# Equivalent Fractions

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

## Is 12/15 equal to 4/5?

#### Explanation:

Reducing 12/15 to lowest terms;
12/15 = (2 × 2 × 3)/(3 × 5) = 4/5

## Are 9/12 and 12/18 equal?

#### Explanation:

Reducing 9/12 to lowest terms;
9/12 = (3 × 3)/(2 × 2 × 3) = 3/(2 × 2) = 3/4
Reducing 12/18 to lowest terms;
12/18 = (2 × 2 × 3)/(2 × 3 × 3) = 2/3
Since 3/4 and 2/3 are not equal, therefore 9/12 and 12/18 are not equal.

## Find the equivalent fraction of 5/8 which has a denominator of 24?

#### Explanation:

Multiplying the fraction by 3/3 in order to get a denominator of 24:
5/8 × 3/3 = 15/24
Therefore, 15/24 is the equivalent fraction of 5/8 which has a denominator of 24.

## What is the equivalent fraction of 2/9 which has a numerator of 8?

#### Explanation:

Multiplying the fraction by 4/4 in order to get a numerator of 8:
2/9 × 4/4 = 8/36
Therefore, 8/36 is the equivalent fraction of 2/9 which has a numerator of 8.

## How to find equivalent fractions:

Multiplying the numerator and the denominator of a fraction by the same nonzero whole number will change that fraction into an equivalent fraction, but it will not change its value. Equivalent fractions may look different, but they have the same value. Let's look at some more examples of equivalent fractions.

For Example : to find equivalent fraction of 2/3 we multiply both numerator and denominator by 2 then we get equivalent fraction 4/6 .

## How to check two fractions are Equivalent fraction:

Simplify all fractions. If they reduce to be the same fraction, then the fractions are equivalent

For example : we will check the fractions fractions 6/15 and 10/50 are equivalent.

we will simplify both the fractions-

6/15= (2 * 3)/(5*3)=2/5

10/50= (2 * 5)/(2*5*5)=1/5

the fractions 2/5 and 1/5 are not same, hence fractions are not equivalent

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