Step-by-step Maths Level 5: Adding in columns with carrying
Part of the Step-by-step Maths Level 5 adding and subtracting whole numbers to a million chapter. Chapter overview · whole chapter on one page
Adding in columns with carrying
Line up the digits in columns, so that ones are under ones and thousands are under thousands. Start from the right.
When a column adds up to ten or more, write the ones digit and carry the ten to the next column on the left.
Key ideas
- Line up the columns, with the ones on the right.
- Add one column at a time, starting from the right.
- Carry a ten into the next column on the left.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 7 in the ones column.4 + 3 = 7
- Add the tens column. Write 5 and carry 1 to the hundreds column.8 + 7 = 15
- Add the hundreds column. Write 3 and carry 1 to the thousands column.3 + 9 + 1 carried = 13
- Add the thousands column. Write 4 and carry 1 to the ten thousands column.5 + 8 + 1 carried = 14
- Add the ten thousands column. Write 1 and carry 1 to the hundred thousands column.6 + 4 + 1 carried = 11
- Add the hundred thousands column. Write 3 in the hundred thousands column.2 + 0 + 1 carried = 3
- Write the answer. Put the digits together, with commas between groups of three.314,357
Check. Check: 314,357 - 48,973 = 265,384.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 2 and carry 1 to the tens column.5 + 7 = 12
- Add the tens column. Write 1 and carry 1 to the hundreds column.6 + 4 + 1 carried = 11
- Add the hundreds column. Write 0 and carry 1 to the thousands column.7 + 2 + 1 carried = 10
- Add the thousands column. Write 0 and carry 1 to the ten thousands column.8 + 1 + 1 carried = 10
- Add the ten thousands column. Write 0 and carry 1 to the hundred thousands column.9 + 0 + 1 carried = 10
- Add the hundred thousands column. Write 0 and carry 1 to the millions column.6 + 3 + 1 carried = 10
- Write the last carried 1. It goes in front of the other digits.1 in the millions column
- Write the answer. Put the digits together, with commas between groups of three.1,000,012
Check. Check: 1,000,012 - 301,247 = 698,765.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 3 and carry 1 to the tens column.6 + 7 = 13
- Add the tens column. Write 2 and carry 1 to the hundreds column.5 + 6 + 1 carried = 12
- Add the hundreds column. Write 4 and carry 1 to the thousands column.4 + 9 + 1 carried = 14
- Add the thousands column. Write 6 and carry 1 to the ten thousands column.8 + 7 + 1 carried = 16
- Add the ten thousands column. Write 6 in the ten thousands column.3 + 2 + 1 carried = 6
- Write the answer. Put the digits together, with commas between groups of three.66,423
Check. Check: 66,423 - 27,967 = 38,456.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Watch out
Watch out. Carried tens go into the next column, not the one under it. Add the carried number first.
Exam tip
Grown-up tip. Ask the child to say the carry aloud: “Seven and five is twelve, write two and carry one.”
Exercise 2A Practice: adding in columns
Non-calculatorMethod. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 8 in the ones column.1 + 7 = 8
- Add the tens column. Write 1 and carry 1 to the hundreds column.8 + 3 = 11
- Add the hundreds column. Write 8 in the hundreds column.6 + 1 + 1 carried = 8
- Add the thousands column. Write 0 and carry 1 to the ten thousands column.2 + 8 = 10
- Add the ten thousands column. Write 4 and carry 1 to the hundred thousands column.7 + 6 + 1 carried = 14
- Add the hundred thousands column. Write 8 in the hundred thousands column.2 + 5 + 1 carried = 8
- Write the answer. Put the digits together, with commas between groups of three.840,818
Check. Check: 840,818 - 568,137 = 272,681.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 1 and carry 1 to the tens column.9 + 2 = 11
- Add the tens column. Write 6 and carry 1 to the hundreds column.9 + 6 + 1 carried = 16
- Add the hundreds column. Write 5 and carry 1 to the thousands column.9 + 5 + 1 carried = 15
- Add the thousands column. Write 1 and carry 1 to the ten thousands column.9 + 1 + 1 carried = 11
- Add the ten thousands column. Write 8 in the ten thousands column.2 + 5 + 1 carried = 8
- Add the hundred thousands column. Write 6 in the hundred thousands column.5 + 1 = 6
- Write the answer. Put the digits together, with commas between groups of three.681,561
Check. Check: 681,561 - 151,562 = 529,999.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 3 and carry 1 to the tens column.5 + 8 = 13
