Multi-Digit Subtraction with Regrouping
Subtract multi-digit numbers with borrowing — including across zeros — and check with addition.
1 Borrow when the top digit is too small
Subtract column by column from the right. When the top digit is smaller than what you subtract, borrow 1 from the next place — the top digit grows by 10.
73 − 28: the ones need 3 − 8, so borrow — 13 − 8 = 5, then 6 − 2 = 4.
73 − 28: ones 13 − 8 = 5; tens 6 − 2 = 4. Total 45.
2 Borrowing across zeros
You cannot borrow from 0 — keep moving left until you find a non-zero digit. 400 becomes 3 hundreds, 9 tens, 10 ones.
400 − 138: regroup 400 → 3 hundreds, 9 tens, 10 ones. Then 10 − 8 = 2, 9 − 3 = 6, 3 − 1 = 2. Total 262.
3 Check every subtraction with addition
Subtraction undoes addition: if 503 − 276 = 227, then 227 + 276 must equal 503. Always check.
503 − 276 = 227. Check: 227 + 276 = 503. Correct.
4 Multi-step word problems
Read carefully, solve one step at a time, and estimate first so you know what “close” looks like.
712 − 398 = 314. Estimate: 700 − 400 = 300 — close, so it is reasonable.
5 Common mistakes
Two borrowing traps.
Wrong: in 400 − 138, turning the tens 0 into 0. Right: borrow across: 400 → 3 hundreds, 9 tens, 10 ones.
Wrong: 73 − 28 → ones 8 − 3 = 5 (flipped!). Right: borrow first — the top digit must grow (13 − 8) before you subtract.
6 Quick checks
Try these yourself, then reveal the answer.
7 Key points and vocabulary
| Word | What it means |
|---|---|
| Borrow (regroup) | Taking 1 from the next place to make the top digit bigger by 10. |
| Difference | The result of a subtraction. |
| Check | Verifying with addition: difference + subtracted = start. |
| Across zeros | Borrowing through one or more zero digits. |
Remember
- Borrow first — the top digit must grow before you subtract.
- Borrow across zeros: 400 → 3 hundreds, 9 tens, 10 ones.
- Check with addition every time.
- Estimate first (round to hundreds) to catch big mistakes.