Question

(2) Which is bigger and which is smaller?

(i) $\frac{-5}{7},\frac{1}{2}$
(ii) $\frac{-14}{9},\frac{-10}{9}$
(iii) $\frac{25}{25},\frac{17}{25}$

Answer 1

(i) $\frac{-5}{7},\frac{1}{2}$
L.C.M of 7 and 2 is 14.
$$\begin{gathered} \therefore \frac{-5}{7}=\frac{-5\times 2}{7\times 2}=\frac{-10}{14} \\ \mathrm{And}\frac{1}{2}=\frac{1\times 7}{2\times 7}=\frac{7}{14} \end{gathered}$$
Denominators of both the numbers are same. Therefore, the rational number with the greater numerator will be greater.
$$\begin{gathered} \therefore \frac{7}{14}>\frac{-10}{14} \\ \therefore \frac{1}{2}>\frac{-5}{7} \end{gathered}$$

(ii) $\frac{-14}{9},\frac{-10}{9}$
Denominators of both the numbers are same. Therefore, the rational number with the greater numerator will be greater.
$$\begin{gathered} \therefore \frac{-10}{9}>\frac{-14}{9} \\ \therefore \frac{-14}{9}<\frac{-10}{9} \end{gathered}$$

(iii) $\frac{25}{25},\frac{17}{25}$
Denominators of both the numbers are same. Therefore, the rational number with the greater numerator will be greater.
$\therefore \frac{25}{25}>\frac{17}{25}$