Skip to main content
MathidiaMathematics Academy
Calculations and problem solving
Lesson 14 of 75
Challenge

Inverse operations

Objective. Use inverse operations to find missing values and check results.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Inverse operations undo each other: addition undoes subtraction, and multiplication undoes division. They help find missing numbers and check answers. For example, if □ × 6 = 42, then □ = 42 ÷ 6 = 7. To check 384 ÷ 12 = 32, multiply back: 32 × 12 = 384, so it is correct.

Worked example

Use inverse operations to find the missing number: □ × 6 − 15 = 27.

-11-8-5-1258−15
Number line from -11 to 8 with a jump of 15 backwards from 6
  1. 1Undo the last step first: the inverse of subtracting 15 is adding 15.
  2. 227 + 15 = 42, so □ × 6 = 42.
  3. 3The inverse of multiplying by 6 is dividing by 6: 42 ÷ 6 = 7.
  4. 4Check: 7 × 6 − 15 = 42 − 15 = 27 ✓

Answer: 7

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. A common mistake is using the same operation instead of its inverse, for example solving □ − 15 = 40 by doing 40 − 15 = 25. Undo subtracting 15 by adding 15: □ = 55.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard