# Topic B: Addition with Carrying

When the digits of one column add up to a two digit number (10 or more), you must carry the digit to the next column.$\begin{array}{r}\end{array}$

Example A: 27 + 55

Step 1: Add the ones. 7 ones + 5 ones = 12 ones

Rename 12 ones as 1 ten and 2 ones. Write the 2 ones under the ones column and carry the ten to be added with the tens column.

Step 2:Add the tens. 1 ten + 2 tens + 5 tens = 8 tens

Example B: 58 + 76

Step 1: Add the one. 8 ones + 6 ones = 14 ones

Rename the 14 ones as 1 ten and 4 ones.

Write the 4 ones under the ones column and carry the ten to be added with the tens column.

Step 2: Add the tens. 1 ten + 5 tens + 7 tens = 13 tens

The 1 hundred can just be written in the sum because there are no other hundreds to add it to.

Exercise One

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

1. $\begin{array}[t]{rr}&62\\+&18 \\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&46\\+&37 \\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}&49\\+&42 \\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}&44\\+&26 \\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&17\\+&79 \\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&23\\+&82 \\ \hline \\ \end{array}$
7. $\begin{array}[t]{rr}&28\\+&91 \\ \hline \\ \end{array}$
8. $\begin{array}[t]{rr}&54\\+&58 \\ \hline \\ \end{array}$
9. $\begin{array}[t]{rr}&68\\+&49 \\ \hline \\ \end{array}$
10. $\begin{array}[t]{rr}&66\\+&35 \\ \hline \\ \end{array}$
11. $\begin{array}[t]{rr}&99\\+&88 \\ \hline \\ \end{array}$
12. $\begin{array}[t]{rr}&89\\+&74 \\ \hline \\ \end{array}$
13. $\begin{array}[t]{rr}&37\\+&15 \\ \hline \\ \end{array}$
14. $\begin{array}[t]{rr}&55\\+&27 \\ \hline \\ \end{array}$
15. $\begin{array}[t]{rr}&29\\+&76 \\ \hline \\ \end{array}$
16. $\begin{array}[t]{rr}&35\\+&69 \\ \hline \\ \end{array}$
17. $\begin{array}[t]{rr}&54\\+&17 \\ \hline \\ \end{array}$
18. $\begin{array}[t]{rr}&72\\+&33 \\ \hline \\ \end{array}$
19. $\begin{array}[t]{rr}&26\\+&56 \\ \hline \\ \end{array}$
20. $\begin{array}[t]{rr}&38\\+&80 \\ \hline \\ \end{array}$

1. 80
2. 83
3. 91
4. 70
5. 96
6. 105
7. 119
8. 112
9. 117
10. 101
11. 187
12. 163
13. 52
14. 82
15. 105
16. 104
17. 71
18. 105
19. 82
20. 118

Need some extra practice? Who’s the Pig? A Game of Chance.

• This game is played by two people with one set of dice. Ask your instructor for one set of dice.
• The first player to reach 100 or more points is the winner. Players take turns rolling the dice.
• You add the amounts on the dice to find your score.
• When it is your turn, you may roll as many times in a row as you like. Therefore, it is possible to score 100 or more points in one turn.
• However, during your turn if you roll a 1 on either die, you lose all your points for that turn, and your turn is over.
• If you roll a 1 on both dice, you lose all the points you have, and you have to
• start all over again at zero, and your turn is over.

Example C: 45 + 37 + 69

Step 1: Add the ones. 5 ones + 7 ones + 9 ones = 21 ones

Rename 21 ones as 2 tens and 1 one.

Write the one in the sum under the ones column and carry the 2 tens to the tens column.

Step 2: Add the tens. 2 tens + 4 tens + 3 tens + 6 tens = 15 tens

15 tens is 1 hundred and 5 tens.

The one hundred can just be written in the sum because there are no other hundreds to add it to.

