How to do column addition and subtraction — with examples
How do you do column addition and subtraction?
Column addition and subtraction are the tidy way to calculate with large numbers: write them one under the other by place value, and work column by column from the ones leftwards. The real difficulty starts when a column "does not fit" — when an addition gives more than 9, or when you cannot subtract in the ones column. In this guide we go through both situations step by step.
Worked examples, step by step
What is 34 plus 25?
- Line up: ones under ones (4 under 5), tens under tens (3 under 2)
- Add the ones column: 4 plus 5 is 9
- Add the tens column: 3 plus 2 is 5
- Answer: 59
What is 47 plus 38?
- Add the ones: 7 plus 8 is 15 — that is more than 9, so carry: write 5 in the ones column and carry one ten (1) to the tens column
- Add the tens: 4 plus 3 is 7, and add the 1 we carried — 7 plus 1 is 8
- Answer: 85
What is 52 minus 28?
- In the ones column you cannot subtract 8 from 2 (2 is smaller than 8), so exchange one ten from the tens — it becomes 10 ones and joins the 2 already there, making 12
- Subtract the ones: 12 minus 8 is 4
- In the tens column 4 tens are left (after exchanging: 5 minus 1), so subtract: 4 minus 2 is 2
- Answer: 24
What is 300 minus 124?
- The ones column has 0, and you cannot subtract 4 from it — and the tens column has 0 too, so exchange across both columns: take one hundred (300 becomes 2 hundreds and 10 tens)
- Exchange one ten out of the 10 tens: 9 tens remain, and the 10 ones that were exchanged move to the ones column
- Ones: 10 minus 4 is 6. Tens: 9 minus 2 is 7. Hundreds: 2 minus 1 is 1
- Answer: 176
Now try it yourself
Frequently asked questions
What is the difference between carrying and exchanging?
Both are moves between place values, in opposite directions. In an addition you carry: when a column passes 9, you bundle 10 small units into one bigger unit and pass it along (carry 1). In a subtraction you exchange: when there is not enough in a column, you break one bigger unit into 10 smaller units and add them to the column.
Why do you start from the ones column and not the tens?
Because a carry or an exchange always "flows" towards the bigger column — from the ones to the tens, from the tens to the hundreds. If you started from the tens you might write a result there and then discover the ones need a carry that changes it. Working from the ones leftwards guarantees every column is written exactly once.
How do you exchange when the ones and tens columns are both zero, as in 300?
Exchange in a "chain": open up the nearest hundred into 10 tens, and immediately exchange one of those tens into 10 ones. That leaves 9 tens (not 10, because one was exchanged) and 10 ones available for the subtraction. This is the point where most pupils slip, so it is worth practising separately.
What is the best way to practise column addition and subtraction at home?
Start with calculations that need no carrying or exchanging to secure the lining-up by place value, and only then move on to ones that do. Printed worksheets with answers let a child check themselves, and short regular practice (a few calculations a day) beats one long session a week.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specificationsLast updated: