Multi-Digit Addition with Regrouping
Add two- and three-digit numbers with regrouping — and understand why carrying works.
1 Add column by column, right to left
Line up the ones columns, then add ones, tens, hundreds — always starting at the right.
Write the carried digit small above the next column — never skip it.
58 + 37: ones 8 + 7 = 15 (write 5, carry 1); tens 5 + 3 + 1 = 9. Total 95.
2 Carrying means regrouping
When a column reaches 10, regroup: 15 ones = 1 ten + 5 ones. The 1 moves left; the 5 stays.
247 + 186: ones 7 + 6 = 13 (3, carry 1); tens 4 + 8 + 1 = 13 (3, carry 1); hundreds 2 + 1 + 1 = 4. Total 433.
3 Why regrouping works
Place value is the reason: 10 ones are 1 ten. Carrying does not change the total — it just repacks it.
305 + 297: ones 5 + 7 = 12 (2, carry 1); tens 0 + 9 + 1 = 10 (0, carry 1); hundreds 3 + 2 + 1 = 6. Total 602.
4 Estimate first, then compute
Round to hundreds before you add: 487 + 312 ≈ 500 + 300 = 800. If your exact answer is far from 800, recheck.
487 + 312 = 799 — close to the estimate 800, so it is reasonable.
5 Common mistakes
Two regrouping traps.
Wrong: 58 + 37 = 85 (the carried 1 vanished from the tens). Right: write the carried digit small above the next column — 5 + 3 + 1 = 9, so 95.
Wrong: stacking 45 over 327 starting at the left edge. Right: align the ones column; the 5 sits under the 7.
6 Quick checks
Try these yourself, then reveal the answer.
7 Key points and vocabulary
| Word | What it means |
|---|---|
| Regroup | Trading 10 of one place for 1 of the next. |
| Carry | Moving the regrouped ten to the next column. |
| Column | A vertical place-value line: ones, tens, hundreds. |
| Estimate | A rounded, close-enough answer used to check work. |
Remember
- Right to left: ones, then tens, then hundreds.
- Write the carried digit small above the next column — never skip it.
- Align ones, not left edges.
- Estimate first to catch big mistakes.