Percentages flashcards
11 cards on Percentages: the key points, worked examples and the slips to watch. Swipe through them, or print them.
Card 1 of 11
Percentages
Fractions, decimals and percentages
How do you change between fractions, decimals and percentages?
Answer it in your head, then turn the card over.
Fractions, decimals and percentages
Key points
- Per cent means out of 100: 45% = = 0.45.
- Percentage to decimal: divide by 100. Decimal to percentage: multiply by 100.
- Fraction to percentage: divide the top by the bottom, then multiply by 100.
- Percentage to fraction: write it over 100, then simplify.
Example
: 3 ÷ 8 = 0.375, and 0.375 × 100 = 37.5%
0.07 × 100 = 7%
35% = =
Watch out
0.07 is 7%, not 70%: it takes 0.7 to make 70%.
Percentages
Equivalents to know by heart
Which fractions, decimals and percentages should you know without working them out?
Answer it in your head, then turn the card over.
Equivalents to know by heart
Key points
- = 0.5 = 50%, = 0.25 = 25% and = 0.75 = 75%.
- = 0.1 = 10%, and fifths go up in 20s: = 20%, = 40%.
- = 0.125 = 12.5%, half of a quarter.
- = 0.333… = 33.3% to 1 decimal place, and = 66.7%.
12.5% as a fraction
12.5% is half of 25%, and 25% =
So 12.5% =
Watch out
The bottom is not the percentage: is 20%, not 5%.
Percentages
Percentages of amounts without a calculator
How do you find a percentage of an amount without a calculator?
Answer it in your head, then turn the card over.
Percentages of amounts without a calculator
Key points
- Find 10% by dividing by 10, and 1% by dividing by 100.
- 5% is half of 10%, and 20% is double 10%.
- Build the percentage you want from those pieces, then add them up.
35% of £60
10% = £6, so 30% = £18
5% = half of £6 = £3
35% = £18 + £3 = £21
Watch out
Dividing by 5 finds a fifth, which is 20%. For 5%, halve 10% or divide by 20.
Percentages
Percentages of amounts with a calculator
How do you find a percentage of an amount on a calculator?
Answer it in your head, then turn the card over.
Percentages of amounts with a calculator
Key points
- Change the percentage to a decimal by dividing by 100: 17.5% = 0.175.
- Multiply the amount by that decimal.
- Check it roughly: 17.5% of £240 should be a bit under a fifth.
17.5% of £240
17.5 ÷ 100 = 0.175
0.175 × 240 = £42
Watch out
Multiplying by 1.175 gives the amount after a 17.5% rise, not 17.5% of it.
Percentages
Percentage increase and decrease
How do you increase or decrease an amount by a percentage in one step?
Answer it in your head, then turn the card over.
Percentage increase and decrease
Key points
- Use a multiplier: the percentage you end with, as a decimal.
- Increase by 12%: you end with 112%, so multiply by 1.12.
- Decrease by 15%: 85% is left, so multiply by 0.85.
- One multiplication finds the new amount: no need to work out the change and add it.
Example
£250 up by 12%: 250 × 1.12 = £280
£80 down by 15%: 80 × 0.85 = £68
Watch out
A 5% rise is × 1.05, not × 1.5 (that is a 50% rise), and a 15% fall is × 0.85, not × 0.15.
Percentages
One percentage change after another
How do you work out the effect of two percentage changes, one after the other?
Answer it in your head, then turn the card over.
One percentage change after another
Key points
- Multiply the multipliers together: never add or subtract the percentages.
- The second change is a percentage of the new amount, not the original.
- The product of the multipliers gives the overall change.
Up 10%, then down 10%
1.1 × 0.9 = 0.99, so you end with 99%
£100 → £110 → £99: an overall fall of 1%
Watch out
A 10% rise then a 10% fall is not back to the start: the fall is 10% of a bigger amount.
Percentages
Compound interest
How do you work out compound interest over several years?
Answer it in your head, then turn the card over.
Compound interest
Key points
- Each year's interest is added on, so the next year earns interest on the interest too.
- Multiply by the multiplier once for every year: a power does it in one step.
- Take the original amount away at the end if the question asks for the interest only.
Formula
amount = original × multiplier^years
£2000 at 3% a year for 4 years
2000 × 1.03⁴ = 2251.0176…
= £2,251.02 to the nearest penny
Interest = £251.02
Watch out
4 × 3% = 12% is simple interest; compound interest grows faster, because 1.03⁴ is more than 1.12.
Percentages
One amount as a percentage of another
How do you write one quantity as a percentage of another?
Answer it in your head, then turn the card over.
One amount as a percentage of another
Key points
- Divide the part by the whole, then multiply by 100.
- Put both quantities in the same units first.
- The whole is the total the part is out of: the bottom of the fraction.
Example
34 out of 40: 34 ÷ 40 × 100 = 85%
45p of £3: 45 out of 300 pence, 45 ÷ 300 × 100 = 15%
Watch out
Mixed units give nonsense: 45p of £3 is 45 out of 300 pence, not 45 out of 3.
Percentages
Percentage change, profit and loss
How do you work out a percentage change, such as a percentage profit or loss?
Answer it in your head, then turn the card over.
Percentage change, profit and loss
Key points
- Find the change: the difference between the new and the original amounts.
- Divide the change by the original amount, then multiply by 100.
- Profit is a percentage increase on the cost price; loss is a percentage decrease.
Formula
percentage change = change ÷ original × 100
Bought for £150, sold for £180
Profit = 180 − 150 = £30
30 ÷ 150 × 100 = 20% profit
Watch out
Divide by the original, never the new amount: 30 ÷ 180 gives 16.7%, which is not the profit.
Percentages
Simple interest
What is simple interest, and how do you work it out?
Answer it in your head, then turn the card over.
Simple interest
Key points
- Simple interest is worked out on the original amount only.
- So it is the same amount every year: one year's interest × the number of years.
- Add it to the original if the question asks for the total in the account.
£600 at 3% a year for 4 years
3% of £600 = £18 a year
4 × £18 = £72 interest
Total = £600 + £72 = £672
Watch out
Read whether the question wants the interest (£72) or the total in the account (£672).
Percentages
Reverse percentages
How do you find the original amount after a percentage increase or decrease?
Answer it in your head, then turn the card over.
Reverse percentages
Key points
- The amount you are given is a percentage of the original: 120% after a 20% rise, 85% after 15% off.
- Divide by the multiplier to undo the change.
- Check by multiplying your answer by the multiplier: you should get back the amount given.
Example
£70 after a 25% rise: 70 ÷ 1.25 = £56
£68 after 15% off: 68 ÷ 0.85 = £80
Check: 80 × 0.85 = 68
Watch out
Never take 20% off the new price to undo a 20% rise: £54 becomes £43.20 that way, not £45.
Print these cards
Four cards to an A4 sheet, each the size of a standard A6 revision card.
One-sided
Each card prints on one face: the question at the top, the notes under it.
Two-sided
Questions on the front, notes on the back. Print double-sided and flip on the long edge, then cut along the lines.
Put it into practice
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