Exercise Two

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

1. $\begin{array}[t]{rr}& 67\\&78\\+&55\\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}& 42\\&13\\+&25\\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}& 31\\&12\\+&49\\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}& 23\\&27\\+&84\\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}& 41\\&52\\+&65\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}& 63\\&74\\+&21\\ \hline \\ \end{array}$
7. $\begin{array}[t]{rr}& 47\\&18\\+&55\\ \hline \\ \end{array}$
8. $\begin{array}[t]{rr}& 12\\&24\\+&89\\ \hline \\ \end{array}$
9. $\begin{array}[t]{rr}& 73\\&21\\+&37\\ \hline \\ \end{array}$
10. $\begin{array}[t]{rr}& 25\\&60\\+&47\\ \hline \\ \end{array}$
11. $\begin{array}[t]{rr}& 53\\&60\\+&71\\ \hline \\ \end{array}$
12. $\begin{array}[t]{rr}& 14\\&24\\+&51\\ \hline \\ \end{array}$
13. $\begin{array}[t]{rr}& 56\\&23\\+&67\\ \hline \\ \end{array}$
14. $\begin{array}[t]{rr}& 78\\&45\\+&89\\ \hline \\ \end{array}$
15. $\begin{array}[t]{rr}& 22\\&52\\+&64\\ \hline \\ \end{array}$
16. $\begin{array}[t]{rr}& 35\\&11\\+&75\\ \hline \\ \end{array}$
17. $\begin{array}[t]{rr}& 34\\&32\\+&85\\ \hline \\ \end{array}$
18. $\begin{array}[t]{rr}& 27\\&51\\+&96\\ \hline \\ \end{array}$
19. $\begin{array}[t]{rr}& 25\\&46\\+&43\\ \hline \\ \end{array}$
20. $\begin{array}[t]{rr}& 36\\&47\\+&52\\ \hline \\ \end{array}$
21. $\begin{array}[t]{rr}& 53\\&67\\+&81\\ \hline \\ \end{array}$
22. $\begin{array}[t]{rr}& 41\\&59\\+&99\\ \hline \\ \end{array}$
23. $\begin{array}[t]{rr}& 31\\&83\\+&27\\ \hline \\ \end{array}$
24. $\begin{array}[t]{rr}& 76\\&62\\+&25\\ \hline \\ \end{array}$

1. 200
2. 80
3. 92
4. 134
5. 158
6. 158
7. 120
8. 125
9. 131
10. 132
11. 184
12. 89
13. 146
14. 212
15. 138
16. 121
17. 151
18. 174
19. 114
20. 135
21. 201
22. 199
23. 141
24. 163

Use the same method for carrying when you add the columns of tens, hundreds, thousands, ten thousands, and so on. Look at these examples:

Example D: 347 + 438

4 ones + 8 ones = 12 ones = 1 ten and 2 ones

Write the 2 ones in the sum. Carry the 1 ten to the tens column.

7 + 3 + 1 ten you carried = 11 tens = 1 hundred and 1 ten Write the 1 ten. Carry the 1 hundred to the hundreds column.

3 + 4 + 1 hundred you carried = 8 hundreds. Write 8.

Example E: 4 974 + 2 385 + 6 890

Step 1: Add the ones. 9 ones (write 9 ones in the sum)

Step 2: Add the tens. 24 tens = 2 hundreds + 4 tens (write 4 tens) Carry the 2 hundreds to the hundreds column.

Step 3: Add the hundreds and the 2 hundreds you carried.

22 hundreds = 2 thousands + 2 hundreds (write 2 hundreds)

Step 4: Add the thousands and the 2 thousands you carried.

14 thousands = 1 ten thousand + 4 thousands Write 14 thousands in the sum.

Example F: 246 476 + 873 706

Step 1: Add the ones. 12 ones = 1 ten + 2 ones Write 2 ones in the sum, carry the 1 ten over.

Step 2: Add the tens. 8 tens

Write 8 tens in the sum, nothing to carry.

Step 3: Add the hundreds. 11 hundreds = 1 thousand + 1 hundred Write 1 hundred in the sum, carry the 1 thousand.

Step 4: Add the thousands. 10 thousands = 1 ten thousand + 0 thousands Be sure to write the 0 to hold the thousands place in the sum.

Carry the 1 ten thousand.

Step 5: Add the ten thousands.

12 ten thousands = 1 hundred thousand + 2 ten thousands

Write the 2 ten thousands in the sum, carry the 1 hundred thousand.

Step 6: Add the hundred thousands.

11 hundred thousands = 1 million + 1 hundred thousand Write 1 million and the 1 hundred thousand in the sum.

And to read the answer, say, one million, one hundred twenty thousand, one hundred eight-two.

