Inverse Operations Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Inverse Operations.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Pairs of operations that undo each other: addition/subtraction and multiplication/division are inverse pairs.

Adding 5 then subtracting 5 brings you back to where you started.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Inverse operations let us isolate unknowns and solve equations.

Common stuck point: Squaring and square root are inverses (mostly—watch for \pm).

Sense of Study hint: Ask yourself: what was done to the number? Then do the opposite operation to undo it.

Worked Examples

Example 1

easy
Show that adding and subtracting the same number leaves you where you started: start with 15, add 8, then subtract 8. What do you get?

Solution

  1. 1
    Start: 15.
  2. 2
    Add 8: \(15 + 8 = 23\).
  3. 3
    Subtract 8: \(23 - 8 = 15\).
  4. 4
    You are back to 15. This shows \(a + b - b = a\).

Answer

15 (back to the start)
Addition and subtraction are inverse operations. Adding then subtracting the same number always returns you to the original value.

Example 2

medium
You start with a mystery number. You multiply it by 6 and get 54. Use the inverse operation to find the mystery number.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Start with 20. Subtract 7, then add 7. What is the result? What property does this show?

Example 2

medium
A number divided by 4 equals 8. What is the number? Use inverse operations.
← Back to Inverse Operations Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

additionsubtractionmultiplicationdivision