# Maths

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If you get  out of  in a test, you can write your score as .

expressed as a fraction of  is .

Similarly, if there are  socks in a drawer and  of them are blue, of the socks are blue.

expressed as a fraction of  is . We can put this into its simplest form by dividing the top and bottom numbers by , so we get .

Fractions can be illustrated by dividing a shape into equal parts, and shading a certain number of these parts. The bottom number is the number of equal parts that diagram has been cut into, and the top number is the number of equal parts that has been shaded.

Cutting the cake into six equal pieces and eating two is equivalent to cutting the cake into three equal pieces and eating one. You eat the same amount of cake in both cases.

When writing equivalent fractions, do the same multiplication or division to the top and bottom numbers. For example, if you multiply the top by 2, you must also multiply the bottom by 2.

You know that:

and  have a common factor, namely , so  can be written as  (divide the top and the bottom by ).

and  have a common factor, namely , so  can be written as (divide the top and the bottom by ).

However,  and  have no common factors, so  cannot be simplified. When a fraction cannot be simplified we say that it is its simplest form.

A whole number can be written as , etc.

So  can be written as:

# Mixed numbers

is known as a mixed number, because it is made up of a whole number and a fraction.

# Improper fractions

is called an improper fraction, because the top number is bigger than the bottom number.