Inverse Operations — Working Backward (Grades 5–6)
Every operation has an opposite that undoes it: addition ↔ subtraction, multiplication ↔ division.
Understanding inverse operations — working backward
In algebra, that pairing is the tool for getting a letter on its own. In x + 5 = 12, 5 was added to x, so subtract 5 from both sides: x = 7. In 5n = 20, n was multiplied by 5, so divide both sides by 5: n = 4. Whatever you do to one side, you do to the other, so the equation stays balanced.
Seeing it in action
Worked example
A number had 5 added, giving 12. What was it?
As an equation: n + 5 = 12. Adding was done, so subtract 5 from both sides: n = 12 − 5 = 7.
Undo addition with subtraction.
Worked example 2
A number was multiplied by 3, then 2 was added, giving 14. Find it.
As an equation: 3n + 2 = 14. Undo the last step first: subtract 2 from both sides (3n = 12), then divide both sides by 3: n = 4.
A common mistake, and the fix
Undoing the steps in the same order they were done.
For “multiplied by 3, then 2 was added, giving 14”, dividing by 3 first gives 14 ÷ 3, which isn’t even a whole number. Undo the last step first: 14 − 2 = 12, then 12 ÷ 3 = 4, and check by running the steps forward: 4 × 3 + 2 = 14.
Try a few
A number ×4 = 28. The number?
A number −3 then ×2 = 10. The number?
undo ×2 first: 10 ÷ 2 = 5, then 5 + 3.
A number ÷2 = 9. The number?
Function Foundry
A calm pre-algebra game for function machines, inverse operations, and solving for an unknown.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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