Column Subtraction with Exchanging: Step by Step
The Department for Education’s guidance calls regrouping in subtraction “exchanging”: when a top digit is too small, one ten is exchanged for ten ones (or one hundred for ten tens). The digit that gives one away is crossed out and its new value written above.
The worked example, 932 − 457, is the one used in Appendix 1 of the National Curriculum.
When is it taught?
- Year 3: add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction.
- Year 4: numbers with up to 4 digits. Year 5: numbers with more than 4 digits.
Worked example: 932 − 457
932−457
81212932−457475
Left: the problem. Right: the worked answer with the exchanges shown, as in our answer keys.
Step by step
- 1Ones: 2 is less than 7, so exchange 1 ten for 10 ones: 12 − 7 = 5.
- 2The tens digit 3 is crossed out and becomes 2. Tens: 2 is less than 5, so exchange 1 hundred for 10 tens: 12 − 5 = 7.
- 3The hundreds digit 9 is crossed out and becomes 8. Hundreds: 8 − 4 = 4.
- 4The difference is 475.
- 5Check by adding: 475 + 457 = 932.
Common mistakes
- Taking the smaller digit from the larger in every column instead of exchanging.
- Exchanging but forgetting to cross out and reduce the digit that gave one away.
- Checking with the inverse: add the answer to the number subtracted.
Column subtraction worksheets
- Column subtraction with 3-digit numbersYear 3 · National Curriculum Year 3
- Column subtraction with 4-digit numbersYear 4 · National Curriculum Year 4