# Percentages

Basic stuff on how percentages work
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What is a percentage?
A percentage is the top part of a fraction whose bottom part is 100.
So 50% means 'half of' and 25% means 'a quarter of'. 100% means the complete quantity.
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Why bother with them?
Percentages are useful because they make it very easy to compare things.
For example, suppose the marks in two successive tests are 67/80 and 51/60. It is not very easy to say which of these was best. Percentages use our ordinary number system of 10's, 100's etc and, because they are out of 100 rather than 10, we avoid a lot of the decimal points which make some people twitchy.
Changing a fraction to a %
Taking the example of the test mark of 67 out of 80,
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Multiplying both sides of this equation by 100 gives us
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RULE:- to change a fraction to a %, multiply it by 100.
Question:- What is the second test mark of 51/60 as a %? Try this yourself before looking.
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so the mark in the second test was higher.

**Update** (Jan 2004)   I've had some emails asking for help to turn a single number into a percentage. It can't be done! You have to know as a percentage of what.
For example, a drinks bill of £20 for a party costing £80 in total means that the drinks cost 20/80 or 1/4 or 25% of the total. The £20 on its own can't be turned into a percentage.
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Changing a % to a fraction
RULE:- You simply turn it into a fraction by writing it over 100.
Then cancel down if possible.
Example:- What is 35% as a fraction?
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cancelling down to the simplest form by dividing the top and bottom by 5.
*** Remember that the value of a fraction remains unchanged when you multiply or divide both the top and the bottom by the same number. ***
Changing a decimal to a %