# Equivalent  Fractions

Equivalent fractions : The fractions having the same value are called equivalent-fractions.

There are two ways of obtaining equivalent-fractions.

1) By multiplying its numerator and denominator by the same number.

Example :

Write 3 equivalent-fractions of 2/3.

Solution :
2 2 x 2 4
--- = ----- = ----
3 3 x 2 6
So 4/6 is the 1st equivalent-fraction of 2/3 .

2nd equivalent-fraction is (2 x 3)/(3 x 3) = 6/9

3rd equivalent-fraction is ( 2 x 4)/(3 x 4) = 8/12

Some more examples :

Example : Write two equivalent-fractions of 7/5

Solution :
To get first equivalent-fraction of 7/5,
multiply both numerator and denominator by 2
(7 x 2)/(5 x 2) = 14/10

To get 2nd equivalent-fraction of 7/5,
multiply both numerator and denominator by 3
(7 x 3) / (5 x 3) = 21/15

So
two equivalent-fractions of 7/ 5 are 14/10 and 21/15.

Note : To find equivalent-fractions, multiply the numerator and denominator first by 2,3,4,…so on

To check whether the two fractions are equivalent then use the following method.

The product of the numerator of the 1st and the denominator of the 2nd is equal to the product of the denominator of the 1st and the numerator of the 2nd .

In example 1) you can see that products are equal so 2/5 and 6/15 are equivalent-fractions.

In example 2) you can see that products are not equal so they are not equivalent-fractions.
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Practice

1) Write 4 equilvatent-fractions of 3/8

2) Write 3 equilvatent-fractions of 1 ½.

3) Write 2 equilvatent-fractions of 3 ⅛.

4) Write 4 equilvatent-fractions of -2 ⅓.

5) Write 2 equilvatent-fractions of -7/6.

Fraction

Types of Fractions
Conversion of improper to mixed fraction
Equivalent Fractions
Fractions in Simplest form
Like and Unlike Fractions