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.