Step-by-step Maths Level 5: Carrying across several places
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
Carrying across several places
Some sums carry in every column. Each carried 1 is added to the next column, so it can make another ten.
Check by subtracting one of the numbers from the total. You should get the other number back.
Key ideas
- Carries can happen in several columns in one sum.
- Add the carried 1 before you add the next pair of digits.
- Check the total by taking away one of the numbers.
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 4 and carry 1 to the hundreds column.4 + 9 + 1 carried = 14
- Add the hundreds column. Write 4 and carry 1 to the thousands column.5 + 8 + 1 carried = 14
- Add the thousands column. Write 4 and carry 1 to the ten thousands column.6 + 7 + 1 carried = 14
- Add the ten thousands column. Write 5 and carry 1 to the hundred thousands column.8 + 6 + 1 carried = 15
- 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.854,441
Check. Check: 854,441 - 567,892 = 286,549.
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. Check by using the inverse: subtract for a sum, or add back for a difference.
- Take one number away from the answer. If the sum is correct, taking one number away gives the other.700,001 - 582,463 = 117,538
- Compare with the other number. Is 117,538 the same as 117,538?Same
- Write Yes or No. Yes if the check works; No if it does not.Yes
Check. The correct answer is 700,001.
Watch out. A check that does not work means the answer is wrong. Find the mistake in the columns.
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.
Watch out
Watch out. A total of 1,000,000 or more has seven digits. Make sure the answer has the right number of digits.
Exam tip
Grown-up tip. Ask the child to check every big sum by subtracting one number from the total.
Exercise 2B Practice: carrying across several places
Non-calculatorMethod. 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 1 and carry 1 to the hundreds column.7 + 3 + 1 carried = 11
- Add the hundreds column. Write 7 and carry 1 to the thousands column.9 + 7 + 1 carried = 17
- Add the thousands column. Write 3 in the thousands column.2 + 0 + 1 carried = 3
- Add the ten thousands column. Write 6 in the ten thousands column.0 + 6 = 6
- Add the hundred thousands column. Write 6 in the hundred thousands column.4 + 2 = 6
- Write the answer. Put the digits together, with commas between groups of three.663,713
Check. Check: 663,713 - 260,737 = 402,976.
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.5 + 5 = 10
- Add the tens column. Write 2 in the tens column.1 + 0 + 1 carried = 2
- Add the hundreds column. Write 5 and carry 1 to the thousands column.7 + 8 = 15
- Add the thousands column. Write 8 in the thousands column.2 + 5 + 1 carried = 8
- Add the ten thousands column. Write 8 in the ten thousands column.0 + 8 = 8
- Add the hundred thousands column. Write 8 in the hundred thousands column.8 + 0 = 8
- Write the answer. Put the digits together, with commas between groups of three.888,520
Check. Check: 888,520 - 85,805 = 802,715.
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 and carry 1 to the tens column.8 + 9 = 17
- Add the tens column. Write 9 in the tens column.2 + 6 + 1 carried = 9
- Add the hundreds column. Write 0 and carry 1 to the thousands column.4 + 6 = 10
- Add the thousands column. Write 1 in the thousands column.0 + 0 + 1 carried = 1
- Add the ten thousands column. Write 3 and carry 1 to the hundred thousands column.5 + 8 = 13
- Add the hundred thousands column. Write 3 in the hundred thousands column.0 + 2 + 1 carried = 3
- Write the answer. Put the digits together, with commas between groups of three.331,097
Check. Check: 331,097 - 280,669 = 50,428.
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 5 and carry 1 to the tens column.9 + 6 = 15
- Add the tens column. Write 9 in the tens column.6 + 2 + 1 carried = 9
- Add the hundreds column. Write 8 in the hundreds column.1 + 7 = 8
- Add the thousands column. Write 5 and carry 1 to the ten thousands column.6 + 9 = 15
- 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.995,895
Check. Check: 995,895 - 119,726 = 876,169.
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.3 + 7 = 10
- Add the tens column. Write 4 and carry 1 to the hundreds column.6 + 7 + 1 carried = 14
- Add the hundreds column. Write 9 in the hundreds column.4 + 4 + 1 carried = 9
- Add the thousands column. Write 1 and carry 1 to the ten thousands column.7 + 4 = 11
- Add the ten thousands column. Write 4 and carry 1 to the hundred thousands column.6 + 7 + 1 carried = 14
- Add the hundred thousands column. Write 8 in the hundred thousands column.7 + 0 + 1 carried = 8
- Write the answer. Put the digits together, with commas between groups of three.841,940
Check. Check: 841,940 - 74,477 = 767,463.
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.8 + 2 = 10
- Add the tens column. Write 8 in the tens column.5 + 2 + 1 carried = 8
- Add the hundreds column. Write 5 and carry 1 to the thousands column.6 + 9 = 15
- Add the thousands column. Write 3 and carry 1 to the ten thousands column.6 + 6 + 1 carried = 13
- Add the ten thousands column. Write 4 in the ten thousands column.1 + 2 + 1 carried = 4
- Add the hundred thousands column. Write 4 in the hundred thousands column.1 + 3 = 4
- Write the answer. Put the digits together, with commas between groups of three.443,580
Check. Check: 443,580 - 326,922 = 116,658.
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 6 in the ones column.4 + 2 = 6
- Add the tens column. Write 8 in the tens column.2 + 6 = 8
- Add the hundreds column. Write 1 and carry 1 to the thousands column.7 + 4 = 11
- Add the thousands column. Write 2 and carry 1 to the ten thousands column.3 + 8 + 1 carried = 12
- Add the ten thousands column. Write 6 in the ten thousands column.3 + 2 + 1 carried = 6
- Add the hundred thousands column. Write 5 in the hundred thousands column.5 + 0 = 5
- Write the answer. Put the digits together, with commas between groups of three.562,186
Check. Check: 562,186 - 28,462 = 533,724.
