Topics
5. Fractions
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Australia
Year 6

5.02 Fractions of a quantity

Lesson
Practice
Lesson

Are you ready?

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?

An image showing 12 ice creams arranged in 3 rows of 4.
A
An image showing 12 ice creams arranged in 3 rows of 4. 2 ice creams are inside a rectangle.
B
An image showing 12 ice creams arranged in 3 rows of 4. 9 ice creams are inside a rectangle.
C
An image showing 12 ice creams arranged in 3 rows of 4. 6 ice creams are inside a rectangle.
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
An image showing 12 ice creams arranged in 3 rows of 4. 3 ice creams are inside a rectangle.

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

An image showing 12 ice creams. 9 ice creams are encircled.

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.

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Examples

Example 2

What is \dfrac15 of 20?

Worked Solution
Create a strategy

Divide the whole number by the denominator.

Apply the idea
\displaystyle 20\div 5\displaystyle =\displaystyle 4Divide by the denominator

\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.

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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
\displaystyle 55\div 11\displaystyle =\displaystyle 5Divide the amount by the denominator
\displaystyle 5\times 6\displaystyle =\displaystyle 30Multiply the answer by the numerator

\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

AC9M6N07

solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate

AC9M6N09

use mathematical modelling to solve practical problems, involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made

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