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

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Solution

Given numbers are $\frac{8}{7}, \frac{- 9}{8}, \frac{- 3}{2}, \frac{2}{5}$
First, we convert the given rational numbers into number with the same denominators.
LCM of 7, 8, 2, 5 $= 2 \times 7 \times 4 \times 5 = 280$
Now, $\frac{8}{7} = \frac{8}{7} \times \frac{40}{40} = \frac{320}{280}$
$\frac{- 9}{8} = \frac{- 9}{8} \times \frac{35}{35} = \frac{- 315}{280} \frac{- 3}{2} = \frac{- 3}{2} \times \frac{140}{140} = \frac{- 420}{280} \frac{2}{5} = \frac{2}{5} \times \frac{56}{56} = \frac{112}{280}$
In descending order,
$∵ \frac{320}{280} > \frac{112}{280} > \frac{- 315}{280} > \frac{- 420}{280} \Rightarrow \frac{8}{7} > \frac{2}{5} > \frac{- 9}{8} > \frac{- 3}{2}$

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