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In order to access this I need to be confident with:

Multiplying and dividing

Highest common factor

Proper fractions

This topic is relevant for:

Here we will learn about equivalent fractions including how to simplify fractions and how to work out equivalent fractions.

There are also equivalent fractions* *worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Equivalent fractions** are fractions that have the **same value**. We use equivalent fractions to write a fraction in its simplest terms. To do this we look at the **numerator **(the top number) and the **denominator **(the bottom number) and find a **common factor** to cancel. The numerator and denominator are always whole numbers.

Equivalent fractions can be used to compare fractions when they have different denominators. Knowledge of equivalent fractions can also be used to write a set of values in order of size.

Here are some examples of the concept of equivalent fractions:

This is one half:

\[\frac{1}{2}=\frac{2}{4}\]

This is two thirds:

\[\frac{2}{3}=\frac{6}{9}\]

In order to simplify fractions:

- Look at the numerator and the denominator and find the Highest Common Factor.
- Divide both the numerator and the denominator by the HCF.
- Write the fraction in its simplest terms.

In order to calculate equivalent fractions:

- Look at the denominators in both fractions and work out the multiplier.
- Multiply the numerator of one of the fractions by the multiplier.
- Complete the second fraction.

Get your free equivalent fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONGet your free equivalent fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONWrite the following fraction in its simplest form:

\[\frac{12}{14}\]

**Look at the numerator and the denominator and find the Highest Common Factor**.

The numerator of the fraction is

The denominator of the fraction is

They are both multiples of

2**Divide both the numerator and the denominator by the HCF**.

\[\frac{12}{14}=\frac{6\times2}{7\times2}\]

The HCF of

The new numerator is

3**Write the fraction in its simplest terms**.

\[\frac{12}{14}=\frac{6}{7}\]

Write the following fraction in its simplest form:

\[\frac{15}{20}\]

**Look at the numerator and the denominator and find the Highest Common Factor**.

The numerator for the fraction is

The denominator of the fraction is

They are both multiples of

**Divide both the numerator and the denominator by the HCF**.

\[\frac{15}{20}=\frac{3\times5}{4\times5}\]

The HCF of

The new numerator is

**Write the fraction in its simplest terms**.

\[\frac{15}{20}=\frac{3}{4}\]

Write the following fraction in its simplest form:

\[\frac{24}{30}\]

**Look at the numerator and the denominator and find the Highest Common Factor**.

The numerator for the fraction is

The denominator of the fraction is

They are both multiples of

**Divide both the numerator and the denominator by the HCF**.

\[\frac{24}{30}=\frac{4\times6}{5\times6}\]

The HCF of

The new numerator is

**Write the fraction in its simplest terms**.

\[\frac{24}{30}=\frac{5}{6}\]

Find the missing value of these equivalent fractions:

\[\frac{3}{5}=\frac{?}{20}\]

**Look at the denominators in both fractions and work out the multiplier**.

The denominator of the first fraction is

\[20\div5=4\]

The multiplier is

**Multiply the numerator of one of the fractions by the multiplier**.

\[3\times4=12\]

\[\frac{3}{5}=\frac{3\times4}{5\times4}\]

The missing value is

**Complete the second fraction**.

\[\frac{3}{5}=\frac{12}{20}\]

Find the missing value of these equivalent fractions:

\[\frac{2}{7}=\frac{?}{21}\]

**Look at the denominators in both fractions and work out the multiplier**.

The denominator of the first fraction is

\[21\div7=3\]

The multiplier is

**Multiply the numerator of one of the fractions by the multiplier**.

\[2\times3=6\]

\[\frac{2}{7}=\frac{2\times3}{7\times3}\]

The missing value is

**Complete the second fraction**

\[\frac{2}{7}=\frac{6}{21}\]

Find the missing value of these equivalent fractions:

\[\frac{5}{8}=\frac{?}{72}\]

**Look at the denominators in both fractions and work out the multiplier**.

The denominator of the first fraction is

\[72\div8=9\]

The multiplier is

**Multiply the numerator of one of the fractions by the multiplier**.

\[5\times9=45\]

\[\frac{5}{8}=\frac{5\times9}{8\times9}\]

The missing value is

**Complete the second fraction**.

\[\frac{5}{8}=\frac{45}{72}\]

**Write a fraction in its simplest form**

You can simplify a fraction by using any of the common factors of the numerator and the denominator of a fraction. But you may need to cancel more than once to make sure you have written the fraction in its simplest form. Using the Highest Common Factor means that you will only have to cancel once

E.g.

