 # 7.09 Order and count with fractions

Lesson

## Ideas

You have previously looked at how to  represent fractions with models  . Lets practise identifying fractions given the area model below.

### Examples

#### Example 1

What fraction is shown here?

Worked Solution
Create a strategy

We want to use a fraction to say how much of the shape is shaded. A fraction is written as:

\dfrac{\text{number of shaded parts}}{\text{total number of parts}}

Apply the idea

There are 7 shaded parts and 9 total parts.\text{Fraction}=\dfrac{7}{9}

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.

## Order and count fractions

Watch this video to learn about counting and ordering fractions in words, symbols and pictures.

### Exploration

Using the geogebra applet, slide the slider to find out the fraction you want.

The numerator (top number) tells us how many parts are shaded. The denominator (bottom number) tells us how many parts the shape is divided into.

### Examples

#### Example 2

Georgia was counting fractions in the thirds. Fill in the gaps for her.

Worked Solution
Create a strategy

Count the number of parts that are shaded in the middle triangle.

Apply the idea

#### Example 3

Order these fractions from smallest to largest.

Worked Solution
Create a strategy

Write each fraction with the same denominator.

Apply the idea

2 fifths is equal to \dfrac{2}{5}.

The shape has 5 parts and 3 are shaded. So it represents the fraction \dfrac{3}{5}.

So we have to order the fractions: \dfrac{1}{5}, \, \dfrac{3}{5}, \, \dfrac{2}{5}.

1 is the smallest numerator, then 2 and then 3. So the fractions in order are: \dfrac{1}{5}, \, \dfrac{2}{5}, \, \dfrac{3}{5}.

The order of the original fractions is:

Idea summary

Remember to count up all the pieces to find the denominator, not just the unshaded ones. Count the shaded pieces to find the numerator.

### Outcomes

#### MA2-7NA

represents, models and compares commonly used fractions and decimals