# 7.10 Compare fractions

Lesson

## Ideas

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

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:

We can write this fraction as:

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:

## Compare fractions

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

### Examples

#### Example 2

Which fraction is larger?

A
B
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.

### Examples

#### Example 3

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

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