Topics
7. Fractions
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AustraliaNSW
Stage 2

7.10 Compare fractions

Lesson
Practice
Lesson

Are you ready?

Being able to identify how many equal parts are in a  fraction model  will help us compare fractions in this lesson. Let's try this problem to review.

Examples

Example 1

Here is a shape divided into parts, use it to complete the statements.

A triangle divided into 3 equal parts
a

This shape has ⬚ equal parts.

Worked Solution
Create a strategy

Count the number of smaller parts.

Apply the idea

There are 3 small triangles in the shape.

This shape has 3 equal parts.

b

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

Worked Solution
Create a strategy

One shaded part would look like this:

A triangle divided into 3 equal parts. 1 part is shaded.

We can write this fraction as:

Ask your teacher for more information.
Apply the idea

There is 1 shaded part out of 3 total parts.

Each part is \dfrac{1}{3} of the whole.

Idea summary

We can write a fraction from a fraction model as:

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

Compare fractions

This video will show us how to compare fractions using models.

Loading video...

Examples

Example 2

Which fraction is larger?

A
A pentagon divided into 5 parts and 1 part shaded and the fraction one-fifth.
B
A pentagon divided into 5 parts and 2 parts shaded and the fraction two-fifths.
Worked Solution
Create a strategy

All of the pieces are equal in size, so we need to count which shape has more shaded pieces.

Apply the idea

Option A has 1 shaded piece while option B has 2. So option B is the larger fraction.

Idea summary

To compare fractions using fraction models with the same size pieces, count the number of pieces shaded.

Complements to one whole

Let's look at finding complements to 1 whole.

Loading video...

Examples

Example 3

If I have 1 third, how many more thirds do I need to make a whole?

A triangle divided into 3 equal parts. 1 part is shaded.
Worked Solution
Create a strategy

Count the number of parts you need to shade to cover the whole shape.

Apply the idea

There are 2 more parts to be shaded to cover the whole.\text{Number of thirds} = 2

Idea summary

When comparing fractions, if the denominators are the same, then we can compare the numerators. The denominator also tells us how many parts make up one whole.

Outcomes

MA2-7NA

represents, models and compares commonly used fractions and decimals

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