How to Check Your Arithmetic Answers
Even experienced mathematicians make arithmetic mistakes. The habit of checking your work is what separates careful, reliable maths from careless errors. Here are four proven methods.
Method 1 – Use the Inverse Operation
After any calculation, apply the inverse operation to verify the result. If you get back to your starting number, the answer is correct.
| Original calculation | Check using inverse | Correct? |
|---|---|---|
| 48 + 35 = 83 | 83 − 35 = 48 ✓ | Yes |
| 7 × 9 = 62 | 62 ÷ 9 = 6.8... ✗ | No — should be 63 |
| 144 ÷ 12 = 12 | 12 × 12 = 144 ✓ | Yes |
Method 2 – Estimation Check
Before or after calculating, estimate the answer using rounded numbers. If your exact answer is far from the estimate, you probably made an error.
Calculate 47 × 8 = 376. Check: 50 × 8 = 400. 376 is close to 400 — reasonable. ✓
If you got 47 × 8 = 3760, the estimate of 400 reveals the error immediately. ✗
Method 3 – Digit Sum (Casting Out Nines)
Add all digits of each number until you reach a single digit. Apply the same operation to these single digits and check the result matches the digit sum of your answer.
Check 34 × 12 = 408: 3+4=7, 1+2=3, 7×3=21, 2+1=3. Digit sum of 408: 4+0+8=12, 1+2=3 ✓
Method 4 – Redo the Calculation a Different Way
Rearrange the calculation or use a different strategy. If both approaches give the same answer, confidence is high.
Calculate 6 × 24 = 144. Redo as 24 × 6 = 24 + 24 + 24 + 24 + 24 + 24 = 144 ✓
When to Check
- Always check in examinations where marks are at stake.
- When the answer will be used in further calculations — one error cascades.
- When dealing with money, measurements or important quantities.
Key Takeaways
- The most reliable check is to apply the inverse operation.
- An estimation check quickly reveals wildly incorrect answers.
- Digit sums catch many multiplication errors.
- Build checking into your workflow — do not treat it as optional.
Practice Questions
- Check 95 − 38 = 57 using an inverse operation.
- Use estimation to check whether 63 × 7 = 441 is reasonable.
- Use the digit sum method to check 25 × 14 = 350.
- A student calculated 1200 ÷ 4 = 48. Use estimation to identify the error.
- Why is checking answers important even when you feel confident?