Math · Stage 6
Reverse percentages and percentage increase / decrease (change)
Turn a percentage increase or decrease into a single multiply, work out the percentage change between two amounts, and reverse a percentage to find the original whole.
✦ Math📘 Stage 6 · S6⏱ ~15 min🧒 Ages 10–12★ Free to start
I can reverse percentages and percentage increase / decrease (change).
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Kavi and the Clever Price Tag 🏷️
The shop clipped 20% OFF every umbrella 🌂, and Kavi spots a puzzle. "A change is really just one multiply," she hoots. "20% off means you keep 80% — times 0.8. And if I only know the sale price, I can work backwards to the first price by dividing by 0.8. Grow it, shrink it, or un-change it — percentages bend both ways ⚡."
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What your child will learn
1A percentage change is one multiplyA 20% increase is the whole (100%) plus 20% more = 120% = ×1.20. A 20% decrease keeps 80% = ×0.80. One multiply does the whole job — no need to find the part and add it on separately.
2Find the percentage changeTo find a percentage change, compare the change to what you started with — never to the new amount. The rule is change ÷ original × 100.
3Reverse a percentageThe price you see is not 100%. After a discount it is less than 100%; after a rise it is more than 100%. To reverse a change, divide by the same multiplier to scale back to 100%.
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A peek inside
Increase £240 by 15%.
100% + 15% = 115% = ×1.15, so 240 × 1.15
Try this at home: Increase 60 by 20%: __
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 6 · S6 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.