Question

The smallest rational number among the following is

• A. $\frac{-3}{7}$
• B. $\frac{-7}{3}$
• C. $\frac{-5}{6}$
• D. $\frac{-5}{2}$

Answer 1

The correct option is D

$\frac{-5}{2}$

From the options we have $\frac{-3}{7},\frac{-7}{3},\frac{-5}{6},\frac{-5}{2}$

$LCM(7,3,6,2)=42$

Thus,

$$\begin{gathered} \frac{-3}{7}=\frac{-3\times 6}{7\times 6}=\frac{-18}{42} \\ \frac{-7}{3}=\frac{-7\times 14}{3\times 14}=\frac{-98}{42} \\ \frac{-5}{6}=\frac{-5\times 7}{6\times 7}=\frac{-35}{42} \\ \frac{-5}{2}=\frac{-5\times 21}{2\times 21}=\frac{-105}{42} \end{gathered}$$

Since,

$$\begin{gathered} \frac{105}{42}>\frac{98}{42}>\frac{35}{42}>\frac{18}{42} \\ \Rightarrow \frac{-105}{42}<\frac{-98}{42}<\frac{-35}{42}<\frac{-18}{42} \\ \Rightarrow \frac{-5}{2}<\frac{-7}{3}<\frac{-5}{6}<\frac{-3}{7} \end{gathered}$$

Therefore, $\frac{-5}{2}$is the smallest.

Hence, option (d) is correct.