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Numbers, units and arithmetic
Numbers, units and arithmetic

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3.11 Multiplication of fractions

Multiplication by a whole number is really just repeated addition, 4 × 3 is 4 times 3:

In the same way,

Just add the numerators since the denominators are the same.

You may have noticed that the answer is the same as if you had multiplied the numerator of by 4:

Now look at an example where two fractions are multiplied.

Example 22

Isaac and Jasmine are helping themselves to some pizza. Isaac takes of the pizza and gives of this portion to Jasmine. How much pizza does Jasmine get?

Answer

She gets of , which just means .

Isaac's portion is of the pizza. Divide the (i.e. ) into 4 portions and Jasmine gets 3 of them. Each piece is of the whole pizza, and three of these pieces constitute of the whole pizza. So the answer is that Jasmine gets three twelfths of the pizza. The calculation to which this corresponds is

Notice that , so an equivalent answer is that Jasmine gets a quarter of the pizza.

Notice that in the example above, when multiplying two fractions together you could just multiply the numerators and multiply the denominators, i.e.

This is true in general.

To give the answer in its simplest form, divide top and bottom by the common factor 3 to give

You can confirm from the diagram above that Jasmine's share is a quarter of the whole pizza. There is a quicker way of getting to the answer in its simplest form, known as cancelling. Look again at the fraction

Divide top and bottom by 3, and show this by crossing off, or cancelling, the threes,

To multiply fractions, multiply the denominators together and the numerators together, cancelling any factors which the numerators and denominators have in common.