# Fractions, Ratios and Percentages

Fractions, ratios and percentages all ways of expressing proportions. This means they show the relationship between two or more numbers.

## Fractions

The term "fraction" means that a quantity is part of a whole and is the result of dividing the whole number into a number of equal parts. As an example, if you say that you have eaten one quarter of a cake (written as 1/4 or ¼) then you are dividing the cake into four equal parts (the bottom number) and saying you have eaten one of those parts (the top number). After you have taken your fraction (¼), three of the four quarters will remain - so you can describe the remains as three-quarters or ¾. The numbers ¼ and ¾ are examples of fractions.

Fractions can be written in two different ways: one quarter can be written as ¼ or 1/4. Due to the limitations of HTML and how it displays information on the web, we will generally use the second method - especially for large numbers. If you are writing out your calculations on paper or in a word processing package you may find it easier and more readable to use the first method (¼).

Most fractions can be written in a variety of equivalent forms. As another example, two quarters of the cake can be written as 2/4 (meaning two of the four equal parts) which is the same amount as one half of the cake - 1/2. As a result of this 1/2 and 2/4 are said to be "equivalent fractions."

Fractions are usually expressed with the smalled possible whole numbers on the top and bottom - for example instead of 2/4 it would be more common to see 1/2. Working out the equivalent fraction with the smallest numbers is a case of finding numbers that can be divided into both the top number and the bottom number. For example: 80/400 = 16/80 = 4/20 = 2/10 = 1/5- meaning these are all equivalent fractions. In this example we first divided by 5 to get 16/80, then by 4 to get 4/20, then by 2 to get 2/10 and by 2 again to get 1/5. As mentioned before, although these are all equal fractions it is more normal to show this as the smallest (1/5).

Working out an eqivalent fraction with the smallest numbers can be done step by step as shown here. In this approach it is best to start with simple numbers like 10, 5 and 2. If the first numbers end in a 0, starting with a division by 10 is often a good way to bring them into a manageable size.