# Equivalent Fractions

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## Equivalent Fractions

What are equivalent fractions? You may have already learnt about fractions, what they are and what they look like, but in this equivalent fractions video you will learn all about how to find and work out equivalent fractions. Below you will find an in depth explanation of equivalent fractions with examples to help. Becoming confident with equivalent fractions in year 4 and developing further on what you may have learnt in year 3 about equivalent fractions will help you become successful in mastering fractions!

## Equivalent Fractions – Definition

What does it mean when two fractions are equivalent? A simple definition for equivalent fractions is as follows:

The word equivalent means the same, so an equivalent fraction is the same fraction but written differently. Equivalent fractions are fractions that are from the same whole with numerators and denominators different from one another but identical in value.

## Identifying Equivalent Fractions

How do you find equivalent fractions? Models help us to find equivalent fractions. We can compare the value of different fractions from the same whole using models called fraction bars. Fraction bars show us whether or not the fractions are equivalent, or equal in value. When thinking about how to explain equivalent fractions, using the method: draw and label two models that show equivalent fractions, can be helpful.

Assuming the fractions are from the same whole, when two fractions are equivalent it means that their numerator and denominator are different from each other but the value of the fraction is the same.

## Equivalent Fractions – Example

Let’s begin by thinking about equivalent fractions for $\frac{1}{2}$ such as one-half and two-quarters. To determine if they are equal in value, the first step is to draw equivalent fractions models for both fractions. Represent the first fraction by shading that bar to represent one-half.

Then, represent the second fraction on a bar of identical size by shading it to represent two-quarters.

Finally, compare the shaded values of both bars to see if fractions are equivalent. Each fraction bar has the same quantity shaded, which means they are equal in value. Since they are equal in value, the fractions one-half and two quarters are equivalent. A similar method can also be used to find equivalent fractions for $\frac{3}{4}$.

Let’s try one more example using four-sixths and two-fifths to tell whether the fractions are equivalent. We will see if they are equivalent fractions with models. To determine if they are equal in value, we will draw the fraction bar to represent the first fraction. Shade that fraction bar to represent four-sixths.

Then, draw a second fraction bar of identical size to represent the second fraction. Shade that fraction bar to represent two-fifths.

Finally, compare the shaded value of both bars. Since the shaded values are different, four sixths and two fifths are not equivalent fractions.

## Equivalent Fractions – Summary of Steps

What does it mean when two fractions are equivalent? Assuming the fractions are from the same whole, when two fractions are equivalent it means that their numerator and denominator are different from each other but the value of the fraction is the same. As an introduction to equivalent fractions, we model equivalent fractions. We can compare the value of different fractions from the same whole using models called fraction bars. Fraction bars show us whether or not the fractions are equivalent, or equal in value. To determine if two fractions from the same whole are equivalent:

• First, draw and shade a fraction bar to represent the first fraction.

• Then, draw and shade another fraction bar of identical size to represent the second fraction.

• Finally, compare the shaded values of both bars.

• If they are equal in value, the fractions are equivalent.

Step # What to do
1 Draw and shade a fraction bar to
represent the first fraction.
2 Draw and shade another fraction bar of
identical size to represent the second fraction.
3 Compare the shaded values of both bars.
4 If they are equal in value,
the fractions are equivalent.

Below is an overview of some common equivalent fractions which you might encounter frequently.

Original fraction Possible equivalent fractions
Equivalent fractions for $\frac{1}{3}$ $\frac{2}{6}$ $\frac{3}{9}$ $\frac{4}{12}$
Equivalent fractions for $\frac{1}{4}$ $\frac{2}{8}$ $\frac{3}{12}$ $\frac{4}{16}$
Equivalent fractions for $\frac{1}{2}$ $\frac{2}{4}$ $\frac{3}{6}$ $\frac{4}{8}$ $\frac{5}{10}$

## Equivalent Fractions – Practice

Now that you have looked at the examples of equivalent fractions, you can do some more practise using the interactive exercises and worksheets on equivalent fractions to develop your understanding of equivalent fractions for ks2. It can be helpful to also have a look at the equivalent fractions worksheet in year 5 or year 6, to consolidate understanding. Before you know it you will be an expert at finding equivalent fractions!

## Equivalent Fractions exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Equivalent Fractions.
• ### Can you match the fraction to the picture?

Hints

Look at the numerator (top part of the fraction). It should match the amount filled in.

Look at the denominator (bottom part of the fraction). It should match the number of equal parts.

This bottle shows $\frac{3}{4}$.

The bottle is split into 4 equal parts. The milk is filled to the 3rd line.

Solution

This image shows the correct fraction for each bottle.

The denominator is the number of equal parts your whole is broken into.
The denominator in $\frac{2}{3}$ is 3
The bottle is broken into 3 equal parts.

The numerator is the number of parts shaded, filled in and taken from the whole.
The numerator in $\frac{2}{3}$ is 2 The bottle shows the milk filled to 2 of the 3 parts.

• ### Find the equivalent fraction.

Hints

Look at the fraction bar. What is equivalent to $\frac{4}{6}$ ?

Equivalent fractions show the same value.

Solution

Equivalent fractions represent the same value with different numerators and denominators .

In order to determine if fractions are equivalent, you can draw fraction bars.
Each bar should represent each fraction.
If the shaded portion of each fraction bar is equal to each other, then they are equivalent .

Even though the bottles are broken into different equal parts, because the bottles are the same size, when the milk is filled to the same height, they have the same amount.

• ### Sort the fractions into the correct label.

Hints

Equivalent fractions represent the same value.

Both rectangles have $\frac{1}{2}$ shaded and the amount shaded is the same.

Solution

Equivalent fractions represent the same value.
Equivalent fractions have different numerators and denominators.

• ### Match the fraction bar to the equivalent fraction.

Hints

Draw a fraction bar for the given fraction.

The shaded portion of the fraction bars should be the same if they are equivalent.

How many fifths are equivalent to $\frac{4}{10}$ ?

Solution

Equivalent fractions have different numerators and denominators but represent the same value.

To determine if fractions are equivalent, you can create fraction bars.

If the shaded portion for each fraction bar is the same size, that means the fractions are equivalent.

• ### Make the fractions equivalent.

Hints

Look at the fraction bars, what fraction is equivalent to two thirds?

How many sixths do you need to colour to match $\frac{2}{3}$ ?

Solution

To determine if fractions are equivalent, you can draw fraction bars.

First, show $\frac{2}{3}$ in a fraction bar.

Second, make a fraction bar divided into six equal parts.

Third, colour each sixth until it is equivalent in size to $\frac{2}{3}$ .

• ### Select which fraction is equivalent.

Hints

Draw fraction bars to determine if the fractions are equivalent.

To make fractions equivalent, the shaded part of the fraction bars should be equal.

$\frac{3}{6}$ is the same as a half. What other fraction is equivalent to a half?

Solution

Equivalent fractions are fractions with different numerators and denominators but represent the same value.

You can draw fraction bars to determine if fractions are equivalent.