Inverse Operations — Working Backward (Grades 5–6)
Every operation has an opposite that undoes it: addition ↔ subtraction, multiplication ↔ division. Inverse operations are how you solve equations — and how you work backward from an answer to a starting number. If a number was multiplied by 5 to get 20, divide by 5 to get back to 4. To reverse a chain of steps, undo them in the opposite order.
Understanding inverse operations — working backward
Every operation has an opposite that undoes it: addition ↔ subtraction, multiplication ↔ division. Inverse operations are how you solve equations — and how you work backward from an answer to a starting number. If a number was multiplied by 5 to get 20, divide by 5 to get back to 4. To reverse a chain of steps, undo them in the opposite order.
Key Idea
Every operation has an opposite that undoes it: addition ↔ subtraction, multiplication ↔ division. Inverse operations are how you solve equations — and how you work backward from an answer to a starting number. If a number was multiplied by 5 to get 20, divide by 5 to get back to 4. To reverse a chain of steps, undo them in the opposite order.
Seeing it in action
Worked example
A number had 5 added, giving 12. What was it?
Adding was done, so undo with subtraction: 12 − 5 = 7.
Undo addition with subtraction.
Worked example 2
A number was multiplied by 3, then 2 was added, giving 14. Find it.
Undo in reverse: 14 − 2 = 12, then 12 ÷ 3 = 4.
Try a few
A number ×4 = 28. The number?
A number −3 then ×2 = 10. The number?
A number ÷2 = 9. The number?
Function Foundry
A calm pre-algebra game for function machines, inverse operations, and solving for an unknown.
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