Reverse percentages

Objective. Find an original amount after a percentage change.

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

Learn: the key idea

Reverse percentages develops a connected mathematical idea rather than an isolated trick. Use multipliers to model repeated percentage change. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

After a 20% increase an amount is 480. Find the original.

1 $Identify the known information, the unknown and any conditions.$
2 $Choose a diagram, table, graph or algebraic representation that exposes the structure.$
3 $Apply the relevant rule one justified step at a time, keeping exact values where useful.$
4 $Check by substitution, inverse reasoning or estimation. The result is 400.$

Answer: 400

Concept mastery

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Practice

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Common mistake. A common error in reverse percentages is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

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