Topics
7. Fractions
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AustraliaVIC
Level 3

7.08 Fractions with objects

Lesson
Practice
Lesson

Are you ready?

We have looked at fractions on  fraction bars  and  fractions on a number line  .

Examples

Example 1

Here is a shape divided into parts, use it to answer the following questions.

A square divided into 4 equal parts.
a

This shape has ⬚ equal parts.

Worked Solution
Create a strategy

Count the number of smaller squares that make up the big square.

Apply the idea

This shape has 4 equal parts.

b

Each part is \dfrac{⬚}{⬚} of the whole.

Worked Solution
Create a strategy

Each part looks like this:

A square divided into 4 equal parts. One part is shaded.

We can write this fraction as:

A fraction with parts explained. Ask your teacher for more information.
Apply the idea

Each part is \dfrac{1}{4} of the whole.

Idea summary

  • The numerator (top number) is the number of parts shaded to represent the fraction.

  • The denominator (bottom number) is the number of equal parts the shape is divided into.

Fractions of groups

Fractions can also be used to divide a collection of items into equal groups. To do this we use the:

  • denominator to divide the items into equal groups
  • numerator to select the number of groups

Let's watch a video to learn more:

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Examples

Example 2

Which of the following shows that \dfrac{1}{3} of these ice creams have been selected?

An image showing 12 ice creams.
A
An image showing 12 ice creams. 3 ice creams are circled.
B
An image showing 12 ice creams. 4 ice creams are circled.
C
An image showing 12 ice creams. 6 ice creams are circled.
Worked Solution
Create a strategy

For each option, think about how many groups of the same size are possible.

Apply the idea

For option A:

Three ice creams are selected, so 4 groups of 3 can be created out of 12 ice creams. So this group is \dfrac{1}{4} of the ice creams.

For option B:

Four ice creams are selected, so 3 groups of 4 can be created out of 12 ice creams. So this group is \dfrac{1}{3} of the ice creams.

For option C:

Six ice creams are selected, so 2 groups of 6 can be created out of 12 ice creams. So this group is \dfrac{1}{2} of the ice creams.

So the correct answer is Option B.

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.

Outcomes

VCMNA136

Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole

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