Percentage change, multipliers and reverse percentages
The starting amount is a 100% bar. An increase makes the bar longer (120%), a decrease shorter (85%). Use the bars to find multipliers, percentage changes and original prices.
- UK: Year 8
- France: grade 8
- Germany: grade 6
- Afghanistan: grade 8
- Ukraine: grade 5
- Russia: grade 6
Guide
This studio follows the Key Stage 3 aims to "interpret percentage changes multiplicatively", including changes "greater than 100%", to solve "original value problems" and to "express one quantity as a fraction of another". The starting amount is always the 100% bar; the other bars use parts of the same size, so a 120% bar is longer. The number beside each bar is its percentage of the starting amount.
A 20% increase makes the new amount 120% of the old one, so we multiply by 1.2. A 15% decrease leaves 85%: multiply by 0.85. This number is the multiplier.
In an original value problem we know the price after the change. After 20% off, the sale price is 80% of the original, so 1% is the sale price ÷ 80 and 100% is a hundred times that.
Common slips: using 0.2 as the multiplier for a 20% increase; thinking that +10% then −10% gets back to the start; dividing the change by the new value instead of the original; adding 20% of the sale price to find the original; and writing "one quantity as a fraction of another" upside down.