Equivalent fractions





Equivalent fractions are fractions that represent the same value or the same part of an object.

Consider the below fractions.

1/2, 2/4, 3/6, 4/8, 5/10

Each fraction represents same value 1/2. So these are equivalent to each other.

For example , consider the following diagram. Here the fractions are represented by each color,is 4/8. But each color represents only half of the whole rectangle. So 4/8 is equivalent to 1/2.

In the following rectangle, the rectangle is divided into 6 parts, and only 3 parts are colored with pink color. So the fraction representing the shaded portion is 3/6. But the colored portion represents only half of the rectangle. So 3/6 is equivalent to 1/2

     So in general Fractions having different denominators and numerators, but equal to the same value are called equivalent

How to write a fraction to the equivalent form:

To write fractions equivalent to a given fraction, we have to multiply the numerators and denominators of the given fraction by the same number.

Example 1

Write 5 fractions which are equivalent to the given fractions.
(i)1/2 (ii) 1/3 (iii) 2/5 (iv)3/7

Solution:

(i) To get a fraction which is equivalent to 1/2, let us multiply 1/2 (both numerator as well as the denominator) by, 2, 3, 4, 5 and 6.

1/2 x 2/2 = 2/4

1/2 x 3/3 = 3/6

1/2 x 4/4 = 4/8

1/2 x 5/5 = 5/10

1/2 x 6/6 = 6/12

So equivalent-fractions for 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12.

Similarly
(ii)equivalent fraction for 1/3 are 2/6, 3/9, 4/12, 5/15, 6/18

(iii)Fraction which are equivalent for 2/5 to 4/10, 6/15, 8/20, 10/50,12/30

(iv)Equivalent-fraction for 3/7 are 6/14, 9/21, 12/28, 15/35,18/42 .




Example 2

Write 5 fractions equivalent to the given fractions.(i)1/5 (ii) 2/3 (iii) 1/6 (iv)2/75

Solution:

(i) To get equivalent-fraction for 1/5, let us multiply 1/5 (both numerator as well as the denominator) by, 2, 3, 4, 5 and 6.

1/5 x 2/2 = 2/10

1/5 x 3/3 = 3/15

1/5 x 4/4 = 4/20

1/5 x 5/5 = 5/25

1/5 x 6/6 = 6/30

So equivalent-fraction for 1/2 are 2/10, 3/15, 4/20, 5/25, 6/30.

Similarly (ii) equivalent-fraction of 2/3 are4/6, 6/9, 8/12, 10/15, 12/18

(iii) Equivalent-fraction for 1/6 are 4/10, 2/12, 8/20, 10/50, 12/30

(iv) Equivalent-fraction for 3/7 are 6/14, 9/21, 12/28, 15/35, 18/42.

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