You can round to the nearest 10 or 100, and you can add and subtract three-digit numbers. Put them together and you get a fast check: round first, do the easy math in your head, and see if your exact answer is close.
Why it works
Rounding moves each number only a little: at most 5 when you round to tens, at most 50 when you round to hundreds. So the rounded answer can only be a little off. If your exact answer is far from the estimate, something went wrong, often a missed regroup.
Key idea
Estimate = round each number, then add or subtract. The exact answer should be close to the estimate.
Worked example: An estimate
Estimate $386 + 412$ by rounding to the nearest hundred.
- $386$ rounds to $400$; $412$ rounds to $400$.
- $400 + 400 = 800$.
- The exact sum is $798$, very close.
Answer: about $800$
Worked example: Is it reasonable?
Sam says $523 - 286 = 337$. Is that reasonable?
- Round to tens: $520 - 290 = 230$.
- $337$ is about 100 away from $230$, too far.
- Redo it: $523 - 286 = 237$. Sam broke a hundred into tens but forgot to take it away from the hundreds.
Answer: No; the answer is $237$.
Common mistake
Skipping the estimate. Some people think an estimate is just a wrong answer. It is a check! For $468 + 257$, forgetting the regrouped hundred gives $625$. The estimate $470 + 260 = 730$ shows right away that $625$ is too small. The right sum is $725$.