Albert Teen YOU ARE LEARNING:  Multiplying Fractions  # Multiplying Fractions ### Multiplying Fractions

You can multiply fractions following a particular rule.

1

How much of this pizza is left? Give your answer as a fraction.  2

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  3

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 $\frac{2}{3}\times \frac{1}{2}$ 4

How much of the original whole pizza does each of the two people get? Give your answer as a fraction.  5

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

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

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? 2

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

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. 4

How many slices are left of this pizza now after it has been divided into 9ths?  5

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

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?  7

So!

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

Now, look only at the maths in this example

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

You got to the denominator $9$ by ______________ the denominators in the other fractions.  3

You also got to the numerator $2$ in the result by ______________ the numerators in the other fractions.  4

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) $\frac{a}{c} \times \frac{b}{d}=\frac{a \times b}{c \times d}$  5

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. 1

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 $25$ 2

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. 3

What is the highest number that both $10$ and $25$ can be divided by (their highest common factor)?  4

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

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

What is the highest common factor between $7$ and $21$?  6

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

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

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?  1

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. 2

What is the highest common factor between $14$ and $35$?  3

What is the highest common factor between $18$ and $12$?  4

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?  5

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. 1

Summary! You can multiply a fraction with another fraction

You multiply the numerators in the two fractions and then the denominators. 2

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. 