# Good knowledge of multiplying fractions!

Before you start this lesson about multiplying fractions, I recommend that you become familiar with the multiplication table.

Multiplying fractions is very easy. However, I would like to introduce the topic with an interesting example about pizza.

Suppose that you bought a medium pizza and the pizza has 8 slices.

If someone eats half of your pizza, or 4 slices, you are left with
4 / 8
From the illustration below, you can also see that the leftover is the same as
1 / 2 If you decide that you are only going to eat 1 slice out of the 4 slices remaining, you are eating
1 / 4
of the leftover.

Remember that the leftover is
1 / 2
You can also argue that you only ate 1 slice out of 8 slices or
1 / 8 Thus, we can see that eating 1/4 of 1/2 is the same as eating 1/8.

Another way to get
1 / 8
is to perform the following multiplication:

 1 / 4 × 1 / 2 = 1 / 8

We get this answer by multiplying the numbers on top (numerators): 1 × 1 = 1

and by multiplying the numbers at the bottom (denominators): 4 × 2 = 8

This is an interesting result, but all you need to remember is the following:

When you multiply fractions, multiply the numerators together

Then multiply the denominators together.

Notice also that the word 'of' means multiplication.

More examples

 3 / 5 × 4 / 7 = 12 / 35

Sometimes, it is a good idea to simplify the fractions before multiplying.

Take a look at the following example:

 10 / 20 × 3 / 15

 10 / 20 can be simplified as   1 / 2

Divide the numerator and the denominator by 10

 3 / 15 can be simplified as   1 / 5

Divide the numerator and the denominator by 3

This way, it is easier to do the multiplication to get
1 / 10

Sometimes, it is a good idea to simplify the fractions before multiplying.

Take a look at the following example:

 10 / 20 × 3 / 15

 10 / 20 can be simplified as   1 / 2

After we divide the numerator and the denominator by 10

 3 / 15 can be simplified as   1 / 5

After we divide the numerator and the denominator by 3

This way, it is easier to do the multiplication to get
1 / 10

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