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 the top and bottom of one (or more) of
the fractions by a number to make the denominators the same.
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:
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)
A note on cancelling
Fractions, of course, can often be 'cancelled down' to make them simpler. For
example, 4/6 = 2/3. You can divide or multiply the top and bottom of any
fraction by any number, as long as you do it to both the top and bottom.
However, when there is more than one term on the top and/or bottom, to cancel
you must divide every term in the top and bottom by that number.
Examples
2 + x
2
In this example, some people might
try to cancel the 2s, but you cannot do this. You would have to divide the x by
2 also, to get 1 + ˝x .
2(x + 4) = (x + 4)
4
2
Here there is only one term in the numerator (top) and
denominator (bottom) of the fraction, so you can divide top and bottom by
2.