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# Multiplying Fractions

### Multiplying Fractions

You can multiply fractions following a particular rule.

How much of this pizza is left? Give your answer as a fraction.

If you wanted to split the left-over pizza evenly between two people they would each get _______ of the remaining pizza.

A) half B) a third C) all

So two people split the left-over pizza so they each get half of the remaining pizza

You can express that with fractions like this $\frac{2}{3}\times \frac{1}{2}$

How much of the original whole pizza does each of the two people get? Give your answer as a fraction.

Each of the two people will get $\frac{1}{3}$ of the original pizza

So $\frac{2}{3} \times \frac{1}{2}=\frac{1}{3}$

What if you didn't want to split the remaining $\frac{2}{3}$ between 2 people?

What if you wanted to split it between **3 people**?

When you split between 2 people, you multiplied by $\frac{1}{2}$. If you split between 3 people, you multiply by...

In order to split the left-over pizza evenly, you can split up each of the slices into thirds

This is the same as if the pizza had originally been divided into **9 slices**.

How many slices are left of this pizza now after it has been divided into 9ths?

There are 6 remaining slices and 3 people - if each person gets the same number of slices, how many slices does each person get?

So each of the 3 people get 2 out of the 9 slices in the original pizza. How do you write that as a fraction?

So!

$\frac{2}{3} \times \frac{1}{3}=\frac{2}{9}$

Now, look only at the maths in this example

How did you actually get from $\frac{2}{3} \times \frac{1}{3}$ to $\frac{2}{9}$?

You got to the denominator $9$ by ______________ the denominators in the other fractions.

A) adding B) multiplying

You also got to the numerator $2$ in the result by ______________ the numerators in the other fractions.

So you multiply two fractions by multiplying the numerators and the denominators. How do you write that in a generalised form?

A) $\frac{a}{c} \times \frac{b}{d}=\frac{a + b}{c + d}$ B) $\frac{a}{c} \times \frac{b}{d}=\frac{a \times b}{c \times d}$

So you multiply two fractions like this

$\frac{a}{c} \times \frac{b}{d}=\frac{a \times b}{c \times d}$

What is $\frac{4}{5} \times \frac{2}{3}$? Give your answer as a **fraction**.

What is $\frac{3}{6}\times\frac{4}{3}$? Give your answer as a **fully simplified fraction**.

Sometimes you end up having to multiply numbers that aren't super easy to multiply

For example, here you are meant to multiply $21$ and $25$

There is a trick!

If you can find a number that both the **numerator of one fraction** and the **denominator of the other fraction** can be divided by, you can make the problem easier.

What is the highest number that both $10$ and $25$ can be divided by (their highest common factor)?

So you can now simplify by dividing that numerator and that denominator by $5$

$\frac{10 \div 5}{21} \times \frac{7}{25 \div 5} = \frac{2}{21} \times \frac{7}{5}$

What is the highest common factor between $7$ and $21$?

So you can now simplify further by dividing that numerator and that denominator by $7$

$\frac{2}{21 \div 7} \times \frac{7 \div 7}{5} = \frac{2}{3} \times \frac{1}{5}$

So now you have simplified $\frac{10}{21} \times \frac{7}{25}$ to $\frac{2}{3} \times \frac{1}{5}$. What is the result as a fraction?

It would also be good to simplify this problem

You need to find the **highest common factor** between the numerator of one fraction and the denominator of the other fraction.

What is the highest common factor between $14$ and $35$?

What is the highest common factor between $18$ and $12$?

So now you have simplified $\frac{14}{18} \times \frac{12}{35}$ to $\frac{2}{3} \times \frac{2}{5}$. What is the result as a fraction?

So you could simplify $\frac{14}{18} \times \frac{12}{35}$ to $\frac{2}{3} \times \frac{2}{5}$

That made it easier to work out that $\frac{14}{18} \times \frac{12}{35} = \frac{4}{15}$

Simplify $\frac{16}{24} \times \frac{4}{32}$ and give your answer as a **fully simplified fraction**.

Summary! You can multiply a fraction with another fraction

You multiply the **numerators** in the two fractions and then the **denominators**.

If the multiplication is complicated, you can try to simplify the problem

You find the **highest common factor** between the numerator in one fraction and the denominator in the other fraction.