3.5.2 Multiplying fractions

The expression ‘three times two’ just means there are three lots of two (i.e. 2 + 2 + 2). So multiplying by a whole number is just a form of repeated addition. For example,

three multiplication two equals sum with 3 summands two plus two plus two

This is equally true if you are multiplying a fraction by a whole number:

equation sequence part 1 three multiplication four divided by five equals part 2 sum with 3 summands four divided by five plus four divided by five plus four divided by five equals part 3 12 divided by five

We could write the 3 in the form of its equivalent fraction three divided by one and it is then clear that the same answer is obtained by multiplying the two numerators together and the two denominators together:

equation sequence part 1 three divided by one multiplication four divided by five equals part 2 three multiplication four divided by one multiplication five equals part 3 12 divided by five

In fact, this procedure holds good for any two fractions.

To multiply two or more fractions, multiply numerators (top lines) together and also multiply the denominators (bottom lines) together.

So

equation sequence part 1 two divided by five multiplication three divided by seven equals part 2 two multiplication three divided by five multiplication seven equals part 3 six divided by 35

Sometimes cancelling is possible:

 Previous : 3.5 Doing calculations with fractions
3.5 Doing calculations with fractions
Next : 3.5.3 Dividing fractions 
3.5.3 Dividing fractions