# Properties of Equivalent Fractions

The properties of equivalent fractions are discussed here step-by-step.

1. If the numerator and denominator of a fraction is multiplied by the same number, except zero, the value of the fraction remains the same and an equivalent fraction is obtained.

As:

(i) 2/3 = 2 x 2/3 x 2 = 4/6; 2 x 3/3 x 3 = 6/9; 2 x 4/3 x 4 = 8/12;

2 x 5/3 x 5 = 10/15

So, 2/3, 4/6, 6/9, 8/12, 10/15, etc., are equivalent fractions.

(ii) 5/6 = 5 x 3/6 x 3 = 15/18; 5 x 7/6 x 7 = 35/42; 5 x 4/6 x 4 = 20/24;

5 x 9/6 x 9 = 45/54

So, 5/6, 15/18, 35/42, 20/24, 45/54, etc., are equivalent fractions.

2. If the numerator and denominator of a fraction is divided by the same number, except zero, the value of the fraction remains the same and an equivalent fraction is obtained.

(i) 60/90 = 60 ÷ 10/90 ÷ 10 = 6/9; 60 ÷ 2/90 ÷ 2 = 30/45;

60 ÷ 3/90 ÷ 3 = 20/30, 60 ÷ 5/90 ÷ 5 = 12/18

So, 60/90, 6/9, 30/45, 20/30, 2/3 etc., are equivalent fractions.

32/72 = 32 ÷ 2/72 ÷ 2 = 16/36, 32 ÷ 4/72 ÷ 4 = 8/18, 32 ÷ 8/72 ÷ 8 = 4/9

So, 32/72, 16/36, 8/18, 4/9 are equivalent fractions.

3. In case of two equivalent fractions, the product of the numerator of one fraction and denominator of the second fraction is equal to the product of the denominator of the first fraction and numerator of the second fraction.

Accordingly, the two fractions are equivalent if:

numerator of the first fraction × denominator of the second fraction = denominator of the first fraction × numerator of the second fraction

As:

 1/3 = 2/6 5/7 = 15/21 So, 1 x 6 = 3 x 2 = 6 So, 5 x 21 = 7 x 15 = 105

4. A fraction may be reduced to its lowest term. If a factor or factors is / are common to numerator and denominator of a fraction, then the common factor or factors may be removed to get it in its lowest term.

If there is a fraction 12/18 and we have to reduce it to its lowest term,

Since, 12 = 2 x 2 x 3 and 18 = 2 x 3 x 3, thus, 2 x 3 = 6 is a common factor in numerator and denominator of 12/18

So, 12 ÷ 6/18 ÷ 6 = 2/3

By dividing both 12 and 18 by 6, we get the fraction 2/3 as the lowest of 12/18.

These are the properties of equivalent fractions explained along with the examples.

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