Q.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 :

(a) \(\frac{2}{12} = \frac{2÷2}{12÷2} = \frac{1}{6} \)
(b) \(\frac{3}{15} = \frac{3÷3}{15÷3} = \frac{1}{5} \)
(c) \(\frac{8}{50} = \frac{8÷2}{50÷2} = \frac{4}{25} \)
(d) \(\frac{16}{100} = \frac{16÷4}{100÷4} = \frac{4}{25} \)
(e) \(\frac{10}{60} = \frac{10÷10}{60÷10} = \frac{1}{6} \)
(f) \(\frac{15}{75} = \frac{15÷15}{75÷15} = \frac{1}{5} \)
(g) \(\frac{12}{60} = \frac{12÷12}{60÷12} = \frac{1}{5} \)
(h) \(\frac{16}{96} = \frac{16÷16}{196÷16} = \frac{1}{6} \)
(i) \(\frac{12}{75} = \frac{12÷3}{75÷3} = \frac{4}{25} \)
(j) \(\frac{12}{72} = \frac{12÷12}{72÷12} = \frac{1}{6} \)
(k)\(\frac{3}{18} = \frac{3÷3}{18÷3} = \frac{1}{6} \)
(l) \(\frac{4}{25} \)
Totally there are 3 groups of equivalent fractions.
\(\frac{1}{6} \)= (a), (e), (h), (j), (k)
\(\frac{1}{5} \) = (b), (f), (g)
\(\frac{4}{25} \) = (c), (d), (i), (l)

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