Subtract whole numbers (written strategies) - With regrouping
Theory
When a top digit is too small to subtract from, borrow ten from the next column to the left. That column drops by one and the digit you are working on gains ten — subtraction with regrouping.
Regrouping, or borrowing, is what you do in subtraction when a top digit is smaller than the digit below it.
Borrow ten from the column to the left: that column drops by one, and the digit you are working on gains ten, so it is big enough to subtract.
Ten from a higher place becomes ten ones, or ten tens, in the place next door — the value is regrouped, not changed.
Borrowing moves ten from one column into the column on its right, so a small top digit becomes big enough to subtract.
| Column | Top | Borrow? | Subtract |
|---|---|---|---|
| Ones | \(2\) | yes → \(12\) | \(12-7=5\) |
| Tens | \(5\rightarrow4\) | no | \(4-3=1\) |
| Hundreds | \(6\) | no | \(6-1=5\) |
How to subtract with regrouping
- Start at the ones. If the top digit is smaller than the bottom, borrow ten from the column to the left.
- Reduce that column by one and add ten to the digit you are working on.
- Subtract the column, then move left, borrowing again if needed.
Ones: \(3-7\) needs a borrow, so \(13-7=6\).
| \(583 - 247\) | \(=\) | \(336\) |
Ones \(11-8=3\); tens \(11-4=7\).
| \(521 - 348\) | \(=\) | \(173\) |
Borrowing is needed in three columns.
| \(4325 - 1876\) | \(=\) | \(2449\) |
| \(1450 - 975\) | \(=\) | \(475\) |
Sam needs $475 more.
Common pitfalls
Frequently asked questions
What is borrowing in subtraction?
Borrowing, or regrouping, moves ten from the next column when a top digit is too small to subtract. The tens drop by one and the ones gain ten.
How do you subtract when the top digit is smaller?
Borrow ten from the column to the left. For \(652-137\) the ones become \(12\), the tens drop from \(5\) to \(4\), and \(12-7=5\).
What does borrowing do to the next column?
It reduces that column by one, because you have taken one ten (or one hundred) out of it and moved it next door.
Can you borrow more than once?
Yes. If the next column is also too small, you borrow again from further left. A borrow can chain across several columns.