Question

Arrange the rational numbers $\frac{-7}{10}$, $\frac{5}{-8}$, $\frac{2}{-3}$ in ascending order.

Answer 1

First write the rational numbers with positive denominator = $\frac{-7}{10}$, $\frac{-5}{8}$, $\frac{-2}{3}$.

LCM of denominators (LCM of 10, 8, 3 is 120)

$\frac{-7}{10}$ = $\frac{(-7\times 12)}{(10\times 12)}=\frac{-84}{120}$

$\frac{-5}{8}$ = $\frac{(-5\times 15)}{(8\times 15)}=\frac{-75}{120}$

$\frac{-2}{3}$ = $\frac{(2\times 40)}{(3\times 40)}=\frac{-80}{120}$

Comparing the numerators of these numbers, we get

- 84 < - 80 < - 75

∴ $\frac{-84}{120}$ < $\frac{-80}{120}$ < $\frac{-75}{120}$ ; $\frac{-7}{10}$ < $\frac{-2}{3}$ < $\frac{-5}{8}$.