Write the following fraction in its simplest form.

\[\frac{20}{60}\]

\[\frac{20}{60}=\frac{2\times10}{6\times10}=\frac{2}{6}\]

But the first fraction has not been written in its simplest form as the new numerator

\[\frac{2}{6}=\frac{1\times2}{3\times2}=\frac{1}{3}\]

The fraction in its simplest form is \frac{1}{3}

**Equivalent fractions can only be made by using common factors**

You cannot make equivalent fractions by using addition.

E.g.

This is incorrect cancelling.

\[\frac{5}{10}=\frac{2+3}{7+3}=\frac{2}{7}\] ✘

This is correct cancelling.

\[\frac{5}{10}=\frac{1\times5}{2\times5}=\frac{1}{2}\] ✔

**Fractions that appear to be different can have equivalence**

E.g.

Because \frac{5}{10} and \frac{1}{2} use different numbers (they have different numerators and denominators) they appear to be different fractions, however they are actually equivalent to each other.

\[\frac{5}{10}=\frac{1\times5}{2\times5}=\frac{1}{2}\]

1. Write the following fraction in its simplest form: \frac{5}{20}

\frac{1}{4}

\frac{1}{3}

\frac{2}{5}

\frac{1}{15}

\frac{5}{20}=\frac{1\times5}{4\times5}=\frac{1}{4}

2. Write the following fraction in its simplest form: \frac{8}{24}

\frac{4}{12}

\frac{2}{6}

\frac{1}{3}

\frac{5}{12}

\frac{8}{24}=\frac{1\times8}{3\times8}=\frac{1}{3}

3. Write the following fraction in its simplest form: \frac{36}{48}

\frac{6}{8}

\frac{18}{24}

\frac{7}{12}

\frac{3}{4}

\frac{36}{48}=\frac{3\times12}{4\times12}=\frac{3}{4}

4. Find the missing value is these equivalent fractions: \frac{3}{4}=\frac{?}{24}

\frac{23}{24}

\frac{18}{24}

\frac{19}{24}

\frac{21}{24}

\frac{3}{4}=\frac{3\times6}{4\times6}=\frac{18}{24}

5. Find the missing value is these equivalent fractions: \frac{6}{7}=\frac{?}{28}

\frac{18}{28}

\frac{24}{28}

\frac{12}{28}

\frac{24}{28}

\frac{6}{7}=\frac{6\times4}{7\times4}=\frac{24}{28}

6. Find the missing value is these equivalent fractions: \frac{5}{9}=\frac{?}{63}

\frac{35}{63}

\frac{25}{63}

\frac{30}{63}

\frac{42}{63}

\frac{5}{9}=\frac{5\times7}{9\times7}=\frac{35}{63}

1. Here is a list of four fractions.

\frac{15}{20} \frac{5}{25} \frac{3}{15} \frac{2}{10}

One of these fractions is **not** equivalent to \frac{1}{5}

Write down this fraction.

**(1 mark)**

Show answer

\frac{15}{20}

**(1)**

2. Here is a list of four fractions.

\frac{18}{24} \frac{15}{20} \frac{28}{40} \frac{36}{48}

One of these fractions is **not** equivalent to \frac{3}{4}

Write down this fraction.

**(1 mark)**

Show answer

\frac{28}{40}

**(1)**

3. (a) Show that \frac{3}{5} is bigger than \frac{5}{9} .

(b) Find a fraction which is bigger than \frac{3}{5} but smaller than \frac{3}{4} .

**(4 marks)**

Show answer

(a)

\frac{3\times9}{5\times9}=\frac{27}{45} \frac{5\times5}{9\times5}=\frac{25}{45}

*for converting one fraction to an equivalent fraction*

**(1)**

*for both fractions with a common denominator*

**(1)**

\frac{3}{5}=\frac{27}{45} \frac{5}{9}=\frac{25}{45}

(b)

\frac{3\times4}{5\times4}=\frac{12}{20} \frac{3\times5}{4\times5}=\frac{15}{20}

*for converting one fraction to an equivalent fraction*

**(1)**

*for a correct answer between 0.6 and 0.75*

**(1)**

\frac{13}{20} or \frac{14}{20} or \frac{7}{10}

You have now learned how to:

- Simplify fractions
- Write an equivalent fraction for a given fraction

- Ordering fractions
- Adding fractions
- Subtracting fractions
- Improper fractions
- Using the bar model
- Mixed numbers
- Decimals

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