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÷ 3 ÷ 3 ÷ 3 ÷ 3 If the numerator and the
Similarly: 81 = 27 = 9 = 3 = 1 denominator do not have
243 81 27 9 3 any common factor other
÷ 3 ÷ 3 ÷ 3 ÷ 3 than 1, the fraction is said
to be in its simplest form.
2 1
example 1. Write the next two fractions equivalent to . Here, is the simplest
2 2 2 4 2 2 3 6 4 3 81
Solution. =× = and = ×= form of .
4 4 2 8 4 4 3 12 243
2 4 6
So, the next two equivalent fractions of are and .
4 8 12
example 2. Fill in the boxes to make equivalent fractions.
1 4 12
a. = b. =
2 12 7
Solution. a. We multiply 2 by 6 in order to make the denominator 12. So, we also

1 1 6 6
multiply the numerator by 6. Thus, =× =
2 2 6 12
b. We multiply 4 by 3 in order to make the numerator 12. So, we also multiply

4 4 3 12
the denominator by 3. Thus, =× =
7 7 3 21

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

example 3. Are the following fractions equivalent?

2 4 3 12 5 15
a. and b. and c. and
3 6 4 16 6 17
2 4
Solution. a. . Here, 2 × 6 = 12 and 3 × 4 = 12. Both products are equal.
3 6
2 4
Hence, and are equivalent fractions.
3 6
3 12
b. . Here, 3 × 16 = 48 and 4 × 12 = 48. Both products are equal.
4 16
3 12
Hence, and are equivalent fractions.
4 16

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Fractions