Question

Write the following rational numbers in descending order. $\frac{8}{7},-\frac{9}{8},-\frac{3}{2},0,\frac{2}{5}$

Answer 1

Descending orders of rational numbers:

The given rational numbers are $\frac{8}{7},-\frac{9}{8},-\frac{3}{2},0,\frac{2}{5}$.

To compare rational numbers. first, we have to make denominators of all the rational numbers to be equal.

After taking LCM of the denominators$7,8,2,\mathrm{and}5$ we get $280$

$$\begin{gathered} \frac{8}{7}=\frac{8}{7}\times \frac{40}{40}=\frac{320}{280} \\ -\frac{9}{8}=-\frac{9}{8}\times \frac{35}{35}=-\frac{315}{280} \\ -\frac{3}{2}=-\frac{3}{2}\times \frac{140}{140}=-\frac{420}{280} \\ \frac{2}{5}=\frac{2}{5}\times \frac{56}{56}=\frac{112}{280} \end{gathered}$$

When the denominators of the rational numbers are the same. Then, the rational number with a larger numerator will be greater.

$$\begin{gathered} \because \frac{320}{280}>\frac{112}{280}>0>-\frac{315}{280}>-\frac{420}{280} \\ \therefore \frac{8}{7}>\frac{2}{5}>0>-\frac{9}{8}>-\frac{3}{2} \end{gathered}$$

Hence, descending order is $\frac{\mathbf{8}}{\mathbf{7}}\mathbf{>}\frac{\mathbf{2}}{\mathbf{5}}\mathbf{>}\mathbf{0}\mathbf{>}\mathbf{-}\frac{\mathbf{9}}{\mathbf{8}}\mathbf{>}\mathbf{-}\frac{\mathbf{3}}{\mathbf{2}}$.