Reverse Percentages
This topic covers 4 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- What Are Reverse Percentages?
Find the original amount before a percentage change - Reverse From Increase
Work backwards from a percentage increase - Reverse From Decrease
Work backwards from a percentage decrease - Challenge — Complex Reverse Problems
Multi-step reverse percentage problems
Common Mistakes
- Adding the percentage back on instead of dividing (e.g. "The price after a 20% increase is £60, so the original was £60 − 20% = £48")
After a 20% increase, the new price IS 120% of the original. So you divide by 1.2, not subtract 20%. £60 ÷ 1.2 = £50. The original was £50, because £50 + 20% of £50 = £60. - Using the wrong multiplier for a decrease (e.g. dividing by 1.3 instead of 0.7 when the price dropped by 30%)
A 30% decrease means the sale price is 70% of the original, so you divide by 0.7, not 1.3. If the sale price is £35, the original was £35 ÷ 0.7 = £50.
Tips for Parents
- Use shop sales as a starting point: "This jacket is £36 after a 10% discount. What was the original price?" Help your child see that £36 is 90% of the original, so divide by 0.9.
- Draw a bar model: draw a whole bar labelled 100%, shade the percentage that remains, and label the known amount. It makes the division step much clearer.
- Practise turning percentage changes into multipliers: a 25% increase means ×1.25, a 15% decrease means ×0.85. This is the key skill for reverse work.
- Try real examples from online shopping: "This phone was reduced by 20% and now costs £320. What was it before?" Work it out together before checking.
Key Words
- Reverse percentage — Working backwards from a result to find the original amount before a percentage change was applied.
- Multiplier — The decimal you multiply by to apply a percentage change — 1.15 for a 15% increase, 0.85 for a 15% decrease.
- Original amount — The starting value before the percentage increase or decrease was applied.
- Percentage increase — When a value goes up by a given percent — a 20% increase on £50 gives £60.
- Percentage decrease — When a value goes down by a given percent — a 20% decrease on £50 gives £40.
Where This Fits
Before this topic: Children should be confident finding a percentage of an amount and calculating percentage increases and decreases.
After this topic: Reverse percentages lead to more complex financial maths including compound interest, repeated percentage change, and algebraic approaches to growth and decay.
How MathCraft Teaches This
In MathCraft, Reverse Percentages is taught through the Number & Fractions adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 4 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Reverse Percentages with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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