Topics
4. Fractions
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Stage 3

4.03 Fractions of objects

Lesson
Practice
Lesson

Are you ready?

Do you know how to find a fraction of a  collection of objects  ?

Examples

Example 1

Which of the following shows that \dfrac{1}{2} of these flowers have been selected?

An image showing 16 flowers arranged in 4 rows of 4 flowers.
A
An image showing 16 flowers arranged in 4 rows of 4 flowers. 4 flowers are encircled.
B
An image showing 16 flowers arranged in 4 rows of 4 flowers. 2 flowers are encircled.
C
An image showing 16 flowers arranged in 4 rows of 4 flowers. 8 flowers are encircled.
Worked Solution
Create a strategy

Count the number of flowers and halve it.

Apply the idea

There are 16 flowers. Half of 16 is 8.

Option C has 8 flowers circled, so option C is the answer.

Idea summary

To find a fraction of an amount, use the:

  • denominator (bottom number) to divide the items into equal groups.
  • numerator (top number) to select the number of groups.

Fractions of collections

This video looks at how to use fractions to divide up a group of objects.

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Examples

Example 2

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.

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