Class 6 Maths Fractions | Making Equivalent fractions |

__Making Equivalent fractions __

In order to make equivalent number, we have to multiply both the numerator and the denominator by the same number. For eg we get the following fractions when we keep on dividing both the numerator and the denominator by the number 2.

These fractions are equivalent since all of them can be reduced to the simplest fraction - ½.

Equivalent fraction can also be made by __dividing__ both the numerator and the denominator by the same number.

It is important to note that the number by which we divide has to be such that the number divides both the numerator and the denominator perfectly.

Therefore, we can first find the HCF of the numerator and the denominator then divide them by the HCF.

These fractions are equivalent since all of them can be reduced to the simplest fraction- ½.

It is to be remembered that a fraction is said to be in the __simplest (or lowest)__ form if its numerator and denominator have no common factor except 1. For e.g. ½.

__Problem__: Write the fractions. Are all these fractions equivalent?

Solution:

1/2 = 2/4 = 3/6 = 4/8 = ½

All these fractions are equivalent since all these fractions can be reduced to the simplest fraction of the value ½.

__Problem__: Find the equivalent fraction of 36/48 with a) numerator 9 b) denominator 4

Numerator of the value 9 can be obtained by dividing both the numerator and the denominator by 4 since the numerator, 36/4 =9.

__36/4 __ = 9/12

48/4

Denominator of the value 4 can be obtained by dividing both the numerator and the denominator by 12 since the denominator,

48/12 = 4.

= __36/12 __ = 3/4

48/12

__Problem:__ Ram has 20 pencils, Sheelu has 50 pencils and Jamaal has 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

Thus, it can be seen that each of the children used the same fraction of pencils in 4 months.

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