Question

In each of the following, find an equivalent form of the rational number having a common denominator:
(i) $\frac{3}{4}\mathrm{and}\frac{5}{12}$
(ii) $\frac{2}{3},\frac{7}{6}\mathrm{and}\frac{11}{12}$
(iii) $\frac{5}{7},\frac{3}{8},\frac{9}{14}\mathrm{and}\frac{20}{21}$

Answer 1

Equivalent forms of the rational number having common denominator are:

(i) $\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}\mathrm{and}\frac{5}{12}$.

(ii)
$$\begin{gathered} \frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}\mathrm{and}\frac{7}{6}=\frac{7\times 2}{6\times 2}=\frac{14}{12}and\frac{11}{12} \\ \mathrm{Forms}\mathrm{are}\frac{8}{12},\frac{14}{12}\mathrm{and}\frac{11}{12} \end{gathered}$$


(iii)
$$\begin{gathered} \frac{5}{7}=\frac{5\times 24}{7\times 24}=\frac{120}{168},\frac{3}{8}=\frac{3\times 21}{8\times 21}=\frac{63}{168},\frac{9}{14}=\frac{9\times 12}{14\times 12}=\frac{108}{168}and\frac{20}{21}=\frac{20\times 8}{21\times 8}=\frac{160}{168} \\ \mathrm{Forms}\mathrm{are}\frac{120}{168},\frac{63}{168},\frac{108}{168}\mathrm{and}\frac{160}{168} \end{gathered}$$