Column Subtraction With Borrowing (Exchanging) Explained
By the TimesTable.co team · Updated · 3 min read
Column subtraction is where many children come unstuck, usually at the moment they need to "borrow". Schools today call it exchanging, which is a better description of what actually happens, and it's worth using the same word at home so your child isn't confused. Here's the method, including the tricky case of subtracting from numbers with zeros.
How do you set out column subtraction?
Put the bigger number on top and line up the digits on the right: ones under ones, tens under tens. Always subtract the bottom digit from the top digit, starting with the ones. Column subtraction practice sets this out with place-value headings.
What does exchanging (borrowing) mean?
52 − 17
- Ones: 2 − 7? You can't take 7 from 2.
- Exchange: take one ten from the 5 tens (cross out 5, write 4). That ten becomes ten ones, so the 2 becomes 12.
- Ones: 12 − 7 = 5.
- Tens: 4 − 1 = 3.
- Answer: 35.
Show it with money: 52p as five 10p coins and two 1p coins. To pay 7p, swap one 10p for ten 1p coins first.
How do you subtract across zeros?
This is the part that trips everyone up. 400 − 128
- Ones: 0 − 8? No. Tens: 0, so nothing to exchange from.
- Go to the hundreds: 4 hundreds → 3, and the tens become 10.
- Now exchange from the tens: 10 tens → 9, and the ones become 10.
- Ones: 10 − 8 = 2. Tens: 9 − 2 = 7. Hundreds: 3 − 1 = 2.
- Answer: 272.
A shortcut some children like: 400 is "39 tens and 10 ones", so the digits become 3, 9, 10 in one go.
What mistakes do children make most?
- Smaller from bigger: for 52 − 17, doing 7 − 2 = 5 in the ones column. The answer 45 looks reasonable, which is why it's so common.
- Forgetting to reduce the column they exchanged from.
- Zeros: not knowing where to exchange from.
- Misaligned numbers when one has fewer digits.
How do you subtract decimals?
Line up the decimal points and fill gaps with zeros: 83.62 − 18.75 works exactly like whole numbers, and the point drops straight down into the answer: 64.87. The Decimals level of column subtraction practises this.
How do you check the answer?
Add it back: 35 + 17 should be 52. This uses column addition, and checking every answer this way quickly builds confidence.
How can you practise at home?
Start with problems that need no exchanging, then one exchange, then zeros. The subtraction tool walks through each column and shows exchanges as they happen, and the worksheet generator makes subtraction sheets with answers. Solid subtraction is also the key to long division, where every step includes a subtraction.
For younger children, counting back on a number line is a good bridge to the written method, and when subtraction is secure, short division is the natural next step.
Frequently asked questions
What is borrowing in subtraction?
When the top digit in a column is smaller than the bottom digit, you take one from the next column to the left. That one is worth ten in the current column, so 2 becomes 12.
Why do schools call it exchanging instead of borrowing?
Because nothing is given back. One ten is exchanged for ten ones, like swapping a 10p coin for ten 1p coins, so "exchanging" describes what really happens.
How do you subtract from a number with zeros, like 400 − 128?
Go left until you find a digit you can exchange from. Take one hundred, turning 4 hundreds into 3 and giving 10 tens; then take one ten, leaving 9 tens and giving 10 ones. Now 10 − 8, 9 − 2 and 3 − 1 give 272.
What year is column subtraction taught?
In England, the formal column method is introduced in Year 3 and extended to bigger numbers in Year 4 and decimals in Years 5 and 6.
What is the most common column subtraction mistake?
Taking the smaller digit away from the bigger one regardless of which is on top: for 52 − 17, writing 7 − 2 = 5 in the ones column instead of exchanging.
How can you check a subtraction answer?
Add the answer to the number you took away. You should get back the number you started with: 35 + 17 = 52.