- Add the tens column. Write 7 and carry 1 to the hundreds column.7 + 9 + 1 carried = 17
- Add the hundreds column. Write 7 in the hundreds column.2 + 4 + 1 carried = 7
- Add the thousands column. Write 9 in the thousands column.1 + 8 = 9
- Add the ten thousands column. Write 6 and carry 1 to the hundred thousands column.8 + 8 = 16
- Add the hundred thousands column. Write 5 in the hundred thousands column.3 + 1 + 1 carried = 5
- Write the answer. Put the digits together, with commas between groups of three.569,773
Check. Check: 569,773 - 188,498 = 381,275.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 8 in the ones column.2 + 6 = 8
- Add the tens column. Write 6 in the tens column.1 + 5 = 6
- Add the hundreds column. Write 7 in the hundreds column.2 + 5 = 7
- Add the thousands column. Write 4 and carry 1 to the ten thousands column.8 + 6 = 14
- Add the ten thousands column. Write 2 and carry 1 to the hundred thousands column.2 + 9 + 1 carried = 12
- Add the hundred thousands column. Write 9 in the hundred thousands column.1 + 7 + 1 carried = 9
- Write the answer. Put the digits together, with commas between groups of three.924,768
Check. Check: 924,768 - 796,556 = 128,212.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 7 in the ones column.6 + 1 = 7
- Add the tens column. Write 7 in the tens column.2 + 5 = 7
- Add the hundreds column. Write 9 in the hundreds column.7 + 2 = 9
- Add the thousands column. Write 5 and carry 1 to the ten thousands column.6 + 9 = 15
- Add the ten thousands column. Write 6 in the ten thousands column.3 + 2 + 1 carried = 6
- Add the hundred thousands column. Write 9 in the hundred thousands column.8 + 1 = 9
- Write the answer. Put the digits together, with commas between groups of three.965,977
Check. Check: 965,977 - 129,251 = 836,726.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 1 and carry 1 to the tens column.5 + 6 = 11
- Add the tens column. Write 1 and carry 1 to the hundreds column.7 + 3 + 1 carried = 11
- Add the hundreds column. Write 6 in the hundreds column.5 + 0 + 1 carried = 6
- Add the thousands column. Write 5 and carry 1 to the ten thousands column.8 + 7 = 15
- Add the ten thousands column. Write 3 and carry 1 to the hundred thousands column.8 + 4 + 1 carried = 13
- Add the hundred thousands column. Write 9 in the hundred thousands column.8 + 0 + 1 carried = 9
- Write the answer. Put the digits together, with commas between groups of three.935,611
Check. Check: 935,611 - 47,036 = 888,575.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 8 in the ones column.8 + 0 = 8
- Add the tens column. Write 6 and carry 1 to the hundreds column.9 + 7 = 16
- Add the hundreds column. Write 4 in the hundreds column.2 + 1 + 1 carried = 4
- Add the thousands column. Write 9 in the thousands column.4 + 5 = 9
- Add the ten thousands column. Write 5 in the ten thousands column.5 + 0 = 5
- Add the hundred thousands column. Write 9 in the hundred thousands column.8 + 1 = 9
- Write the answer. Put the digits together, with commas between groups of three.959,468
Check. Check: 959,468 - 105,170 = 854,298.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 2 in the ones column.1 + 1 = 2
- Add the tens column. Write 6 and carry 1 to the hundreds column.8 + 8 = 16
- Add the hundreds column. Write 4 and carry 1 to the thousands column.6 + 7 + 1 carried = 14
- Add the thousands column. Write 3 and carry 1 to the ten thousands column.7 + 5 + 1 carried = 13
- Add the ten thousands column. Write 5 and carry 1 to the hundred thousands column.7 + 7 + 1 carried = 15
- Add the hundred thousands column. Write 6 in the hundred thousands column.3 + 2 + 1 carried = 6
- Write the answer. Put the digits together, with commas between groups of three.653,462
Check. Check: 653,462 - 275,781 = 377,681.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 1 and carry 1 to the tens column.7 + 4 = 11
- Add the tens column. Write 0 and carry 1 to the hundreds column.1 + 8 + 1 carried = 10
- Add the hundreds column. Write 2 and carry 1 to the thousands column.5 + 6 + 1 carried = 12
- Add the thousands column. Write 1 and carry 1 to the ten thousands column.6 + 4 + 1 carried = 11
- Add the ten thousands column. Write 5 in the ten thousands column.3 + 1 + 1 carried = 5
- Add the hundred thousands column. Write 5 in the hundred thousands column.1 + 4 = 5
- Write the answer. Put the digits together, with commas between groups of three.551,201
Check. Check: 551,201 - 414,684 = 136,517.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 0 and carry 1 to the tens column.9 + 1 = 10