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 4 in the tens column.2 + 2 = 4
- Add the hundreds column. Write 0 and carry 1 to the thousands column.5 + 5 = 10
- Add the thousands column. Write 0 and carry 1 to the ten thousands column.9 + 0 + 1 carried = 10
- Add the ten thousands column. Write 8 in the ten thousands column.3 + 4 + 1 carried = 8
- 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.680,049
Check. Check: 680,049 - 440,523 = 239,526.
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.7 + 3 = 10
- Add the tens column. Write 7 in the tens column.2 + 4 + 1 carried = 7
- Add the hundreds column. Write 3 and carry 1 to the thousands column.7 + 6 = 13
- Add the thousands column. Write 9 in the thousands column.8 + 0 + 1 carried = 9
- Add the ten thousands column. Write 6 in the ten thousands column.6 + 0 = 6
- Add the hundred thousands column. Write 5 in the hundred thousands column.2 + 3 = 5
- Write the answer. Put the digits together, with commas between groups of three.569,370
Check. Check: 569,370 - 300,643 = 268,727.
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 6 in the ones column.1 + 5 = 6
- Add the tens column. Write 0 and carry 1 to the hundreds column.7 + 3 = 10
- Add the hundreds column. Write 3 and carry 1 to the thousands column.4 + 8 + 1 carried = 13
- Add the thousands column. Write 4 and carry 1 to the ten thousands column.4 + 9 + 1 carried = 14
- Add the ten thousands column. Write 2 in the ten thousands column.0 + 1 + 1 carried = 2
- Add the hundred thousands column. Write 6 in the hundred thousands column.6 + 0 = 6
- Write the answer. Put the digits together, with commas between groups of three.624,306
Check. Check: 624,306 - 19,835 = 604,471.
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 5 in the ones column.2 + 3 = 5
- Add the tens column. Write 3 in the tens column.0 + 3 = 3
- Add the hundreds column. Write 2 and carry 1 to the thousands column.6 + 6 = 12
- Add the thousands column. Write 2 and carry 1 to the ten thousands column.2 + 9 + 1 carried = 12
- Add the ten thousands column. Write 9 in the ten thousands column.5 + 3 + 1 carried = 9
- Add the hundred thousands column. Write 8 in the hundred thousands column.5 + 3 = 8
- Write the answer. Put the digits together, with commas between groups of three.892,235
Check. Check: 892,235 - 339,633 = 552,602.
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 and carry 1 to the tens column.9 + 8 = 17
- Add the tens column. Write 9 in the tens column.8 + 0 + 1 carried = 9
- Add the hundreds column. Write 9 in the hundreds column.6 + 3 = 9
- Add the thousands column. Write 7 in the thousands column.6 + 1 = 7
- Add the ten thousands column. Write 1 and carry 1 to the hundred thousands column.3 + 8 = 11
- Add the hundred thousands column. Write 9 in the hundred thousands column.5 + 3 + 1 carried = 9
- Write the answer. Put the digits together, with commas between groups of three.917,997
Check. Check: 917,997 - 381,308 = 536,689.
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 1 and carry 1 to the hundreds column.1 + 9 + 1 carried = 11
- Add the hundreds column. Write 3 and carry 1 to the thousands column.5 + 7 + 1 carried = 13
- Add the thousands column. Write 7 in the thousands column.6 + 0 + 1 carried = 7
- Add the ten thousands column. Write 4 in the ten thousands column.3 + 1 = 4
- Add the hundred thousands column. Write 8 in the hundred thousands column.3 + 5 = 8
- Write the answer. Put the digits together, with commas between groups of three.847,313
Check. Check: 847,313 - 510,797 = 336,516.
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 and carry 1 to the tens column.9 + 5 = 14
- Add the tens column. Write 4 and carry 1 to the hundreds column.5 + 8 + 1 carried = 14
- Add the hundreds column. Write 8 in the hundreds column.6 + 1 + 1 carried = 8
- Add the thousands column. Write 5 in the thousands column.5 + 0 = 5
- Add the ten thousands column. Write 3 in the ten thousands column.0 + 3 = 3
- 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.935,844
Check. Check: 935,844 - 130,185 = 805,659.
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.7 + 1 = 8
- Add the tens column. Write 0 and carry 1 to the hundreds column.4 + 6 = 10
- Add the hundreds column. Write 2 and carry 1 to the thousands column.9 + 2 + 1 carried = 12
- Add the thousands column. Write 7 in the thousands column.4 + 2 + 1 carried = 7
- Add the ten thousands column. Write 1 and carry 1 to the hundred thousands column.3 + 8 = 11
- Add the hundred thousands column. Write 9 in the hundred thousands column.5 + 3 + 1 carried = 9
- Write the answer. Put the digits together, with commas between groups of three.917,208
Check. Check: 917,208 - 382,261 = 534,947.
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.8 + 3 = 11
- Add the tens column. Write 1 in the tens column.0 + 0 + 1 carried = 1
- Add the hundreds column. Write 9 in the hundreds column.5 + 4 = 9
- Add the thousands column. Write 1 and carry 1 to the ten thousands column.3 + 8 = 11
- Add the ten thousands column. Write 5 in the ten thousands column.2 + 2 + 1 carried = 5
- Add the hundred thousands column. Write 7 in the hundred thousands column.7 + 0 = 7
- Write the answer. Put the digits together, with commas between groups of three.751,911
Check. Check: 751,911 - 28,403 = 723,508.
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.