11+ Maths: Using Inverse Operations to Check Answers

19 October 2026

Why check answers using inverse operations

Checking answers with the inverse operation is a simple but powerful habit. It helps children spot mistakes quickly and build confidence in their maths. For 11+ preparation, this skill is especially useful, as it encourages careful, independent work.

Key insight: The inverse operation means doing the opposite, for example, checking addition with subtraction, or multiplication with division.

Addition and subtraction checks

If your child solves an addition problem, they can check it by subtracting one of the numbers from their answer. For example, if 438 + 267 = 705, then 705 − 267 should return 438. The same principle works in reverse for subtraction: check 705 − 267 = 438 by adding 267 back to 438, which should give 705.

Key insight: This method works for any addition or subtraction problem, no matter how large the numbers.

Multiplication and division checks

Multiplication and division are also inverse operations. If your child calculates 34 × 27 = 918, checking with division means 918 ÷ 27 should give 34. For division, such as 157 ÷ 9 = 17 remainder 4, you can check by multiplying 17 × 9 and adding the remainder: 153 + 4 = 157.

Key insight: For division with a remainder, always add the remainder back after multiplying.

Estimate before checking

Before using the inverse operation, encourage your child to estimate the answer. Rounding numbers and making a quick estimate helps spot major errors before spending time on a detailed check. For example, 438 + 267 is close to 440 + 270, which is about 710. If the answer is very different from the estimate, it's worth rechecking the calculation.

Key insight: Estimating first saves time and helps children develop number sense.