Borrowing (also called regrouping) is what you do when a digit on top is too small to subtract the digit below it. You take one from the next place to the left, which is worth ten in this place.
Try it with your own problem ↓
The steps
- Line up the numbers so ones are over ones, tens over tens, and so on. The bigger number goes on top.
- Start at the ones column. If the top digit is at least as big as the bottom digit, subtract and move left.
- If the top digit is smaller, borrow: cross out the digit to its left and reduce it by 1, then add 10 to your small digit.
- If the digit to the left is 0, go further left to a digit that isn't zero, and borrow from it. Each 0 along the way becomes 9.
- Subtract each column, then check by adding the answer to the number you subtracted.
A worked example
Work out 5,003 − 1,278.
- Ones: 3 is smaller than 8, and the tens and hundreds are 0, so reach left to the thousands.
- Borrow from the 5: the thousands become 4 and the hundreds become 10. Borrow 1 hundred: the hundreds are 9 and the tens are 10. Borrow 1 ten: the tens are 9 and the ones are 13.
- Ones: 13 − 8 = 5.
- Tens: 9 − 7 = 2.
- Hundreds: 9 − 2 = 7.
- Thousands: 4 − 1 = 3.
5,003 − 1,278 = 3,725. Check: 3,725 + 1,278 = 5,003. ✓
Common mistakes
- Subtracting the smaller digit from the bigger. Don't turn 3 − 8 into 8 − 3. Borrow instead.
- Forgetting to reduce the digit you borrowed from. After borrowing, that digit is one less.
- Leaving a zero as 0 in the middle. When you borrow through zeros, each one becomes 9.
- Putting the smaller number on top. Subtraction is not the same in both directions.
Questions people ask
Why does borrowing work?
One ten is the same as ten ones, so taking 1 from the tens column and adding 10 to the ones column doesn't change the number. It just rewrites it so you can subtract.
How do I borrow when there is a zero?
Move left past the zeros to the first digit that is not zero, borrow from it, and pass the value down: each zero in between becomes 9, and the last one becomes 10 for the column that needed it.
Is borrowing the same as regrouping or trading?
Yes. Different books use different words for the same move.
Keep learning
Show The Steps is free, with no accounts or ads, and everything is worked out in your own browser. Start at the home page.