# Multiplying fractions

## How do you multiply fractions?

This is really straightforward. The basic rules you need to remember are

For example, consider how to multiply fractions 1/2 and 3/4.

Multiply the numerators

1   x   3   =   3

and multiply the denominators

2   x   4   =   8

So

1/2   x   3/4   =   3/8

## What if there are 3 fractions?

For instance

2/5   x   1/3   x   5/6

Again multiply the numerators

2   x   1   x   5   =   10

and multiply the denominators

5   x   3   x   6   =   90

Therefore

1/3   x   2/5   x   5/6   =   10/90

Here you can also simplify by dividing numerator and denominator to give the equivalent fraction 1/9

i.e.  1/3  x  2/5  x  5/6  =  1/9

## Apply the same rules to multiply 4 fractions!

Let's multiply fractions

2/3          1/2          3/4          1/3

Multiplying the numerators

2   x   1   x   3   x   1   =   6

Multiplying the denominators

3   x   2   x   4   x   3   =   72

So

2/3   x   1/2   x   3/4   x   1/3   =   6/72

Divide numerator and denominator by 6 to simplify to the fraction of equivalent value 1/12

i.e.  2/3  x  1/2  x  3/4  x  1/3  =  1/12.

Notice that when you multiply fractions it’s just a matter of multiplying the numerators and multiplying the denominators, however many fractions are being multiplied!

Try to work out the following

6/7   x   1/3   x   1/2

2/3   x   1/3   x   3/2   x   1/2

2/2   x   3/8

1/2   x   2/3   x   1/2   x   1/3   x   1/2

Don’t sweat over the improper fractions (3/2 and 2/2, numerator greater than or equal to denominator) – just multiply the numerators and multiply the denominators in the usual manner.

The correct answers to the above questions in order are

(6 x 1 x 1) / (7 x 3 x 2)   =   6/42   =   1/7

(2 x 1 x 3 x 1) / (3 x 3 x 2 x 2)   =   6/36   =   1/6

(2 x 3) / (2 x 8)   =   6/16   =   3/8

(1 x 2 x 1 x 1 x 1) / (2 x 3 x 2 x 3 x 2)   =   2/72   =   1/36

## Moving on from multiplying fractions

The great news is that once you've practiced multiplying fractions, you're ready to find out how to divide fractions.

In fact, the method you've learned to multiply fractions can also be used when dividing fractions!

More more on fractions click:

What is a fraction?

Equivalent fractions

Simplifying fractions

How to subtract fractions

How to divide fractions

Improper fractions

Mixed fractions (mixed numbers)

Comparing fractions

Ordering fractions

Fraction to decimal chart

Decimal to fraction

Fraction to percent