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1. October 4, 2012
Percentages
2. Expressing one quantity
as a percentage of another.
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2. Explanation October 4, 2012
Sometimes you need to find out what percentage one
quantity is of another.
What is 10p as a percentage of £1?
100 100010 10%
× = =
1 100
100
You may see right away that it is 10%, but when you
have less obvious quantities, you need to write the first
quantity as a fraction of the second.
Then use any of the methods you have learnt to change
this fraction into a percentage.
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3. Example October 4, 2012
You may need to work out which is the denominator.
What percentage of £4 is £1.25?
12500 31.25%
100 125
× =400 =
1 400
What percentage of 1.5 litres is 600 millilitres?
millilitres
600 100 60000
× = = 40%
1500 1500
1convert to millilitres
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4. Example October 4, 2012
You can use this technique to work out percentage
increase and decreases.
A showroom tries to sell a car for £8995. After three
months, they drop the price to £7000. What percentage
decrease is this, to two significant figures?
8995 – 7000 = 1995 × 100 = 22%
8995 1
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5. Explanation October 4, 2012
A percentage of a number can be worked out by
converting the percentage to a fraction or decimal.
In a sale, a shop is selling a bed for 30% less.
The original price was £800. What is
the new price?
30% = 30
100
800 × 30 = 800 × 0.30 = 240
100
800 – 240 = 560
The bed now costs £560
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6. Example October 4, 2012
The cost of a zone 1 ticket on the London Underground
is increasing 20%, from £1.20. What is the new price?
20
120 × = 120 × 0.2 = 20
100
120 + 20 = 140
The cost of a new ticket is £1.40
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7. Explanation October 4, 2012
You can shorten the process of adding a percentage by
using a multiplier method.
Adding 50% to a biscuit is the
same as working out what
100% and another 50% is.
This makes 150% of one biscuit.
150
150% is the same as which is the same as 1.5
100
So
To add 50% to an amount, multiply it by 1.5
To add 35%, multiply by 1.35
To add 80%, multiply by 1.8
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8. Explanation October 4, 2012
You can also shorten the process of subtracting a
percentage by using a multiplier method.
Subtract 25% from a biscuit.
You need to remove the
percentage you are
decreasing by, from 100%.
100% – 25% = 75% which is the same as 75 = 0.75
100
So
To subtract 25% from an amount, multiply it by 0.75
To subtract 35%, multiply by 0.65
To add 80%, multiply by 0.2
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