Fractions

In GCSE we need to be able to add, subtract, multiply
and divide fractions.

This is not only important for work on fractions, it also comes into
so many areas of maths. Fractions are particularly used in Probability
and algebra. Being comfortable with and able to change fractions around
is a major tool that needs to be well learned.

We will look at the easiest first

Multiplying fractions
Just multiply the numerators together (the tops) and multiply the denominators
together (the bottoms)
Example 2/3 X 3/5 = (2X3)/(3X5) = 6/15 simplifies to 2/5 by dividing top
and bottom by 3

Dividing fractions
First we turn the second fraction upside down and then multiply the two
fractions together
Example 2/3 Divided by 3/5 = 2/3 X 5/3
Which gives us (2X5)/(3X3) = 10/9 This is known as a top heavy fraction
(it is bigger than 1)
Simplifies to 1 and 1/9

Multiply Divide fractions pdf from mathutor.ac.uk

Adding fractions
You have to first find a common denominator, best shown by an example
One of the easiest ways is to multiply the denominators together (guaranteeing
a common denominator) and then cross multiply the numerators.
Example 2/3 + 3/5 = (2X5)/(3X5) + (3X3)/(3X5) = 10/15 + 9/15 =19/15
Simplified answer 1 and 4/15

Subtracting fractions
You follow the same procedure for adding i.e. finding common denominator
etc but then just subtract numerators
Example 2/3 - 3/5 = 10/15 - 9/15 = 1/15

Add subtract fractions pdf from mathtutor.ac.uk