Column subtraction explained for parents

What it is

Place value

What each digit is worth because of where it sits. In 432, the 4 is worth 4 hundreds, the 3 is worth 3 tens and the 2 is worth 2 ones.

Column subtraction

Writing one number under the other, with ones under ones, tens under tens and hundreds under hundreds, then subtracting each column. The national curriculum calls it columnar subtraction.

Exchanging

Swapping 1 ten for 10 ones, or 1 hundred for 10 tens, when a column doesn't have enough to subtract from. Some schools call it regrouping.

Column subtraction works because of place value. Each column only ever holds ones, tens or hundreds, so your child can subtract one small calculation at a time instead of the whole number at once.

Children start with calculations where no top digit is smaller than the one below it, so no exchanging is needed:

  5 8 6
- 2 4 3
-------
  3 4 3

Exchanging comes in when a top digit is smaller than the digit below it. Nothing is really borrowed, because nothing is given back. Instead, your child swaps 1 from the next column into 10 of the column they're working on. The total stays the same, just arranged differently.

How it's taught at school

In Year 2, children record adding and subtracting in columns to build their understanding of place value. In Year 3, the national curriculum expects them to add and subtract numbers with up to three digits using formal written methods of columnar addition and subtraction. They go on to 4-digit numbers in Year 4, and bigger numbers in Year 5.

DfE guidance for teachers suggests that children learn column addition first, then subtraction. They lay the digits out carefully in their columns and work from right to left, starting with the ones. At first, the guidance suggests using place-value equipment such as Dienes: blocks for ones, sticks of ten and flat squares of a hundred.

Teachers also use careful language, such as "5 ones minus 3 ones is equal to 2 ones". Saying "tens" and "hundreds" reminds your child what each digit is worth. Here is a calculation with two exchanges, step by step:

  4 3 2
- 1 5 7
-------
  2 7 5

1. Ones: 2 take away 7 can't be done. Exchange 1 ten for 10 ones. Now there are 2 tens and 12 ones. 12 − 7 = 5.
2. Tens: 2 tens take away 5 tens can't be done. Exchange 1 hundred for 10 tens. Now there are 3 hundreds and 12 tens. 12 − 5 = 7.
3. Hundreds: 3 − 1 = 2.
4. Answer: 275. To check, add it back on: 275 + 157 = 432.

Schools usually show each exchange by crossing out digits and writing the new amounts as small digits above or beside them. The national curriculum notes that exactly where these small digits go varies with the method, so if a worksheet looks different from how you'd do it, follow the school's way.

Children are also taught to estimate first and to check with the opposite calculation. Some teachers draw a bar model (a long rectangle split into the parts of the calculation) to show what is being taken away. Children also learn when not to use columns: for 402 − 398, it's quicker to see that the numbers are only 4 apart.

Common mistakes (and how to help)

Taking the smaller digit from the bigger one in each column

For 432 − 157, this gives 7 − 2 = 5, then 5 − 3 = 2, and an answer of 325. Remind your child that the bottom number is always the one being taken away. If the top digit is smaller, that's the signal to exchange.

Exchanging, but forgetting to make the next column smaller

For 452 − 127, a child who exchanges a ten but still uses 5 tens gets 335 instead of 325. Encourage your child to cross out the digit and write the new one every time they exchange.

Lining the numbers up from the left, such as putting 41 under the 35 of 352

Always line up the ones first. It helps to say "ones under ones, tens under tens" while writing the calculation out.

Getting stuck when there's a zero to exchange from, as in 305 − 128

There are no tens to exchange, so first exchange 1 hundred for 10 tens, then 1 ten for 10 ones. That leaves 2 hundreds, 9 tens and 15 ones, and the answer is 177. Coins or drawings make this much easier to see.

Three quick activities at home

Questions parents ask

Sources

1. Department for Education: National curriculum in England: mathematics programmes of study
2. Department for Education: Teaching mathematics in primary schools (Mathematics guidance: key stages 1 and 2)
3. BBC Bitesize: Subtraction with up to 4-digit numbers (KS2 Maths)