Estimating differences

To estimate a difference, round each number to the nearest 10 or 100, then subtract the rounded numbers.

What estimating a difference means

An estimate is an answer that is close enough, found quickly. We estimate a difference when we only need roughly how much more or how many are left, or to check an exact answer.

To estimate 82 − 37: round 82 to 80 and 37 to 40. Then 80 − 40 = 40. The exact answer is 45, which is close, so the estimate did its job.

We write “about 40” or use the sign ≈: 82 − 37 ≈ 40.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

808590halfway82
82 is nearer to 80 than to 90, so it rounds to 80.
303540halfway37
37 is nearer to 40, so it rounds to 40. Estimate: 80 − 40 = 40.
200250300halfway287
To the nearest 100, 287 is nearer to 300.

How to round

  1. Find the two tens (or hundreds) the number sits between. 37 is between 30 and 40.
  2. Look at the digit to the right of the place you round to.
  3. 5 or more rounds up; 4 or less rounds down. 37 has 7 ones, so it rounds up to 40.

Round both numbers to the same place before subtracting.

Round, then subtract

Change the numbers and the place. Compare the estimate with the exact answer.

Nearest 10 or nearest 100?

Rounding to a bigger place is quicker but less accurate. For 642 − 287:

Subtraction estimates can be further off than addition estimates, because when one number rounds up and the other rounds down, the errors add together instead of cancelling. If an estimate seems far off, round to a smaller place.

A neat trick is to round only the number taken away: 642 − 287 ≈ 642 − 290 = 352. That is often very close and still easy.

When to estimate

In grade 3, the standards ask children to judge whether answers are reasonable using estimation (3.OA.D.8). “Estimate first” is one of the best habits to build.

Estimating in real life

Most real subtraction is estimation: how much money will be left after shopping, how many more days until a birthday, how much further to drive. Ask your child for an estimate first in these moments, then work out the exact answer together if it matters.

Quiz: estimate the difference

Round each number, then subtract the rounded numbers.

Where this fits: subtraction step by step

  1. What is subtraction
  2. Subtraction within 10
  3. Counting back
  4. Subtraction on a number line
  5. Counting up
  6. Fact families
  7. Make 10 subtraction strategy
  8. Subtraction within 20
  9. Subtracting tens and hundreds
  10. 2-digit subtraction
  11. Subtraction with regrouping
  12. 3-digit subtraction
  13. Subtracting across zeros
  14. Mental subtraction strategies
  15. Checking subtraction with addition
  16. Missing number subtraction
  17. Estimating differences (this page)
  18. Multi-digit subtraction
  19. Subtraction word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “About how much is 82 − 37? What ten is 82 close to?” (80.)
  2. “And 37?” (40.)
  3. “So about how much is the difference?” (80 − 40 = 40.)
  4. “Now work it out exactly.” (45.) “Is 45 close to 40?” (Yes!)
  5. “If you got 55, what would the estimate tell you?” (That it is wrong.)

More worked examples

Example 1: 2-digit: 91 − 48

91 rounds to 90 and 48 rounds to 50. 90 − 50 = 40. (Exact: 43.)

Example 2: 3-digit: 734 − 281

To the nearest 100: 700 − 300 = 400. To the nearest 10: 730 − 280 = 450. (Exact: 453.)

Example 3: checking an answer: 612 − 389 = 323?

Estimate: 600 − 400 = 200. 323 is far from 200, so check again. The correct answer is 223.

Example 4: money: ₹500 − ₹268

Round 268 to 270: 500 − 270 = 230. About ₹230 left. (Exact: ₹232.)

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. Round 67 to the nearest 10.
  2. Estimate 78 − 33.
  3. Estimate 92 − 46.
  4. Round 451 to the nearest 100.
  5. Estimate 845 − 312 to the nearest 100.
  6. Estimate 703 − 498 to the nearest 100.
  7. Is 84 − 29 = 65 reasonable?
  8. A book has 312 pages. Raj has read 189. About how many are left?
  9. Stretch: estimate 5,280 − 1,960 to the nearest 1,000.
Show the answers
  1. 70
  2. 80 − 30 = 50
  3. 90 − 50 = 40
  4. 500
  5. 800 − 300 = 500
  6. 700 − 500 = 200
  7. No: about 80 − 30 = 50; exact 55
  8. About 300 − 200 = 100 (exact 123)
  9. 5,000 − 2,000 = 3,000

Common mistakes

Rounding the wrong wayRounds 37 down to 30 because 3 is the first digit.Fix: look at the ones digit: 7, so round up to 40.
Working out the exact answer insteadWrites 82 − 37 = 45 when asked to estimate.Fix: an estimate uses the rounded numbers: 80 − 40 = 40.
Rounding to different placesRounds 642 to 600 and 287 to 290.Fix: round both to the same place, or round only the number taken away.

How to teach it at home

How much is left?

At the shop, estimate the change before paying.

Distance left

On a trip, estimate how many kilometres are left from road signs.

Guess then check

Before every written subtraction, ask for an estimate and write it beside the problem.

By grade

More for each grade: Grade 3 math and the CBSE class 3 maths guide; Grade 4 math and the CBSE class 4 maths guide.

Worksheets and practice

3-digit subtraction worksheet, page 1

3-digit subtraction worksheet: printable PDF with an answer key. · Make a fresh test

Subtraction practice · subtraction speed test · subtraction chart · subtraction for kids

Last reviewed

Questions parents ask

How do you estimate a difference?

Round each number to the nearest 10 or 100, then subtract the rounded numbers. 82 − 37 is about 80 − 40 = 40.

Why is my estimate far from the exact answer?

When one number rounds up and the other rounds down, the errors add up. Round to a smaller place, or round only the number taken away.

Should you round to the nearest 10 or 100?

Round to the place that keeps the numbers easy. Nearest 10 is closer; nearest 100 is quicker for 3-digit numbers.

Why is estimating differences useful?

It checks whether an answer makes sense and answers everyday questions like how much money will be left.

What grade learns estimating differences?

Grade 3 rounds to 10 or 100 and estimates (3.NBT.A.1, 3.OA.D.8). Grade 4 rounds to any place (4.NBT.A.3).