You already add three-digit numbers with blocks or on paper. This topic makes it quick and sure: add ones to ones, tens to tens and hundreds to hundreds. The only tricky part is what happens when a place gets to 10 or more.
Why it works
Each place is worth 10 of the place to its right. So 10 ones and 1 ten are the same amount, and so are 10 tens and 1 hundred. Trading (regrouping) does not change the total. It only lets us write the number the usual way, with one digit in each place.
Key idea
Line the numbers up by place. Add the ones first, then the tens, then the hundreds. When a place makes 10 or more, write the ones of that total and regroup 1 to the next place.
Worked example: One regroup
Find $247 + 135$.
- Ones: $7 + 5 = 12$. That is 1 ten and 2 ones. Write 2 and regroup 1 ten.
- Tens: $4 + 3 + 1 = 8$ tens. Write 8.
- Hundreds: $2 + 1 = 3$ hundreds. Write 3.
Answer: $382$
Worked example: Two regroups
Find $568 + 275$.
- Ones: $8 + 5 = 13$. Write 3 and regroup 1 ten.
- Tens: $6 + 7 + 1 = 14$ tens. That is 1 hundred and 4 tens. Write 4 and regroup 1 hundred.
- Hundreds: $5 + 2 + 1 = 8$. Write 8.
- Check: $570 + 280 = 850$, close to $843$.
Answer: $843$
Common mistake
Forgetting the regrouped ten. $247 + 135$ comes out as $372$ if the extra ten is dropped. A quick estimate catches it: $250 + 140 = 390$, and $372$ is too small.
Lining up by the left edge. In $352 + 47$, the 4 means 4 tens, so it goes under the 5, not under the 3. Lined up wrong you get $822$; lined up by place you get $399$.
Lining up by the left edge. In $352 + 47$, the 4 means 4 tens, so it goes under the 5, not under the 3. Lined up wrong you get $822$; lined up by place you get $399$.
| Place | Add | Total | Write | Regroup |
|---|---|---|---|---|
| Ones | 8 + 5 | 13 | 3 | 1 ten |
| Tens | 6 + 7 + 1 | 14 | 4 | 1 hundred |
| Hundreds | 5 + 2 + 1 | 8 | 8 | none |