• Key Stage 2 • Maths
Column addition and column subtraction are the formal written methods for adding and subtracting larger numbers. Pupils start using them in Year 3 and work with bigger numbers each year. This guide explains both methods step by step, including carrying and exchanging, with worked examples and practice questions.
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The Quick Answer
- In column addition and subtraction, you write the numbers one above the other with the digits lined up by place value.
- You always start with the ones column and work left.
- In addition, if a column adds up to 10 or more, you carry a digit into the next column.
- In subtraction, if the top digit is smaller, you exchange from the next column. Some people call this borrowing.
When Pupils Learn Column Methods
| Year | What the national curriculum says |
|---|---|
| Year 3 | Add and subtract numbers with up to three digits using columnar addition and subtraction |
| Year 4 | Add and subtract numbers with up to 4 digits using columnar addition and subtraction where appropriate |
| Year 5 | Add and subtract whole numbers with more than 4 digits, including using columnar methods |
| Year 6 | Practise columnar addition and subtraction with larger numbers |
How to Do Column Addition
- Write the numbers one above the other, lining up the ones, tens, hundreds and thousands.
- Add the ones column first.
- If the total is 10 or more, write the ones digit and carry the ten into the next column.
- Move left, adding each column and any carried digit.
Worked Example: 4,586 + 2,748
| Column | Working | Write |
|---|---|---|
| Ones | 6 + 8 = 14 | 4, carry 1 |
| Tens | 8 + 4 + 1 = 13 | 3, carry 1 |
| Hundreds | 5 + 7 + 1 = 13 | 3, carry 1 |
| Thousands | 4 + 2 + 1 = 7 | 7 |
Answer: 4,586 + 2,748 = 7,334.
How to Do Column Subtraction
- Write the larger number on top, lining up the digits by place value.
- Subtract the ones column first: top digit minus bottom digit.
- If the top digit is smaller, exchange 1 from the next column to the left. That column goes down by 1 and the column you are working on gets 10 more.
- Move left and repeat.
Worked Example: 6,302 − 2,758
| Column | Working | Write |
|---|---|---|
| Ones | 2 is smaller than 8. The tens digit is 0, so exchange from the hundreds: 3 hundreds become 2 and the tens become 10. Then exchange 1 ten: the tens become 9 and the ones become 12. 12 − 8 = 4 | 4 |
| Tens | 9 − 5 = 4 | 4 |
| Hundreds | 2 is smaller than 7, so exchange 1 thousand: the hundreds become 12 and the thousands become 5. 12 − 7 = 5 | 5 |
| Thousands | 5 − 2 = 3 | 3 |
Answer: 6,302 − 2,758 = 3,544. Check with the inverse: 3,544 + 2,758 = 6,302.
Tip: zeros in the top number cause the most mistakes. Exchanging across a zero takes two steps, so slow down and cross out clearly.
Column Methods with Decimals
Line up the decimal points, not the last digits. Fill any gaps with zeros so both numbers have the same number of decimal places.
For 12.6 + 7.85, write 12.6 as 12.60. Then 12.60 + 7.85 = 20.45.
Column Addition and Subtraction Practice Questions
- 3,457 + 2,186
- 48,906 + 27,395
- 125,640 + 9,875
- 5,000 − 1,876
- 7,214 − 3,859
- 62,105 − 18,347
- 15.7 + 8.45
- 20 − 6.38
- A school raised £4,385 in the autumn and £2,967 in the spring. How much did it raise altogether?
- A library had 12,040 books and lent out 3,875. How many books were left?
Show the answers
- 5,643
- 76,301
- 135,515
- 3,124
- 3,355
- 43,758
- 24.15
- 13.62
- £7,352
- 8,165
Common Mistakes
- Misaligning digits: 352 + 41 must have the 4 under the 5, not under the 3.
- Forgetting to carry: always add the carried digit into the next column.
- Taking the smaller digit from the larger: in 52 − 18, pupils sometimes work out 8 − 2 = 6 in the ones. They need to exchange instead.
- Not lining up decimal points: with decimals, line up the decimal points, not the last digits.
Frequently Asked Questions
What is column addition?
A written method where numbers are lined up by place value and added one column at a time, starting with the ones.
Is exchanging the same as borrowing?
Yes. Exchanging is the term used in many schools. It means taking 1 from the next column and adding 10 to the column you are working on.
What year do children learn column addition?
Year 3, with numbers up to three digits. They work with larger numbers in Years 4 and 5.
How do you subtract from a number with zeros?
Exchange from the first column to the left that is not zero, then work back across the zeros.
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Sources: Department for Education, National curriculum in England: mathematics programmes of study, including Mathematics Appendix 1. Practice questions written by Monster Learning.
