Unit 2: Addition
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.
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.
- [latex]\begin{array}[t]{rr}&62\\+&18 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&46\\+&37 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&49\\+&42 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&44\\+&26 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&17\\+&79 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&23\\+&82 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&28\\+&91 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&54\\+&58 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&68\\+&49 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&66\\+&35 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&99\\+&88 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&89\\+&74 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&37\\+&15 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&55\\+&27 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&29\\+&76 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&35\\+&69 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&54\\+&17 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&72\\+&33 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&26\\+&56 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&38\\+&80 \\ \hline \\ \end{array}[/latex]
Answers to Exercise One
- 80
- 83
- 91
- 70
- 96
- 105
- 119
- 112
- 117
- 101
- 187
- 163
- 52
- 82
- 105
- 104
- 71
- 105
- 82
- 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.
- [latex]\begin{array}[t]{rr}& 67\\&78\\+&55\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 42\\&13\\+&25\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 31\\&12\\+&49\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 23\\&27\\+&84\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 41\\&52\\+&65\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 63\\&74\\+&21\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 47\\&18\\+&55\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 12\\&24\\+&89\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 73\\&21\\+&37\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 25\\&60\\+&47\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 53\\&60\\+&71\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 14\\&24\\+&51\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 56\\&23\\+&67\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 78\\&45\\+&89\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 22\\&52\\+&64\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 35\\&11\\+&75\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 34\\&32\\+&85\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 27\\&51\\+&96\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 25\\&46\\+&43\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 36\\&47\\+&52\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 53\\&67\\+&81\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 41\\&59\\+&99\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 31\\&83\\+&27\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 76\\&62\\+&25\\ \hline \\ \end{array}[/latex]
Answers to Exercise Two
- 200
- 80
- 92
- 134
- 158
- 158
- 120
- 125
- 131
- 132
- 184
- 89
- 146
- 212
- 138
- 121
- 151
- 174
- 114
- 135
- 201
- 199
- 141
- 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
Step 1: Add the ones.
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.
Step 2: Add the tens.
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.
Step 3: Add the hundreds.
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.
- [latex]\begin{array}[t]{rr}&231\\+&452 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&520\\+&239 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&481\\+&306 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&306\\+&83 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&5\,237\\ + 2\,549 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&2\,846 \\+& 1\,437 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&5\,128\\+& 4\,907 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&6\,005\\+& 239 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&8\,106\\+& 3\,923 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&5\,028\\+& 4\,907 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&6\,005\\+& 273 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&2\,648\\+& 1\,838 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&5\,837\\+& 2\,569 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&2\,846\\+& 1\,457 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&3\,517\\+& 4\,296 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&9\,020\\+& 684 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&2\,648 \\+& 1\,238 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&5\,237\\+& 6\,968 \\ \hline \\ \end{array}[/latex]
Answers to Exercise Three
- 683
- 759
- 787
- 389
- 7786
- 4283
- 10035
- 6244
- 12029
- 9935
- 6278
- 4486
- 8406
- 4303
- 7813
- 9704
- 3886
- 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.
Adding Across
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
[latex]\begin{array}[t]{rr}& 263\\+&25\\ \hline &288 \end{array}[/latex]
Example H: 316 + 9 560
[latex]\begin{array}[t]{rr}& 316 \\+ &9 560\\ \hline &9876 \end{array}[/latex]
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.
- 476 + 392 + 483 =
- 986 + 483 + 524 =
- 3714 + 3189 + 4582 =
- 466 + 5973 + 821 + 83 =
- 697 + 7639 + 27 + 5396 =
- 1436 + 844 + 16009 =
- 242100 + 62418 + 32 + 528002 =
- 279661 + 475 + 49264 =
Answers to Exercise Four
- 1351
- 1993
- 11485
- 7343
- 13759
- 18289
- 832552
- 329400
Topic B: Self-Test
Mark /15 Aim 12/15
- Find the sums. Be sure to check your answers. (12 marks)
- [latex]\begin{array}[t]{rr}& 85\\+&57 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 94\\+&48 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 982\\+&743 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 829\\+&303 \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 7\,834\\+& 2\,169\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 5\,976 \\+& 2\,081\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 46\,940\\+& 86\,502\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 41\,801\\+& 39\,199\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 3\,742 \\& 4\,108 \\+& 7\,336\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 12\,350 \\&17\,629\\+& 23\,244\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 352\,641 \\&432\,345 \\+& 720\,250\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 18\,060 \\&62\,549 \\&1\,375 \\+& 399\\ \hline \\ \end{array}[/latex]
- Add these numbers. (3 marks)
- 74 + 32 + 67 + 85 =
- 721 + 8462 + 968 + 99 =
- 389 + 2517 + 2 =
Answers to Topic B Self-Test
-
- 142
- 142
- 1725
- 1132
- 10003
- 8057
- 133442
- 81000
- 15186
- 53223
- 1505236
- 82383
-
- 258
- 10250
- 2908