Percentages one of another

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1. October 4, 2012
Percentages
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2. Expressing one quantity
as a percentage of another.

2. October 4, 2012
Sometimes you need to find out what percentage one
quantity is of another.
What is 10p as a percentage of £1?
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.
100
10
Then use any of the methods you have learnt to change
this fraction into a percentage.
×
1
100
=
100
1000
=10%
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Explanation

3. October 4, 2012
What percentage of £4 is £1.25?
125
400
×
1
100
=
400
12500
=31.25%
What percentage of 1.5 litres is 600 millilitres? 1.5 litres600 millilitres
600
1500 convert to millilitres
100
1
× =
60000
1500
=40%
You may need to work out which is the denominator.
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Example

4. 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
8995
100
1
=× 22%
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Example

5. October 4, 2012
In a sale, a shop is selling a bed for 30% less.
The original price was £800. What is
the new price?
800 =
30
100
×
A percentage of a number can be worked out by
converting the percentage to a fraction or decimal.
800×0.30=240
800 – 240 =560
30% =
30
100
The bed now costs £560
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Explanation

6. 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?
120 =× 120×0.2=20
20
100
120 + 20 = 140
The cost of a new ticket is £1.40
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Example

7. 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%is the same as
150
100
which is the same as1.5
To add 50% to an amount, multiply it by 1.5
So
To add 35%, multiply by
To add 80%, multiply by
1.35
1.8
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Explanation

8. October 4, 2012
You can also shorten the process of subtracting a
percentage by using a multiplier method.
You need to remove the
percentage you are
decreasing by, from 100%.
Subtract 25% from a biscuit.
100% – 25%=75% 75
100
=0.75
To subtract 25% from an amount, multiply it by 0.75
So
which is the same as
To subtract 35%, multiply by
To add 80%, multiply by
0.65
0.2
Explanation
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