Addition

The first rule of addition is that only like quantities can be added; for example, various quantities of quarters. Unlike quantities, such as adding thirds to quarters, must first be converted to like quantities as described below: Imagine a pocket containing two quarters, and another pocket containing three quarters; in total, there are five quarters. Since four quarters is equivalent to one (dollar), this can be represented as follows:

Formula:

See example 1

Adding unlike quantities

To add fractions containing unlike quantities (e.g. quarters and thirds), it is necessary to convert all amounts to like quantities. It is easy to work out the chosen type of fraction to convert to; simply multiply together the two denominators (bottom number) of each fraction.
For adding quarters to thirds, both types of fraction are converted to twelfths, thus:

See example 2

Formula:

Subtraction

The process for subtracting fractions is, in essence, the same as that of adding them: find a common denominator, and change each fraction to an equivalent fraction with the chosen common denominator. The resulting fraction will have that denominator, and its numerator will be the result of subtracting the numerators of the original fractions. For instance:

Formula (like denominators):

See example 3

Formula (unlike denominators):

See example 4

Multiplication

multiplying fractions is the easiest computation, simply multiply the numerators and the same applies for denominators regardless of the denominators being the same or not. Thus:

Formula:

OR:
See example 5

Division

Dividing two fractions is quite simple, just flip one of the fractions then perform multiplication:

Formula:

OR:

See example 6
and example 7