You have subtracted three-digit numbers by breaking a ten or a hundred apart. Now we do it on paper, one place at a time, and check the answer by adding.
Why it works
$352$ is 3 hundreds, 5 tens and 2 ones. It is also 3 hundreds, 4 tens and 12 ones: we only broke one ten into ten ones. The amount is the same, but now there are enough ones to take 8 away. Regrouping changes how the number is shown, never how much it is.
Key idea
Start with the ones. If the top digit is smaller than the bottom digit, break 1 from the next place into 10. Then subtract each place. Check by adding your answer to the number you took away.
Worked example: Regroup twice
Find $352 - 178$.
- Ones: 2 is less than 8. Break 1 ten into 10 ones: now 4 tens and 12 ones. $12 - 8 = 4$.
- Tens: 4 is less than 7. Break 1 hundred into 10 tens: now 2 hundreds and 14 tens. $14 - 7 = 7$.
- Hundreds: $2 - 1 = 1$.
- Check: $174 + 178 = 352$.
Answer: $174$
Worked example: Regroup once
Find $645 - 281$.
- Ones: $5 - 1 = 4$.
- Tens: 4 is less than 8. Break 1 hundred: now 5 hundreds and 14 tens. $14 - 8 = 6$.
- Hundreds: $5 - 2 = 3$.
- Check: $364 + 281 = 645$.
Answer: $364$
Common mistake
Taking the smaller digit from the larger one. For $352 - 178$, some people do $8 - 2$, $7 - 5$ and $3 - 1$ and get $226$. But the 2 ones are on top; you cannot take 8 from 2 without regrouping. The add-back check shows the slip: $226 + 178 = 404$, not $352$.
Another way: count up from the smaller number. From $178$, add 22 to reach $200$, then 152 more to reach $352$. $22 + 152 = 174$.