316\\ \hline \\ \end{array}$
13. $\begin{array}[t]{rr}&9\, 489 \\-& 2\, 079\\ \hline \\ \end{array}$
14. $\begin{array}[t]{rr}&7\, 638 \\-& 6\, 218\\ \hline \\ \end{array}$
15. $\begin{array}[t]{rr}&4\, 759 \\-& 1\, 136\\ \hline \\ \end{array}$
16. $\begin{array}[t]{rr}&8\, 275 \\-& 4\, 073\\ \hline \\ \end{array}$

1. 8104
2. 7064
3. 9523
4. 6245
5. 1171
6. 1103
7. 1222
8. 327
9. 6803
10. 4243
11. 2215
12. 5362
13. 7410
14. 1420
15. 3623
16. 4202

If a subtraction question is written with the numbers side by side, rewrite the question in columns. Put the ones under the ones, the tens under the tens, the hundreds under the hundreds, and so on. The first number is always the top number and the second number is always written below the first number.

Example F: 687 − 52 =

$\begin{array}[t]{rr} &687\\-&52\\ \hline &635\end{array}$

Example G: 9756 − 420 =

$\begin{array}[t]{rr}&9\,756\\-&420\\ \hline &9\, 336\end{array}$

Exercise Six

Rewrite each question in columns and find the differences. Check your work using the answer key at the end of the exercise.

1. $\begin{array}[t]{rr}&43\\-&21\\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&84\\-&30\\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}&975\\-&21\\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}&779\\-&54\\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&695\\-&173\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&863\\-&701\\ \hline \\ \end{array}$
7. $\begin{array}[t]{rr}&965\\-&152\\ \hline \\ \end{array}$
8. $\begin{array}[t]{rr}&849\\-&212\\ \hline \\ \end{array}$

1. 22
2. 54
3. 954
4. 725
5. 522
6. 162
7. 813
8. 637

# Topic B: Self-Test

Mark      /24    Aim 19/24

1. Find the differences.  Be sure to check your answers. (6 marks.)
1. $\begin{array}[t]{rr}&39\\-&15\\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&58\\-&24\\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}&72\\-&60\\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}&49\\-&23\\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&64\\-&10\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&85\\-&71\\ \hline \\ \end{array}$
2. Find the differences. Be sure to check your answers. (6 marks)
1. $\begin{array}[t]{rr}&896\\-& 385\\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&698\\-& 461\\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}&399\\-& 202\\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}&467\\-& 124\\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&752\\-& 231\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&497\\-& 341\\ \hline \\ \end{array}$
3. Find the differences. Be sure to check your answers. (6 marks)
1. $\begin{array}[t]{rr}&8 \,627\\-& 323\\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&9 \,875\\-& 9 \,251\\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}&9 \,751\\-& 7 \,340\\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}&34\, 859\\-& 1\, 336\\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&37\, 698 \\-& 12\, 540\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&96 \,723\\-& 51\, 403\\ \hline \\ \end{array}$
4. Subtract these numbers. (6 marks)
1. 85 − 61 =
2. 724 − 13 =
3. 879  − 152 =
4. 4957 − 821 =
5. 94658 − 12307 =
6. 89653 − 27450 =

1. 24
2. 34
3. 12
4. 26
5. 54
6. 14
1. 511
2. 237
3. 197
4. 343
5. 521
6. 156
1. 8304
2. 624
3. 2411
4. 33523
5. 25158
6. 45320
1. 24
2. 711
3. 727
4. 4136
5. 82351
6. 62203