What are Equivalent Fractions? Definition & Examples

Fractions

Fractions are numbers that represent a part of a whole or a ratio between quantities, where the whole is divided into equal parts. The fraction consists of two parts - numerator-the top part which tells the numbers of the part used and the denominator- the bottom number which tells the total number.

For example - 2/4 where 2 represents the 2 slices of whole pizza and 4 represents all the 4 slices of pizza.

What are Equivalent fractions?

Equivalent fractions are the fraction with two numbers, one on top as numerator and the other one on bottom as denominator.  It has different fractions that have the same value of a total number but when we simplify them, they are equal to the same fraction. The fraction is one half in simple form.

For example, few fractions are ½, 5/10, 15/30 are all equivalent fractions.

Another example:

Manya and Rahul bought a cake. They decided to share the cake. Manya took 2/4 of the cake and Rahul ate 1/2 of the cake. Did they divide the cake equally? 

To find out, first we will simplify both the fractions through the LCM method. And then we see that they have shared the cake equally as both the fractions are equivalent.

How to check the equivalent fractions

1. Make the denominators same

First of all, find out the LCM of both the denominators of the fractions. Then multiply both them with the required digits to find out if they are equivalent.

For example:

Let’s check whether 2/8 and 3/12 are equivalent or not. 

a. Find out the LCM of both the denominators 8 and 12. LCM =24

b. Multiply the actual numbers with the required numbers to make the denominators same.

2x3/8x3 = 6/24 and 3x2/12x2 = 6/24

After multiplying we can find out that both the fractions are the same ie;6/24. Therefore, they are equivalent fractions

How to simplify equivalent fractions

To find out equivalent fractions, we need to multiply the fraction with the required number.

For example:

find out two equivalent fractions for ⅔.

Multiplying the numerator and denominator by 2.

⅔ x 2/2 = 4/6

Multiplying the numerator and denominator by 3.

⅔ x 3/3 = 6/9

Solved Examples

1. Find three equivalent fractions for ⅗.

Multiply 3/2 by 2

3x2/5x2 = 6/10.

Multiply 3/2 by 3,

3x3/5x3 = 9/15.

Multiply 3/2 by 4,

3x4 / 5x4 = 12/20.

Equivalent fractions for 3/5 are 6/10, 9/15, 12/20.

Equivalent Fractions Chart

Some equivalent fractions for unit fractions

1. ½ = 2/4, 3/6, 4/8, 5/10 …

2. ⅓ = 2/6, 3/9, 4/12, 5/15 …

3. ¼ = 2/8, 3/12, 4/16, 5/20…

4. ⅕ = 2/10, 3/15, 4/20, 5/25…

5. ⅙ = 2/12, 3/18, 4/24, 5/30…

6. 1/7 = 2/14, 3/21, 4/28, 5/35…

7. ⅛ = 2/16, 3/24, 4/32, 5/40

8. 1/9 = 2/18, 3/27, 4/36, 5/45

Conclusion 

Finding out equivalent fractions is simple. To find out the equivalent fraction we just need to multiply the numerator and denominator with the same required numbers.

Practice Questions

1. Find the equivalent fraction of 8/10

2. What is the simplest form of 9/81?

3. Find 3 equivalent fraction of ⅘.

4. What is the simplest form of 12/144?

5. If Ann ate 2/4 of the pizza and Maria ate ¼ of the pizza. Did they eat the equivalent part of pizza?

Frequently Asked Questions on Equivalent Fractions

Q1. What are the examples of equivalent fractions?

The examples of equivalent fractions are:

2/4 and 3/6

⅓ and 3/9

⅕ and 5/25

¾ and 12/16

Q2. What are the equivalent fractions of 5/10?

5/10 is equal to ½ after simplification. Hence, the equivalent fractions of 5/10 are:

½, 2/4, 3/6, 4/8 and so on.

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