A multiplication answer that is ten times too big is easy to produce and hard to spot.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Round then multiply
For 32 × 48, round to 30 × 50. That is 1,500, so the real answer should be near it.
Now check
The exact answer is 1,536. That is close to 1,500, so it is believable.
Round both, then multiply
To estimate 387 × 42, round to 400 × 40 = 16,000. The exact answer is 16,254, which is close enough to confirm the calculation is in the right region. The estimate takes seconds and is worth doing every single time.
Know which way you rounded
Rounding 387 up to 400 and 42 down to 40 pulls in opposite directions, so the estimate could land on either side. Rounding both up guarantees an overestimate. Tracking the direction turns a rough check into a bound.
Estimating catches magnitude errors
The errors that matter most in multiplication are off by a factor of ten — a partial product placed in the wrong column. Those change the answer enormously, so even a crude estimate exposes them instantly.
Sometimes the estimate is the answer
If you are asked roughly how many seats a hall holds with 42 rows of 38, "about 1,600" is more useful than 1,596. Knowing when precision is not needed is a real skill, and it is why estimation is taught as a method rather than only as a check.
Step 2: Try It Yourself
Tap and try it out.
302
408
120080
24016
- 30 × 401200
- 2 × 4080
- 30 × 8240
- 2 × 816
- 32 × 481536
The four pieces cover the whole rectangle, so their areas add to 32 × 48.
Step 3: Watch an Example
One step at a time.
Watch Ana Catch a Mistake
Ana works out 32 × 48 and gets 15,360.
- Step 1
She estimates: 30 × 50 is 1,500.
Step 4: Your Turn
Practice makes it stick.
A Rough Answer
Problem 1 of 2
Estimate 41 × 29 by rounding both to the nearest ten.
The Exact One
Problem 2 of 2
Now work out 41 × 29 exactly.
Estimate, Then Check
1 of 3
Estimate 19 × 31 to the nearest ten.
2 of 3
Estimate 58 × 22 to the nearest ten.
3 of 3
Estimate 7 × 68 to the nearest ten.
Step 5: Quick Check
Show what you know.
Question 1 of 2
Estimate 38 × 21 to the nearest ten.
Question 2 of 2
What kind of mistake does an estimate catch best?
What You Learned
- Round both factors, then multiply.
- Compare the exact answer with the estimate.
- It catches answers that are the wrong size entirely.