Percentages
Fractions, decimals and percentages
The same amount, written three ways. Learn a handful of equivalences and most percentage questions become mental arithmetic.
Three ways to say the same thing
PER CENT means 'out of 100'. So a percentage is just a fraction with denominator 100. 50% = 50/100 = 1/2 = 0.5 25% = 25/100 = 1/4 = 0.25 20% = 20/100 = 1/5 = 0.2 10% = 10/100 = 1/10 = 0.1 To turn a percentage into a decimal, divide by 100. To turn a fraction into a percentage, write it with a denominator of 100.
Finding a percentage of an amount
Use the fraction you already know. 50% of 60 g = 1/2 of 60 = 30 g 20% of 60 g = 1/5 of 60 = 12 g 10% of 60 g = 1/10 of 60 = 6 g Once you have 10%, you can build almost anything: 30% is three lots of 10%, and 5% is half of 10%.
Building on a result you already have
If 30% of $70 = $21, you get others for free: 60% of $70 = 2 × $21 = $42 (double it) 15% of $70 = $21 ÷ 2 = $10.50 (halve it) 90% of $70 = 3 × $21 = $63 (triple it) Looking for a link to something you already know is usually faster than starting again.
Fractions with the same denominator
Work out one and the rest follow. 1/8 = 12.5%, so 3/8 = 3 × 12.5% = 37.5%, and 5/8 = 62.5%. The same trick works for fifths, tenths and any other family.
Worked examples
Write 50% as a fraction and a decimal
- Per cent means out of 100, so 50/100.
- Simplify to 1/2, and 50 ÷ 100 = 0.5.
Answer: 1/2 and 0.5
50% of 60 g
- 50% is 1/2.
- Half of 60 is 30.
Answer: 30 g
20% of 60 g
- 20% is 1/5.
- 60 ÷ 5 = 12.
Answer: 12 g
If 30% of $70 is $21, what is 60%?
- 60% is double 30%.
- 2 × 21 = 42.
Answer: $42
And 15% of $70?
- 15% is half of 30%.
- 21 ÷ 2 = 10.50.
Answer: $10.50
If 1/8 = 12.5%, what is 3/8?
- 3/8 is three lots of 1/8.
- 3 × 12.5 = 37.5.
Answer: 37.5%
Where you see this in real life
- A 20% discount is just a fifth off — so on a £60 coat you take away £12.
- Working out a tip: find 10% by moving the decimal point, then double it for 20%.
Key words
- Per cent
- out of 100
- Percentage
- a fraction with a denominator of 100
- Equivalent
- of equal value, written differently
- Fraction
- a part of a whole, written as one number over another
- Decimal
- a number written with a decimal point
- Convert
- change from one form into another