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
The lesson
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 £240. The shop raises the price by 15%. To find the new price in one step, multiply by 1.15 (that's 100% + 15%). £240 × 1.15 = £276.
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 £64 after a 20% discount. The sale price is 80% of the original price, so divide by 0.80 to find it: £64 ÷ 0.80 = £80.
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 £500 at 3% per year, one year's interest is £500 × 0.03 = £15, so after 4 years it's £15 × 4 = £60.
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.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.