Question

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

(a)$\frac{2}{12}$

The given fraction can be simplified as

$$\begin{gathered} =\frac{(1\times 2)}{(6\times 2)} \\ =\frac{1}{6} \end{gathered}$$

(b) $\frac{3}{15}$

The given fraction can be simplified as

$$\begin{gathered} =\frac{(1\times 3)}{(5\times 3)} \\ =\frac{1}{5} \end{gathered}$$

(c) $\frac{8}{50}$

The given fraction can be simplified as

$$\begin{gathered} =\frac{(4\times 2)}{(25\times 2)} \\ =\frac{4}{25} \end{gathered}$$

(d) $\frac{16}{100}$

The given fraction can be simplified as

$$\begin{gathered} =\frac{(4\times 4)}{(25\times 4)} \\ =\frac{4}{25} \end{gathered}$$

(e) $\frac{10}{60}$(g) (h) (i) (j) (k) (l)

The given fraction can be simplified as

$$\begin{gathered} =\frac{(1\times 10)}{(6\times 10)} \\ =\frac{1}{6} \end{gathered}$$

(f) $\frac{15}{75}$

The given fraction can be simplified as

$$\begin{gathered} =\frac{(1\times 15)}{(5\times 15)} \\ =\frac{1}{5} \end{gathered}$$

(g) $\frac{12}{60}$

The given fraction can be simplified as

$$\begin{gathered} =\frac{(1\times 12)}{(5\times 12)} \\ =\frac{1}{5} \end{gathered}$$

(h) $\frac{16}{96}$

The given fraction can be simplified as

$$\begin{gathered} =\frac{(1\times 16)}{(6\times 16)} \\ =\frac{1}{6} \end{gathered}$$

(i) $\frac{12}{75}$

The given fraction can be simplified as

$$\begin{gathered} =\frac{(4\times 3)}{(25\times 3)} \\ =\frac{4}{25} \end{gathered}$$

(j) $\frac{12}{72}$

The given fraction can be simplified as

$$\begin{gathered} =\frac{(1\times 12)}{(6\times 12)} \\ =\frac{1}{6} \end{gathered}$$

(k) $\frac{3}{18}$

The given fraction can be simplified as

$$\begin{gathered} =\frac{(1\times 3)}{(6\times 3)} \\ =\frac{1}{6} \end{gathered}$$

(l) $\frac{4}{25}$

Hence, 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)