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Example 2: Write two equivalent fractions of 27 .
81

Solution: 27 = 27 ÷ 3 = 9 , 27 = 27 ÷ 9 = 3
81 81 ÷ 3 27 81 81 ÷ 9 9

Example 3: Fill in the boxes so that the fractions are equivalent.

(a) 1 = (b) 4 = 12
3 12 7
Solution:

(a) We multiply 3 by 4 in order to make the denominator 12. ×4

4

So, we will also multiply the numerator by 4. 1 = 12
3
Thus, 1 = 1 × 4 = 4 ×4
3 3 × 4 12

(b) We multiply 4 by 3 in order to make the numerator 12. ×3

So, we will also multiply the denominator by 3. 4 = 12
21
7
Thus, 4 = 4 × 3 = 12
7 7 × 3 21 ×3
to check whether two Fractions are equivalent or not

To check whether two fractions are equivalent or not, we cross multiply them, that
is, we multiply the numerator of one fraction with the denominator of the other.

If the products are the same, then the fractions are equivalent. If the products are
different, then the fractions are not equivalent.

Example 4: Check whether the following fractions are equivalent or not.

(a) 2 and 4 (b) 5 and 15
3 6 6 17
Solution:

(a) 2 4
3 6
Here, 2 × 6 = 12 and 3 × 4 = 12. Here, both products are equal.

Hence, 2 and 4 are equivalent fractions.
3 6

(b) 5 15
6 17
Here, 5 × 17 = 85 and 6 × 15 = 90. Here, both products are different.

Hence, 5 and 15 are not equivalent fractions.
6 17

110 Mathematics-4