Page 175 - New Medley 5 Semester 1

1 2 3 5
Here, all the fractions , , and show the same part of the whole circle.
2 4 6 10

1 2 3 5
So, these are equivalent fractions, i.e., = = = .
2 4 6 10

We can get many fractions equivalent to a given fraction by multiplying
or dividing its numerator as well as the denominator with the same whole

number. For example,

By multiplication

2 , 2 × 2 2 × 3 2 × 4 2 × 5 2 = 4 = 6 = 8 = 10
,
,
,
3 3 × 2 3 × 3 3 × 4 3 × 5 ,... or 3 6 9 12 15 = ...
By division

48 48 ÷ 2 48 ÷ 3 48 ÷ 4 48 ÷ 6 48 24 16 12 8
, , , , ... or = = = = = ...
84 84 ÷ 2 84 ÷ 3 84 ÷ 4 84 ÷ 6 84 42 28 21 14

Checking Equivalent Fractions

There are two ways to check whether the fractions those are equivalent
or not.

I. By reducing to the simplest form

II. By cross-multiplication

12 20
Example 1: Check whether the fractions and are equivalent
15 25
or not.

Solution: Method I

Reduce the given fractions to their lowest terms.
12 12 ÷ 3 4 20 20 ÷ 5 4
We have = = and = =
15 15 ÷ 3 5 25 25 ÷ 5 5

12 20 Simplest form is same
Thus, =
15 25

Method II

Multiply the numerator of first fraction with the
denominator of second fraction and vice-versa.

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