Checking Answers Using Inverse Operations
One of the most valuable habits in mathematics is checking your answer using the inverse operation. It takes seconds and catches mistakes before they matter.
The Checking Rules
| Original operation | Check using |
|---|---|
| Addition: a + b = c | c − b = a (or c − a = b) |
| Subtraction: a − b = c | c + b = a |
| Multiplication: a × b = c | c ÷ b = a (or c ÷ a = b) |
| Division: a ÷ b = c | c × b = a |
Worked Examples
Addition Check
438 + 267 = 705. Check: 705 − 267 = 438 ✓
Multiplication Check
34 × 27 = 918. Check: 918 ÷ 27 = 34 ✓
Division with Remainder
157 ÷ 9 = 17 r 4. Check: 17 × 9 + 4 = 153 + 4 = 157 ✓
Estimating as a Quick Check
Before the inverse check, always estimate. If your answer differs wildly from the estimate, recheck before wasting time on the inverse.
438 + 267 ≈ 440 + 270 = 710. Answer 705 is close ✓
Key Takeaways
- Always check using the inverse operation.
- For division with remainder: quotient × divisor + remainder = dividend.
- Estimate first; if the answer is wildly off, a major error occurred.
- Checking takes 10 seconds and saves embarrassment.
Practice Questions
- Calculate 564 + 378 and check using subtraction.
- Calculate 803 − 547 and check using addition.
- Calculate 48 × 23 and check using division.
- Calculate 1,440 ÷ 12 and check using multiplication.
- Calculate 256 ÷ 7 (including remainder) and check.