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Finding Equivalent Fractions

In order to find equivalent fractions, we should multiply or divide the numerator and denominator

with the same number (except 0).
×
×
3 32 6 3 33 9 3 34 12
×
Method 1: By multiplying: = = ; = = and = =
7 72 14 7 73 21 7 74 28
×
×
×
3 6 9 12
Thus, the equivalent fractions of are , , , and so on.
7 14 21 28
5 55 1 6 66 1 7 77 1
÷
÷
÷
Method 2: By dividing: = = ; = = and = =
÷
25 25 5 5 30 30 6 5 35 35 7 5
÷
÷
5 6 7 1
Thus, , and are equivalent fractions because the value of each of these fractions is .
25 30 35 5
Example 8: Write three fractions equivalent to each of the following fractions:
3 7
(a) (b)
5 9
×
×
×
×
×
×
Solution: (a) 3 = 32 = 33 = 34 (b) 7 = 72 = 73 = 74
×
×
×
×
5 52 53 54 9 92 93 94
×
×
3 = 6 = 9 = 12 7 14 21 28
5 10 15 20 9 = 18 = 27 = 36
7
So, the three fractions equivalent to So, the three fractions equivalent to
3 are 6 , 9 and 12 . 14 21 28 9
,
5 10 15 20 are 18 27 and 36 .
Example 9: Fill in the blanks with the correct number.
11 33 3
(a) = (b) =
36 8 40
Solution: (a) Since, 33 ÷ 11 = 3 (b) Since, 40 ÷ 8 = 5
∴ Divide numerator and denominator ∴ Multiply numerator and denominator
of the fraction on RHS by 3. of the fraction on LHS by 5.
33 33 3 11 3 35 15
÷
×
∴ 36 = 36 3 = 12 = LHS ∴ 8 = 85 = 40 = RHS
÷
×
11 33 3 15
∴ 12 = 36 ∴ 8 = 40
Cross Multiplication Method

We can check whether two fractions are equivalent or not, by using this method. In this method, the
product of the numerator of the first fraction and the denominator of the second fraction is equal to

the product of the denominator of the first fraction and the numerator of the second fraction. That is,

Numerator of first fraction × Denominator of second fraction = Numerator of second fraction ×
Denominator of first fraction

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