Functional Skills

Mathematics

Percentages 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.

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

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 % 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 so the mark in the second test was higher. 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? 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 % Dead easy, this one! Suppose we want to write 0.27 as a %.

Since a decimal is a kind of fraction, all we have to do is to multiply by 100.

You just need to remember that each time you multiply by 10 the number becomes larger by a factor of 10 so the decimal point moves one place to the right.

Multiplying by 100 moves it 2 places to the right. This neat rule is because decimals are fractions in our base ten number system.

So we find that 0.27 is the same as (0.27 x 100)% = 27%.

Similarly, 0.735 is the same as (0.735 x 100)% = 73.5%

and 7.46 is the same as (7.46 x 100)% = 746%.

RULE:-

To change a decimal to a % we multiply by 100

which just moves the decimal point 2 places to the right.

Changing a % to a decimal

(Again, dead easy!)

RULE:-

All we have to do is to divide by 100,

so move the decimal point 2 places

to the left.

Here are 3 examples to show you how to deal with all possible snags.

Example (1) What is 37 per cent% as a decimal?

Answer:- 37% per cent is the same as 0.37. Example (2) What is 25.5% per cent as a decimal?

Answer:- 25.5% is the same as 0.255. Example (3) What is 50% per cent as a decimal? Answer:- 50% per cent is the same as 0.50 = 0.5.

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# FS Maths - Percentages

To help students with percentages

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