Fractions

Introduction
1/2 means 1 divided by 2. If you try this on a calculator, you will get an answer of 0.5 . 3/6 means 3 divided by 6. Using a calculator, you will find that this too gives an answer of 0.5 . That is because 1/2 = 3/6 = 0.5 . Fractions such as 3/6 can be cancelled. You can divide the top and bottom of the fraction by 3 to get 1/2 .
With fractions, you are allowed to multiply or divide the top and bottom of the fraction by some number, as long as you multiply (or divide) everything on the top and everything on the bottom by that number.
So 5/12 = 10/24 (multiplying top and bottom by 2).

Adding and subtracting fractions
To add two fractions, the bottom (denominator) of the two fractions must be the same. 1/2 + 3/2 = 4/2 ; 1/10 + 3/10 + 5/10 = 9/10 . If the denominators are not the same, multiply or divide the top and bottom of one of the fractions by a number to make the denominator the same as the other.

Example:
5  +  2  =  5  +  4  =  9  =  3
6      3      6       6      6      2

The same is true when subtracting fractions.

Multiplying fractions
This is simple, just multiply the two numerators (top bits) together, and the two denominators together:

2  ×  5   =    10   =   5
3      8         24       12

Dividing Fractions
If A, B, C and D are any numbers,

A  divided by C   =    A multiplied by D
B                    D         B                        C

So:
1  ÷   2  =    1  ×  3   =  3
2       3        2       2       4

Harder examples
These rules work even when the fractions involve algebra.

2x  ÷  x  =  2x  ×   3  =   6x  =   6      (the x's cancel)
5       3       5       x       5x      5

(See algebraic fractions section for harder examples)

© Matthew Pinkney