Topics
5. Fractions
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AustraliaNSW
Stage 3

5.06 Equivalent fractions

Lesson
Practice
Lesson

Are you ready?

Can you  identify the size of a fraction from a diagram  ?

Examples

Example 1

Below is a fraction bar.

A fraction bar divided into 3 equal parts with 1 shaded part.

What is the fraction of the coloured piece?

A
\dfrac{2}{3}
B
\dfrac{3}{4}
C
\dfrac{1}{4}
D
\dfrac{1}{3}
Worked Solution
Create a strategy

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

Apply the idea

There is 1 shaded part and 3 total parts in the fraction bar. So the fraction is \dfrac{1}{3}.

The correct option is D.

Idea summary

When writing fractions using fraction bars:

  • The denominator shows the number of equal parts the whole is divided into.
  • The numerator shows how many parts are shaded.

Equivalent fractions

This video looks at equivalent fractions up to one whole.

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Examples

Example 2

Fill in the blank to find an equivalent fraction to \dfrac{3}{6}:\dfrac{3}{6}=\dfrac{1}{⬚}

Worked Solution
Create a strategy

To find the equivalent fraction, divide the denominator by the same number as the numerator.

Apply the idea

Notice that 3\div 3=1 in the numerator. Since we divided the top number by 3, we need to divide the bottom number by 3 as well.

\displaystyle \dfrac{3\div 3}{6\div 3}\displaystyle =\displaystyle \dfrac{1}{⬚}Divide the denominator by 3
\displaystyle =\displaystyle \dfrac{1}{2}

So, we have:\dfrac{3}{6}=\dfrac{1}{2}

Idea summary

To find an equivalent fraction, we can divide the numerator and denominator by the same number.

Create equivalent fractions

This video shows us how to create an equivalent fraction.

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Examples

Example 3

Fill in the blank to find an equivalent fraction to \dfrac{5}{8}:\dfrac{5}{8}=\dfrac{50}{⬚}

Worked Solution
Create a strategy

To find the equivalent fraction, multiply the denominator by the same number as the numerator.

Apply the idea

Notice that 5\times 10=50 on the numerator. Since we multiply the top number by 10, we need to multiply the bottom number by 10 as well.

\displaystyle \dfrac{5\times 10}{8\times 10}\displaystyle =\displaystyle \dfrac{50}{⬚}Multiply the denominator by 10
\displaystyle =\displaystyle \dfrac{50}{80}

So, we have:\dfrac{5}{8}=\dfrac{50}{80}

Idea summary

To find an equivalent fraction, we can multiply the numerator and denominator by the same number.

Equivalent fractions with mixed numbers

This video shows us how to handle equivalent fractions with mixed numbers.

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Examples

Example 4

Complete the table with the improper fractions that are equivalent in value to 2 \dfrac{1}{6}.

Mixed NumberImproper fractionEquivalent fraction
\text{}\\ 2\dfrac{1}{6}\text{}\\ \dfrac{⬚}{6}\text{}\\ \dfrac{⬚}{18}
Worked Solution
Create a strategy

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

To find an equivalent fraction, multiply both the numerator and the denominator by the same number.

Apply the idea

First we convert 2 \dfrac{1}{6} to an improper fraction:

\displaystyle 2\dfrac{1}{6}\displaystyle =\displaystyle \dfrac{2\times 6+1}{6}Multiply 2 by 6 and add 1
\displaystyle =\displaystyle \dfrac{13}{6}Find the numerator

To complete the equivalent fraction in the table, we need to multiply the numerator by 3 since 6 \times 3 =18.

\displaystyle \dfrac{13\times 3}{6\times 3}\displaystyle =\displaystyle \dfrac{⬚}{18}Multiply the numerator by 3
\displaystyle =\displaystyle \dfrac{39}{18}

Completing the table, we have:

Mixed NumberImproper fractionEquivalent fraction
2\dfrac{1}{6}\dfrac{13}{6}\dfrac{39}{18}
Idea summary

To find an equivalent fraction for a mixed number, first convert the mixed number to an improper fraction, then multiply (or divide) both the numerator and the denominator by the same number.

Outcomes

MA3-7NA

compares, orders and calculates with fractions, decimals and percentages

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