Question

Find four rational numbers equivalent to each of the following.

(i) $\frac{6}{11}$
(ii) $\frac{-3}{8}$
(iii) $\frac{7}{-15}$
(iv) 8
(v) 1
(vi) −1

Answer 1

(i) Following are the four rational numbers that are equivalent to $\frac{6}{11}$.
$\begin{array}{l}\frac{6\times 2}{11\times 2},\frac{6\times 3}{11\times 3},\frac{6\times 4}{11\times 4}\text{and}\frac{6\times 5}{11\times 5}\\ \\ \mathrm{i}.\mathrm{e}.\frac{12}{22},\frac{18}{33},\frac{24}{44}\text{and}\frac{30}{55}\end{array}$

(ii) Following are the four rational numbers that are equivalent to $\frac{-3}{8}$.
$\frac{-3\times 2}{8\times 2}$,$\frac{-3\times 3}{8\times 3}$, $\frac{-3\times 4}{8\times 4}$ and $\frac{-3\times 5}{8\times 5}$

i.e. $\frac{-6}{16}$, $\frac{-9}{24}$, $\frac{-12}{32}$ and $\frac{-15}{40}$

(iii) Following are the four rational numbers that are equivalent to $\frac{7}{-15}$.
$\begin{array}{l}\frac{\text{7}\times 2}{-15\times 2},\frac{\text{7}\times 3}{-15\times 3},\frac{\text{7}\times 4}{-15\times 4}\text{and}\frac{\text{7}\times 5}{-15\times 5}\\ \\ \text{i}\text{.e}\text{.}\frac{14}{-30}\text{,}\frac{21}{-45},\frac{28}{-60}\text{and}\frac{35}{-75}\end{array}$

(iv) Following are the four rational numbers that are equivalent to 8, i.e. $\frac{8}{1}$.
$\begin{array}{l}\frac{8\times 2}{1\times 2},\frac{8\times 3}{1\times 3},\frac{8\times 4}{1\times 4}\text{and}\frac{8\times 5}{1\times 5}\\ \\ \mathrm{i}.\mathrm{e}.\frac{16}{2},\frac{24}{3},\frac{32}{4}\text{and}\frac{40}{5}\end{array}$

(v) Following are the four rational numbers that are equivalent to ­­-1, i.e. $\frac{1}{1}$.
$\begin{array}{l}\frac{1\times 2}{1\times 2},\frac{1\times 3}{1\times 3},\frac{1\times 4}{1\times 4}\text{and}\frac{1\times 5}{1\times 5}\\ \\ \mathrm{i}.\mathrm{e}.\frac{2}{2},\frac{3}{3},\frac{4}{4}\text{and}\frac{5}{5}\end{array}$
(vi) Following are the four rational numbers that are equivalent to ­­-1, i.e. $\frac{-1}{1}$.
$\begin{array}{l}\frac{-1\times 2}{1\times 2},\frac{-1\times 3}{1\times 3},\frac{-1\times 4}{1\times 4}\text{and}\frac{-1\times 5}{1\times 5}\\ \\ \mathrm{i}.\mathrm{e}.\frac{-2}{2},\frac{-3}{3},\frac{-4}{4}\text{and}\frac{-5}{5}\end{array}$