Column subtraction
Column subtraction is a written method for subtracting numbers too big to do in your head. Line the numbers up by place value, subtract one column at a time from the ones, and exchange 1 from the next column when the top digit is smaller.
Key facts
- Line up the digits by place value: ones under ones, tens under tens (and decimal points under each other).
- Always start with the ones column, on the right.
- Subtracting: if the top digit is smaller, exchange 1 from the next column (1 ten becomes 10 ones).
- Across zeros, exchange from the first non-zero column and work back: 4,000 − 1,236 needs the zeros to become 9s.
- Check: answer + number taken away = the number you started with.
- Estimate first by rounding each number; if your answer is far from the estimate, check your working.
Worked examples
Example 1
473 − 156
- Line up the hundreds, tens and ones.
- Subtract the ones, then the tens, then the hundreds. 473 − 156 = 317
Answer: 317
Example 2
625 − 258
- Line up the hundreds, tens and ones.
- Subtract the ones, then the tens, then the hundreds. 625 − 258 = 367
Answer: 367
Example 3
742 − 386
- Ones: 2 is less than 6, so exchange a ten. The 4 tens become 3. Then 12 − 6 = 6.
- Tens: 3 is less than 8, so exchange a hundred. The 7 hundreds become 6. Then 13 − 8 = 5.
- Hundreds: 6 − 3 = 3.
- Answer: 356
Answer: 356
Example 4
5,003 − 1,847
- Ones: 3 is less than 7, but there are no tens or hundreds to exchange.
- Exchange from the thousands. 5,003 becomes 4 thousands, 9 hundreds, 9 tens and 13 ones.
- Ones: 13 − 7 = 6
- Tens: 9 − 4 = 5
- Hundreds: 9 − 8 = 1
- Thousands: 4 − 1 = 3
- Answer: 3,156
Answer: 3,156
Example 5
A computer game needs 5,000 points to reach the next level. Mia has 2,875 points. How many more points does she need?
- Line up the thousands, hundreds, tens and ones.
- Subtract the ones, then the tens, then the hundreds, then the thousands, exchanging when the top digit is smaller. 5,000 − 2,875 = 2,125
Answer: 2,125