Question

Question 6 :

The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form:
(a) $\frac{2}{12}$ (b) $\frac{3}{15}$ (c) $\frac{8}{50}$ (d) $\frac{16}{100}$ (e) $\frac{10}{60}$ (f) $\frac{15}{75}$ (g) $\frac{12}{60}$ (h) $\frac{16}{96}$ (i) $\frac{12}{75}$ (j) $\frac{12}{72}$ (k) $\frac{3}{18}$ (l) $\frac{4}{25}$

Answer 1

Equivalent fractions are fractions which are obtained by multiplying or dividing the numerator and denominator by the same number.

The simplest form of the equivalent fractions are equal. We reduce the fractions given in the question to their simplest form.

The fractions whose simplest form is same are equivalent fractions.

(a) $\frac{\text{/}2}{\text{/}12}=\frac{1}{6}$ (b) $\frac{\text{/}3}{\text{/}15}=\frac{1}{5}$ (c) $\frac{\text{/}8}{\text{/}50}=\frac{4}{25}$ (d) $\frac{\text{/}16}{\text{/}100}=\frac{4}{25}$ (e) $\frac{\text{/}10}{\text{/}60}=\frac{1}{6}$ (f) $\frac{\text{/}15}{\text{/}75}=\frac{1}{5}$ (g) $\frac{\text{/}12}{\text{/}60}=\frac{1}{5}$ (h) $\frac{\text{/}16}{\text{/}96}=\frac{1}{6}$ (i) $\frac{\text{/}12}{\text{/}75}=\frac{4}{25}$ (j) $\frac{\text{/}12}{\text{/}72}=\frac{1}{6}$ (k) $\frac{\text{/}3}{\text{/}18}=\frac{1}{6}$ (l) $\frac{4}{25}=\frac{4}{25}$

Equivalent groups:

I group : $\frac{1}{5}$ [(b), (f), (g)]

II group : $\frac{1}{6}$ [(a), (e), (h), (j), (k)]

III group : $\frac{4}{25}$ [(c), (d), (i), (l)]