WHAT IS A FRACTION?

What are fractions?

If you cut an object into smaller parts you need a way of expressing what these parts are. For example, you can cut a pie into two equal pieces so that there are two halves. The two halves make up the whole pie.
You can write this mathematically as: 1 over 2 plus 1 over 2 = 1
You can also cut the pie into three equal pieces, ie thirds. The three thirds make up the whole pie. You can write another mathematical expression for this, too. 1 over 3 plus 1 over 3 plus 1 over 3 = 1
This way of expressing a part of a whole mathematically is called a fraction.
The top number (numerator) of a fraction tells how many parts there are.
The bottom number (denominator) of a fraction tells how many parts make a whole.

For example 2/5 means there were 5 parts in the whole and you have 2 of them.
There are several types of fractions.
Common fractions (also called vulgar fractions or proper fractions). This type of fraction is smaller than one but greater than zero.
1 over 5 or 2 over 3

Improper fractions are fractions where the top number (numerator) is larger than the bottom number (denominator). This means that this type of fraction is actually greater than one.
5 over 4 or 3 over 2

Mixed numbers are those where a fraction is written after a whole number.
one and one quarter
An improper fraction can be rearranged to be written as a mixed number
6 over 5 = 1 and 1 fifth
Equivalent fractions are fractions that have the same value as each other.
1 over 2 = 2 over 4 = 4 over 8

Note
If both the numerator and denominator of any fraction are multiplied by the same number the value of the fraction is unchanged.
Shows numerator and denominator being mulitiplied by 2, 3 and 4

Decimal fractions are numbers that are made up of a whole number and a decimal fraction.
A decimal fraction can be considered to be a fraction where the denominator has been divided into the numerator.
1 and 1 quarter = 5 over 4 = 5 divided by 4 = 1.25