 # Finding Equivalent Fractions – Methods, Examples | How to find Equivalent Fractions?

Two or more fractions are said to be equivalent if they result in the same value on simplification. Let us consider two fractions $$\frac { u }{ v }$$, $$\frac { w }{ x }$$ they are said to be equivalent if they result in same value $$\frac { y }{ z }$$ on simplification.

Usually, Equivalent Fractions denote the same portion on a whole. Find details like equivalent fractions definition, how to find equivalent fractions using different methods like multiplication, division with the same numbers. Check out few solved examples on finding the equivalent fractions explained step by step in the later sections.

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### Equivalent Fractions – Definition

Equivalent Fractions are the fractions having the same value irrespective of the numerators and denominators they have. All Equivalent Fractions on reducing will result in the same value after simplification. For Example: $$\frac {3 }{ 4 }$$, $$\frac { 6}{ 8 }$$, $$\frac { 9 }{ 12 }$$, $$\frac { 12 }{ 16 }$$, etc. are all equivalent fractions.

### How to Find Equivalent Fractions?

There are two different ways to find the Equivalent Fractions and they are explained in detail below. They are as follows

• Multiply both the numerator and denominator of the fraction with the same number.
• Divide both the numerator and denominator of the fraction with the same number.

### Multiplying Numerator and Denominator of the Fraction with the Same Number

To get the Equivalent Fraction of any number simply multiply both the numerator and denominator with the same number.
Example:
Find Equivalent Fractions of the Fraction $$\frac { 1 }{ 2 }$$?
Solution:
Equivalent fraction of $$\frac { 1 }{ 2 }$$ can be obtained by multiplying with non-zero numbers.
$$\frac { 1 }{ 2 }$$*2 = $$\frac { 2 }{ 4 }$$
$$\frac { 1 }{ 2 }$$*3 = $$\frac { 3 }{ 6 }$$
$$\frac { 1 }{ 2 }$$*4 = $$\frac { 4 }{ 8 }$$, etc.

Therefore, $$\frac { 2 }{ 4 }$$, $$\frac { 3 }{ 6 }$$, $$\frac { 4 }{ 8 }$$ are all equivalent fractions of $$\frac { 1 }{ 2 }$$.

### Dividing Numerator and Denominator of the Fraction with the Same Number

To get an Equivalent Fraction of a Number simply divide both the numerator and denominator with the same value other than zero.  To divide the fraction with the same number we need to evaluate the common factors that both the denominator and numerator share and then divide with them.

Example:
Find the equivalent fractions of the fraction $$\frac { 16 }{ 24 }$$?
Solution:
To obtain the equivalent fractions of $$\frac { 16 }{ 24 }$$ we will first find the common factors that both 16, 24 share.
Common Factors of 16, 24 are 1,2,4,8
Dividing with common factors we have
$$\frac { 16 }{ 24 }$$ = $$\frac { 16÷2 }{ 24÷2 }$$
= $$\frac { 8 }{ 12 }$$
$$\frac { 16 }{ 24 }$$ = $$\frac { 16÷4 }{ 24÷4 }$$
= $$\frac { 4 }{ 6 }$$
$$\frac { 16 }{ 24 }$$ = $$\frac { 16÷8 }{ 24÷8 }$$
= $$\frac { 2 }{ 3 }$$
Therefore, equivalent fractions of $$\frac { 16 }{ 24 }$$ are $$\frac { 8 }{ 12 }$$, $$\frac { 4 }{ 6 }$$, $$\frac { 2 }{ 3 }$$, etc. and so on.

### Equivalent Fractions Examples

Example 1. Check if the following fractions are equivalent or not?   Solution:

The first figure is shaded half so representing in the fraction we have $$\frac { 1 }{ 2 }$$
In the same way, the second and third figures are given by $$\frac { 4 }{ 8 }$$ and $$\frac { 5 }{ 10 }$$
As all the figures are shaded half they are said to be equivalent fractions.
We can write $$\frac { 4 }{ 8 }$$ = $$\frac { 1 }{ 2 }$$ * 2
$$\frac { 5 }{ 10 }$$ = $$\frac { 1 }{ 2 }$$ * 5
Thus, equivalent fractions are obtained by multiplying numerators and denominators with non-zero numbers.

Example 2.
Find the Equivalent Fractions of the fraction $$\frac { 8 }{ 24 }$$?
Solution:
We can find the Equivalent Fractions of a fraction by either multiplying or dividing the fraction with the same number.
Let us find the equivalent fractions of the fraction $$\frac { 8 }{ 24 }$$ by applying division method.
$$\frac { 8 }{ 24 }$$ = $$\frac { 8÷2 }{ 24÷2 }$$
= $$\frac { 4 }{ 12 }$$
$$\frac { 8 }{ 24 }$$ = $$\frac { 8÷4 }{ 24÷4 }$$
= $$\frac { 2 }{ 6 }$$
$$\frac { 8 }{ 24 }$$ = $$\frac { 8÷8 }{ 24÷8 }$$
= $$\frac { 1 }{ 3 }$$

Therefore, Equivalent Fractions of fraction $$\frac { 8 }{ 24 }$$ are $$\frac { 4 }{ 12 }$$, $$\frac { 2 }{ 6 }$$, $$\frac { 1 }{ 3 }$$

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