What you will learn
- Estimate a sum or difference by rounding to the nearest hundred.
- Decide if an answer is reasonable.
- Check addition by subtracting, and subtraction by adding.
Good mathematicians always check their work. In this lesson you will learn two checks. An estimate tells you if an answer is about right. The inverse tells you if it is exactly right.
Estimate first
To estimate, round each number to the nearest hundred, then add or subtract. You learnt rounding in Lesson 4. If your real answer is close to the estimate, it is reasonable.
Worked example 1
Is 3 482 + 2 615 = 6 097 reasonable?
Show me how
3 482 rounds to 3 500. 2 615 rounds to 2 600.
3 500 + 2 600 = 6 100.
6 097 is close to 6 100, so the answer is reasonable.
Watch out! A common mistake
Sam says 4 718 − 1 293 = 2 425. The estimate is 4 700 − 1 300 = 3 400. Sam’s answer is about 1 000 too small, so it cannot be right. The correct answer is 3 425. Do not skip the estimate just because the working looks neat.
Use the inverse
Addition and subtraction are inverse operations: one undoes the other. To check an addition, take one number away from the answer. You should get the other number. To check a subtraction, add your answer to the number you took away. You should get the first number.
Worked example 2
Check 2 768 + 1 459 = 4 227
Show me how
Subtract: 4 227 − 1 459.
4 227 − 1 459 = 2 768.
You got back 2 768, so the addition is right.
| Th | H | T | O | |
|---|---|---|---|---|
| 34 | 112 | 112 | 177 | |
| − | 1 | 4 | 5 | 9 |
| 2 | 7 | 6 | 8 |
Worked example 3
Check 6 004 − 2 378 = 3 626
Show me how
Add: 3 626 + 2 378.
3 626 + 2 378 = 6 004.
You got back 6 004, the number you started with, so the subtraction is right.
Which check should I use?
An estimate is quick and catches big mistakes, like a missing thousand. The inverse takes longer but catches small slips too. If someone says 2 768 + 1 459 = 4 237, the estimate (2 800 + 1 500 = 4 300) looks fine, but the inverse shows 4 237 − 1 459 = 2 778, not 2 768. There is a mistake of 10. In a test, estimate every answer and use the inverse when you have time.
Try it
TRY ITIs it reasonable?
Round to the nearest hundred, judge answers and choose the number sentence that checks a sum.
TRY ITCheck it with the inverse
Someone has worked out a sum. Undo it in columns and see if you get back the number you started with.
Let’s practise
Work out each one in your copybook. Open Hint if you are stuck, then open Show answer to check your working.
1. Estimate 4 386 + 2 517 by rounding to the nearest hundred.
Hint
Round each number first.
Show answer
4 400 + 2 500 = 6 900
2. Estimate 7 812 − 3 274.
Hint
7 812 rounds to 7 800.
Show answer
7 800 − 3 300 = 4 500
3. Is 3 609 + 2 785 = 5 394 reasonable?
Hint
Estimate: 3 600 + 2 800.
Show answer
No. The estimate is 6 400. The answer is 6 394.
4. Write a subtraction to check 1 846 + 2 375 = 4 221.
Hint
Start with the answer.
Show answer
4 221 − 2 375 = 1 846
5. Write an addition to check 8 000 − 3 465 = 4 535.
Hint
Add the answer to the number taken away.
Show answer
4 535 + 3 465 = 8 000
6. Jo says 5 230 − 1 875 = 3 455. Use the inverse to check.
Hint
Work out 3 455 + 1 875.
Show answer
3 455 + 1 875 = 5 330, not 5 230, so Jo is wrong. The answer is 3 355.
7. A shop had 2 450 bottles of juice and got 1 675 more. Kofi says there are now 4 125. Check him two ways.
Hint
Estimate, then use the inverse.
Show answer
Estimate 2 500 + 1 700 = 4 200, close. 4 125 − 1 675 = 2 450. Kofi is right.
8. What should you get when you check 6 318 − 2 904 = 3 414 by adding?
Hint
Add 3 414 and 2 904.
Show answer
6 318
Quiz
Lesson quiz: 10 questions
Answer every question, then press Check my answers. Score 8 or more to earn the Answer Checker badge.
Checking answers: worksheet
Name: ____________________ Date: ______________
Part A: Let’s practise
1. Estimate 4 386 + 2 517 by rounding to the nearest hundred.
2. Estimate 7 812 − 3 274.
3. Is 3 609 + 2 785 = 5 394 reasonable?
4. Write a subtraction to check 1 846 + 2 375 = 4 221.
5. Write an addition to check 8 000 − 3 465 = 4 535.
6. Jo says 5 230 − 1 875 = 3 455. Use the inverse to check.
7. A shop had 2 450 bottles of juice and got 1 675 more. Kofi says there are now 4 125. Check him two ways.
8. What should you get when you check 6 318 − 2 904 = 3 414 by adding?
Part B: Quiz
1. Round to the nearest hundred and estimate 3 482 + 2 615.
(a) 6 100
(b) 6 000
(c) 6 097
(d) 5 100
2. Round to the nearest hundred and estimate 6 790 − 2 310.
3. 3 000 is a reasonable answer for 1 999 + 2 001.
