 # 5.02 Fractions of a quantity

Lesson

## Ideas

Let's try this problem to review how to identify a  fraction of a group of objects.

### Examples

#### Example 1

Which of the following shows that \dfrac{3}{4} of these ice creams have been selected?

A
B
C
Worked Solution
Create a strategy

Find what \dfrac{1}{4} of the ice creams would look like and choose the option that shows 3 of the 4 equal groups.

Apply the idea

Here is 1 quarter of the ice creams. We can see that 1 quarter of the ice creams means 3 ice creams.\dfrac{1}{4}\text{ of the ice creams }=3

So 3 quarter means 3 of the 4 groups. 3 lots of 3 is 9.\begin{aligned} \dfrac{3}{4} \text{ of the ice creams } &= 3 \times 3 \\ &= 9 \end{aligned}

So the correct answer is Option B because it shows 9 ice creams selected from 12 ice creams.

Idea summary

The denominator tells us the number of equal parts that we need to divide the collection of objects into.

The numerator tells us the number of equal parts that we need to select to represent our fraction.

To find a fraction of a collection, we can first find the unit fraction of the collection, then multiply it so that we get the desired fraction.

## Unit fraction of a quantity

This video looks at finding a unit fraction of a quantity.

### Examples

#### Example 2

What is \dfrac15 of 20?

Worked Solution
Create a strategy

Divide the whole number by the denominator.

Apply the idea

\dfrac15 of 20 is 4.

Idea summary

We can quickly find the unit fraction of a whole number by dividing the whole number by the denominator.

## Fraction of a quantity

This video looks at finding a non-unit fraction of a quantity.

### Examples

#### Example 3

What is \dfrac{6}{11} of \$55? Worked Solution Create a strategy We can find the fraction of the amount by dividing the amount by the denominator, then multiplying the answer by the numerator. Apply the idea \dfrac{6}{11} of \$55 is \\$30.

Idea summary

You can find a fraction of an amount by:

• Dividing the total quantity by the denominator, then multiplying the answer by the numerator, or

• Multiplying the total quantity by the numerator, then dividing the answer by the denominator.

### Outcomes

#### MA3-7NA

compares, orders and calculates with fractions, decimals and percentages