# 5.02 Mixed numbers and improper fractions

Lesson

## Ideas

Let's review how to  identify a fraction  using the shaded area of a shape.

### Examples

#### Example 1

Which of the following shows \dfrac{1}{10} of the area of the shape shaded?

A
B
C
D
Worked Solution
Create a strategy

The numerator tells us how many parts should be shaded. The denominator tells us how many parts to divide the shape into.

Apply the idea

The fraction \dfrac{1}{10} is asking for one part of the shape to be shaded out of 10 total parts. The shape in option C has 10 total parts with 1 shaded part.

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.

## Mixed numbers

How to write and read mixed numbers.

### Examples

#### Example 2

Write 2 and 2 thirds as a mixed number.

Worked Solution
Create a strategy

We can write a mixed number as: \,a\,\dfrac{b}{c} where a is the whole number, b is the number of parts we have, and c is the total number of parts.

Apply the idea

Two thirds is the same as \dfrac{2}{3} and the whole number is 2.

The mixed number is: 2\dfrac{2}{3}

Idea summary

We can write a mixed number as: \,a\,\dfrac{b}{c} where a is the whole number, b is the number of parts we have, and c is the total number of parts.

## Mixed and improper fractions

This video looks at how to change a mixed number into an improper fraction, or an improper fraction to a mixed number.

### Examples

#### Example 3

Rewrite 4\dfrac{1}{2} as an improper fraction.

Worked Solution
Create a strategy

To find the improper fraction, multiply the whole number by the denominator, then add the numerator.

Apply the idea
Reflect and check

We could also draw an array for 4\dfrac{1}{2} where each part represents \dfrac{1}{2}.

We can see that there are 9 shaded parts.

So the improper fraction is \dfrac{9}{2}.

#### Example 4

Rewrite \dfrac{11}{3} as a mixed number.

Worked Solution
Create a strategy

Divide the numerator by the denominator. The remainder will be the numerator of the mixed fraction.

Apply the idea

11 divided by 3 is 3 remainder 2.

So, \dfrac{11}{3} is made up of 3 wholes and 2 out of 3 remaining.\dfrac{11}{3}=3\dfrac{2}{3}

Idea summary

The whole number component of a mixed number tells you how many wholes there are.

### Outcomes

#### VCMNA158

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line