# 5.01 Name and identify fractions

Lesson

We've used fraction bars to help us  name and identify fractions  before. Let's try this problem to help us remember.

### 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.

## Area models

This video shows how to name and identify fractions using area models.

### Examples

#### Example 2

What fraction of the square is shaded blue?

Worked Solution
Create a strategy

Write the fraction as: \,\, \dfrac{\text{Number of shaded parts}}{\text{Total number of parts}}.

Apply the idea

There are 9 squares shaded blue and 16 squares in total.

So, the fraction shaded blue is \,\dfrac{9}{16}.

Idea summary

A fraction from an area model can be written as:\,\, \dfrac{\text{Number of shaded parts}}{\text{Total number of parts}}

## Identify fractions using number lines

This video shows how to name and identify fractions using number lines.

### Examples

#### Example 3

Plot \dfrac{1}{10} on the number line.

Worked Solution
Create a strategy

Apply the idea

Since the number line is already divided into 10 spaces, we just need to move right 1 space.

Idea summary

When plotting a fraction on a number line:

• the denominator (bottom number) shows how many parts there should be between each whole number.

• the numerator (top number) shows the number of parts to move to the right from the previous whole number.

## Mixed numbers and improper fractions

This video shows how to change a fraction written as a mixed number to an improper fraction, and also going the other way.

### Examples

#### Example 4

Rewrite \dfrac{17}{4} 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

17 divided by 4 is 4 remainder 1. This is because 4\times 4=16 and 16+1=17.

So, \dfrac{17}{4} is made up of 4 wholes and 1 out of 4 remaining.\dfrac{17}{4}=4\dfrac{1}{4}

Idea summary

To convert an improper fraction to a mixed number:

• Divide the numerator by the denominator.

• The number of times the denominator goes into the numerator is the whole part of the mixed number.

• The remainder is the numerator of the mixed number.

• The denominator stays the same.

To convert a mixed number to an improper fraction:

• Multiply the denominator and whole part.

• Add the numerator to the result.

• The final result is the new numerator.

• The denominator stays the same.