Question

The largest fraction among $\frac{5}{6},\frac{1}{4},\frac{5}{12},\frac{7}{8}$is :

• A. $\frac{5}{6}$
• B. $\frac{7}{8}$
• C. $\frac{5}{12}$
• D. $\frac{1}{4}$

Answer 1

The correct option is B

$\frac{7}{8}$

We have,$\frac{5}{6},\frac{1}{4},\frac{5}{12},\frac{7}{8}$

LCM of denominator $(6,4,12,8)=2\times 2\times 2\times 3=24$

$$\begin{gathered} \frac{5\times 4}{6\times 4}=\frac{20}{24},\frac{1\times 6}{4\times 6}=\frac{6}{24} \\ \frac{5\times 2}{12\times 2}=\frac{10}{24},\frac{7\times 3}{8\times 3}=\frac{21}{24} \end{gathered}$$

$\Rightarrow \frac{21}{24}>\frac{20}{24}>\frac{10}{24}>\frac{6}{24}$$\iff$$\frac{7}{8}>\frac{5}{6}>\frac{5}{12}>\frac{1}{4}$

Hence, $\frac{7}{8}$will be the largest fraction.