Column subtraction
You learn to subtract big numbers in columns, and to exchange when a column does not work.
How to work it out
- Line up ones under ones.
- Start on the right and subtract bottom from top.
- If not possible, borrow 1 ten from the column to the left.
115
425
−218
207
A worked example
425 − 218
- Ones: 5 − 8 does not work, so exchange a ten: 15 − 8 = 7.
- Tens: the 2 has become 1, and 1 − 1 = 0.
- Hundreds: 4 − 2 = 2.
- The answer is 207.
More examples
812 − 347
- Ones: 2 − 7 does not work, so exchange a ten: 12 − 7 = 5.
- Tens: the 1 has become 0, and 0 − 4 does not work, so exchange a hundred: 10 − 4 = 6.
- Hundreds: the 8 has become 7, and 7 − 3 = 4.
- The answer is 465.
71012
812
−347
465
500 − 263
- The 0 in the tens has nothing to give, so exchange from the 5: it becomes 4, the tens become 9 and the ones become 10.
- Ones: 10 − 3 = 7.
- Tens: 9 − 6 = 3.
- Hundreds: 4 − 2 = 2.
- The answer is 237.
4910
500
−263
237
Watch out
You take the smaller digit away from the bigger one: for 425 − 218 you do 8 − 5 and write 213.
Always take the bottom digit away from the top one. If you cannot, exchange first.
You exchange, but do not make the column on the left smaller: for 425 − 218 you write 217.
Cross out the digit you exchange from, and write one less above it.
Tips
- Check with an addition: 207 + 218 = 425.
- Before you subtract, check whether the top digit is big enough.
Exceptions
- If there is a 0 on top, as in 500 − 263, you cannot exchange from it, so exchange from the next digit first.
Why it works
In columns you only ever subtract small numbers. Sometimes the top digit is too small, as in 5 − 8. Then you exchange (or borrow) 10 from the column on the left: that digit goes down by 1, and your digit goes up by 10. The number stays exactly the same size.