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) $\frac{3}{18}$ (I) $\frac{4}{25}$

Answer 1

a) $\frac{2}{12}=\frac{1\times 2}{6\times 2}$

$=\frac{1}{6}$

b) $\frac{3}{15}=\frac{1\times 3}{5\times 3}$

$=\frac{1}{5}$

c) $\frac{8}{50}=\frac{4\times 2}{25\times 2}$

$=\frac{4}{25}$

d) $\frac{16}{100}=\frac{4\times 4}{25\times 4}$

$=\frac{4}{25}$

e) $\frac{10}{60}=\frac{1\times 10}{6\times 10}$

$=\frac{1}{6}$

f) $\frac{15}{75}=\frac{1\times 15}{5\times 15}$

$=\frac{1}{5}$

g) $\frac{12}{60}=\frac{1\times 12}{5\times 12}$

$=\frac{1}{5}$

h) $\frac{16}{96}=\frac{1\times 16}{6\times 16}$

$=\frac{1}{6}$

i) $\frac{12}{75}=\frac{4\times 3}{25\times 3}$

$=\frac{4}{25}$

j) $\frac{12}{72}=\frac{1\times 12}{6\times 12}$

$=\frac{1}{6}$

k) $\frac{3}{18}=\frac{1\times 3}{6\times 3}$

$=\frac{1}{6}$

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

So, there are $3$ groups of equivalent fractions,

$\frac{1}{6}\Rightarrow \left(a\right),\left(e\right),\left(h\right),\left(j\right),\left(k\right)$

$\frac{1}{5}\Rightarrow \left(b\right),\left(f\right),\left(g\right)$

$\frac{4}{25}\Rightarrow \left(e\right),\left(d\right),\left(i\right),\left(l\right)$