Question

The largest of the fractions $\frac{2}{3},\frac{5}{9},\frac{1}{2}$ and $\frac{7}{12}$ is
(a) $\frac{2}{3}$
(b) $\frac{5}{9}$
(c) $\frac{7}{12}$
(d) $\frac{1}{2}$

Answer 1

(a) $\frac{2}{3}$

Explanation:
L.C.M. of 3, 9, 2 and 12 = ( 2 ⨯ 2 ⨯ 3 ​⨯ 3) = 36
Now, we have:
$$\begin{gathered} \frac{2}{3}=\frac{2\times 12}{3\times 12}=\frac{24}{36} \\ \frac{5}{9}=\frac{5\times 4}{9\times 4}=\frac{20}{36} \\ \frac{1}{2}=\frac{1\times 18}{2\times 18}=\frac{18}{36} \\ \frac{7}{12}=\frac{7\times 3}{12\times 3}=\frac{21}{36} \\ \mathrm{Hence},\frac{24}{36}=\frac{2}{3}\mathrm{is}\mathrm{the}\mathrm{largest}\mathrm{fraction}. \end{gathered}$$