- Add the tens column. Write 8 and carry 1 to the hundreds column.9 + 8 + 1 carried = 18
- Add the hundreds column. Write 5 and carry 1 to the thousands column.6 + 8 + 1 carried = 15
- Add the thousands column. Write 8 in the thousands column.0 + 7 + 1 carried = 8
- Add the ten thousands column. Write 7 in the ten thousands column.6 + 1 = 7
- Add the hundred thousands column. Write 3 in the hundred thousands column.0 + 3 = 3
- Write the answer. Put the digits together, with commas between groups of three.378,580
Check. Check: 378,580 - 317,881 = 60,699.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 2 and carry 1 to the tens column.6 + 6 = 12
- Add the tens column. Write 8 in the tens column.3 + 4 + 1 carried = 8
- Add the hundreds column. Write 1 and carry 1 to the thousands column.9 + 2 = 11
- Add the thousands column. Write 7 in the thousands column.0 + 6 + 1 carried = 7
- Add the ten thousands column. Write 7 in the ten thousands column.4 + 3 = 7
- Add the hundred thousands column. Write 4 in the hundred thousands column.2 + 2 = 4
- Write the answer. Put the digits together, with commas between groups of three.477,182
Check. Check: 477,182 - 236,246 = 240,936.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 7 in the ones column.0 + 7 = 7
- Add the tens column. Write 8 in the tens column.5 + 3 = 8
- Add the hundreds column. Write 0 and carry 1 to the thousands column.6 + 4 = 10
- Add the thousands column. Write 9 in the thousands column.2 + 6 + 1 carried = 9
- Add the ten thousands column. Write 0 and carry 1 to the hundred thousands column.4 + 6 = 10
- Add the hundred thousands column. Write 8 in the hundred thousands column.3 + 4 + 1 carried = 8
- Write the answer. Put the digits together, with commas between groups of three.809,087
Check. Check: 809,087 - 466,437 = 342,650.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 0 and carry 1 to the tens column.6 + 4 = 10
- Add the tens column. Write 8 in the tens column.7 + 0 + 1 carried = 8
- Add the hundreds column. Write 6 in the hundreds column.3 + 3 = 6
- Add the thousands column. Write 3 and carry 1 to the ten thousands column.5 + 8 = 13
- Add the ten thousands column. Write 9 in the ten thousands column.7 + 1 + 1 carried = 9
- Add the hundred thousands column. Write 9 in the hundred thousands column.8 + 1 = 9
- Write the answer. Put the digits together, with commas between groups of three.993,680
Check. Check: 993,680 - 118,304 = 875,376.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 0 and carry 1 to the tens column.1 + 9 = 10
- Add the tens column. Write 7 and carry 1 to the hundreds column.9 + 7 + 1 carried = 17
- Add the hundreds column. Write 2 and carry 1 to the thousands column.9 + 2 + 1 carried = 12
- Add the thousands column. Write 5 and carry 1 to the ten thousands column.9 + 5 + 1 carried = 15
- Add the ten thousands column. Write 6 in the ten thousands column.0 + 5 + 1 carried = 6
- Add the hundred thousands column. Write 6 in the hundred thousands column.5 + 1 = 6
- Write the answer. Put the digits together, with commas between groups of three.665,270
Check. Check: 665,270 - 155,279 = 509,991.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 9 in the ones column.6 + 3 = 9
- Add the tens column. Write 9 in the tens column.4 + 5 = 9
- Add the hundreds column. Write 6 in the hundreds column.6 + 0 = 6
- Add the thousands column. Write 7 in the thousands column.7 + 0 = 7
- Add the ten thousands column. Write 6 in the ten thousands column.4 + 2 = 6
- Add the hundred thousands column. Write 6 in the hundred thousands column.2 + 4 = 6
- Write the answer. Put the digits together, with commas between groups of three.667,699
Check. Check: 667,699 - 420,053 = 247,646.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.
Method. Add the columns from the right. Carry any ten into the next column on the left.
- Add the ones column. Write 4 in the ones column.2 + 2 = 4
- Add the tens column. Write 6 in the tens column.4 + 2 = 6
- Add the hundreds column. Write 3 in the hundreds column.3 + 0 = 3
- Add the thousands column. Write 0 and carry 1 to the ten thousands column.5 + 5 = 10
- Add the ten thousands column. Write 3 in the ten thousands column.1 + 1 + 1 carried = 3
- Add the hundred thousands column. Write 7 in the hundred thousands column.5 + 2 = 7
- Write the answer. Put the digits together, with commas between groups of three.730,364
Check. Check: 730,364 - 215,022 = 515,342.
Watch out. Carry the 1 into the next column. Do not forget it, and do not write it as a digit in its own column.