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
You already know how to find a percentage of an amount. 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.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.