True or False? Circle one: True / False
4. Which number sentence checks 3 456 + 1 278 = 4 734?
(a) 4 734 − 1 278 = 3 456
(b) 4 734 + 1 278 = 3 456
(c) 3 456 − 1 278 = 4 734
(d) 1 278 − 3 456 = 4 734
5. Which number sentence checks 7 000 − 2 645 = 4 355?
(a) 4 355 + 2 645 = 7 000
(b) 4 355 − 2 645 = 7 000
(c) 7 000 + 2 645 = 4 355
(d) 2 645 − 4 355 = 7 000
6. Kim says 5 316 + 2 489 = 7 805. To check, work out 7 805 − 2 489.
7. Ben says 4 600 − 1 850 = 2 850. The inverse shows he is wrong.
True or False? Circle one: True / False
8. Which answer to 2 897 + 3 104 is reasonable?
(a) 6 001
(b) 5 001
(c) 7 001
(d) 9 001
9. Lisa checks 6 004 − 2 378 = 3 626 by adding 3 626 + 2 378. What should she get?
10. Which mistake can an estimate miss?
(a) An answer that is 10 too big
(b) An answer that is 1 000 too big
(c) Leaving out the thousands
(d) Adding instead of subtracting
Answers (for the adult)
Part A
1. 4 400 + 2 500 = 6 900
2. 7 800 − 3 300 = 4 500
3. No. The estimate is 6 400. The answer is 6 394.
4. 4 221 − 2 375 = 1 846
5. 4 535 + 3 465 = 8 000
6. 3 455 + 1 875 = 5 330, not 5 230, so Jo is wrong. The answer is 3 355.
7. Estimate 2 500 + 1 700 = 4 200, close. 4 125 − 1 675 = 2 450. Kofi is right.
8. 6 318
Part B
1. (a) 6 100
2. 4 500
3. False
4. (a) 4 734 − 1 278 = 3 456
5. (a) 4 355 + 2 645 = 7 000
6. 5 316
7. True
8. (a) 6 001
9. 6 004
10. (a) An answer that is 10 too big
Recap
- Estimate by rounding each number to the nearest hundred.
- An answer close to the estimate is reasonable. One far away is wrong.
- Check addition by subtracting from the answer.
- Check subtraction by adding the answer to the number taken away.
- Estimates catch big mistakes. The inverse catches small ones too.
Words to know
- estimate
- A close guess worked out with rounded numbers.
Example: My estimate for 398 + 205 is 600. - reasonable
- Makes sense and is close to the estimate.
Example: 6 097 is a reasonable answer for 3 482 + 2 615. - inverse
- The operation that undoes another one.
Example: Subtraction is the inverse of addition. - check
- Make sure an answer is right.
Example: I check my sum by subtracting. - exact
- Completely correct, not an estimate.
Example: The exact answer is 6 097.
Try it at home
- At the shop, estimate the total of three items before you pay. Compare your estimate with the bill.
- Mini project: an adult writes five sums with answers, and gets one or two wrong on purpose. Use estimates and the inverse to find the wrong ones.
Test tips
Tips for class tests
- Estimate first. If your answer is far from the estimate, work it again.
- If there is time at the end of a test, check with the inverse.
- Show the check in your working. Teachers like to see it.
For parents and teachers
After this lesson, your child should be able to:
- estimate sums and differences by rounding to the nearest hundred;
- decide if an answer is reasonable;
- check addition with subtraction and subtraction with addition.
Rounding was taught in Lesson 4 and the column method in Lessons 7 and 8. Praise your child for checking, even when the first answer was right.
Quiz scores and badges are saved only in this browser on this device. Nothing is sent anywhere. If the browser data is cleared, or another device is used, the badges will be lost.
Previous: Subtracting 4-Digit Numbers – Standard 3 Maths
Next: Money Problems: Bills, Best Buy, Profit and Loss – Standard 3 Maths
Course: Standard 3 Maths
Updates
2026/11/04
– First version of this lesson.
Attributions to media used in this post:
Citizen SLD-100NR calculator.jpg – LoMit – CC BY-SA 4.0 (via Wikimedia Commons)
© 2026 Vedesh Kungebeharry. All rights reserved.
[…] Checking Answers: Estimation and the Inverse – Standard 3 MathsNext: Multiplication Facts to 10 × 10 (coming soon)Course: Standard 3 […]