Percentages (age 12+)
Solve problems involving percentage increase, percentage decrease, finding the original value after a percentage change, and calculating simple interest
What a learner can do afterwards
- Calculate a 15% increase on £240 using a decimal multiplier (× 1.15)
- Find the original price before a 20% discount resulted in a sale price of £64
- Calculate simple interest on £500 at 3% per annum for 4 years
1 · Read
To find a percentage of an amount, turn the percentage into a decimal first. 15% means 15 out of 100, so it is 0.15, and 15% of £240 is £240 × 0.15 = £36. Now you'll use that skill to increase or decrease an amount by a percentage, work backwards to find an original amount, and calculate simple interest on savings.
A jacket costs £180. The shop raises the price by 15%. To find the new price in one step, multiply by 1.15 (that's 100% + 15%). £180 × 1.15 = £207.
A decrease works the same way, but you subtract from 100% instead of adding. A 20% decrease means the new amount is 80% of the original, so you multiply by 0.80. To reverse this and find the original amount, divide the new amount by that same decimal instead of multiplying.
A jumper is on sale for £56 after a 20% discount. The sale price is 80% of the original price, so divide by 0.80 to find it: £56 ÷ 0.80 = £70.
Simple interest is money a bank pays you each year for keeping savings with them. It's always worked out on the original amount, not on any interest already added. Interest = original amount × rate × number of years. For £350 at 4% per year, one year's interest is £350 × 0.04 = £14, so after 3 years it's £14 × 3 = £42.
To change an amount by a percentage, multiply by a decimal; to find the original amount, divide by that same decimal, and simple interest is original amount × rate × years, added fresh every year.
More to read
How to Calculate Percent Change: Formula and Examples
Percent change compares the move to the start. Increase: subtract start from end, divide by start. £240 growing to £276 rises £36, and 36/240 = 15%. Decrease works mirrored: £80 falling to £64 drops £16, and 16/80 = 20%. Multipliers shortcut both: +15% is x 1.15, -20% is x 0.8. Going backwards divides instead: £64 after 20% off means 64/0.8 = £80 before. Always divide by the starting value, never the ending one.
3 Ways to Calculate Percentage Increase
Percentage increase turns growth into one multiplication. Add the percent to 100 and shift the point: +15% becomes x 1.15, so £240 x 1.15 = £276. Decreases flip below one: -10% is x 0.9, so £180 x 0.9 = £162. Simple interest repeats the same gain yearly without compounding: 3% of £500 is £15 a year, and 4 years make £60. Undo any change by dividing: £90 after 25% off is 90/0.75 = £120.
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2 · Watch
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Where this leads
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