Exercise Three

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

1. $\begin{array}[t]{rr}&231\\+&452 \\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}&520\\+&239 \\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}&481\\+&306 \\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}&306\\+&83 \\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}&5\,237\\ + 2\,549 \\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}&2\,846 \\+& 1\,437 \\ \hline \\ \end{array}$
7. $\begin{array}[t]{rr}&5\,128\\+& 4\,907 \\ \hline \\ \end{array}$
8. $\begin{array}[t]{rr}&6\,005\\+& 239 \\ \hline \\ \end{array}$
9. $\begin{array}[t]{rr}&8\,106\\+& 3\,923 \\ \hline \\ \end{array}$
10. $\begin{array}[t]{rr}&5\,028\\+& 4\,907 \\ \hline \\ \end{array}$
11. $\begin{array}[t]{rr}&6\,005\\+& 273 \\ \hline \\ \end{array}$
12. $\begin{array}[t]{rr}&2\,648\\+& 1\,838 \\ \hline \\ \end{array}$
13. $\begin{array}[t]{rr}&5\,837\\+& 2\,569 \\ \hline \\ \end{array}$
14. $\begin{array}[t]{rr}&2\,846\\+& 1\,457 \\ \hline \\ \end{array}$
15. $\begin{array}[t]{rr}&3\,517\\+& 4\,296 \\ \hline \\ \end{array}$
16. $\begin{array}[t]{rr}&9\,020\\+& 684 \\ \hline \\ \end{array}$
17. $\begin{array}[t]{rr}&2\,648 \\+& 1\,238 \\ \hline \\ \end{array}$
18. $\begin{array}[t]{rr}&5\,237\\+& 6\,968 \\ \hline \\ \end{array}$

1. 683
2. 759
3. 787
4. 389
5. 7786
6. 4283
7. 10035
8. 6244
9. 12029
10. 9935
11. 6278
12. 4486
13. 8406
14. 4303
15. 7813
16. 9704
17. 3886
18. 12205

If you are having any problems with this work, ask your instructor to check your method of addition with carrying before you go any further.

If you feel that you need more practice, your instructor will give you more addition questions to do.

If an addition 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.

Example G: 263 + 25

$\begin{array}[t]{rr}& 263\\+&25\\ \hline &288 \end{array}$

Example H: 316 + 9 560

$\begin{array}[t]{rr}& 316 \\+ &9 560\\ \hline &9876 \end{array}$

Exercise Four

Rewrite each question in columns. Be careful to write ones under ones, tens under tens, hundreds under hundreds, and so on. Check your work using the answer key at the end of the exercise.

1. 476 + 392 + 483 =
2. 986 + 483 + 524 =
3. 3714 + 3189 + 4582 =
4. 466 + 5973 + 821 + 83 =
5. 697 + 7639 + 27 + 5396 =
6. 1436 + 844 + 16009 =
7. 242100 + 62418 + 32 + 528002 =
8. 279661 + 475 + 49264 =

1. 1351
2. 1993
3. 11485
4. 7343
5. 13759
6. 18289
7. 832552
8. 329400

# Topic B: Self-Test

Mark   /15    Aim 12/15

1. Find the sums. Be sure to check your answers. (12 marks)
1. $\begin{array}[t]{rr}& 85\\+&57 \\ \hline \\ \end{array}$
2. $\begin{array}[t]{rr}& 94\\+&48 \\ \hline \\ \end{array}$
3. $\begin{array}[t]{rr}& 982\\+&743 \\ \hline \\ \end{array}$
4. $\begin{array}[t]{rr}& 829\\+&303 \\ \hline \\ \end{array}$
5. $\begin{array}[t]{rr}& 7\,834\\+& 2\,169\\ \hline \\ \end{array}$
6. $\begin{array}[t]{rr}& 5\,976 \\+& 2\,081\\ \hline \\ \end{array}$
7. $\begin{array}[t]{rr}& 46\,940\\+& 86\,502\\ \hline \\ \end{array}$
8. $\begin{array}[t]{rr}& 41\,801\\+& 39\,199\\ \hline \\ \end{array}$
9. $\begin{array}[t]{rr}& 3\,742 \\& 4\,108 \\+& 7\,336\\ \hline \\ \end{array}$
10. $\begin{array}[t]{rr}& 12\,350 \\&17\,629\\+& 23\,244\\ \hline \\ \end{array}$
11. $\begin{array}[t]{rr}& 352\,641 \\&432\,345 \\+& 720\,250\\ \hline \\ \end{array}$
12. $\begin{array}[t]{rr}& 18\,060 \\&62\,549 \\&1\,375 \\+& 399\\ \hline \\ \end{array}$
2. Add these numbers. (3 marks)
1. 74 + 32 + 67 + 85 =
2. 721 + 8462 + 968 + 99 =
3. 389 + 2517 + 2 =

1. 142
2. 142
3. 1725
4. 1132
5. 10003
6. 8057
7. 133442
8. 81000
9. 15186
10. 53223
11. 1505236
12. 82383
1. 258
2. 10250
3. 2908