Question

Write the following rational numbers in ascending order:
(i)$\frac{-3}{5}$, $\frac{-2}{5}$, $\frac{-1}{5}$ (ii) $\frac{-1}{3}$, $\frac{-2}{9}$, $\frac{-4}{3}$

Answer 1

(i) All the numbers are negative and their denominator is the same.So, compare the numerator and arrange the rational numbers in ascending order.

∵ -3 < -2 < -1

∴ $\frac{-3}{5}$ < $\frac{-2}{5}$< $\frac{-1}{5}$

(ii) Make the denominators equal.

LCM of 3, 9, and 3 is 9.

$\frac{-1}{3}$ = (-1 × 3)/(3 × 3)= $\frac{-3}{9}$

= $\frac{-2}{9}$

$\frac{-4}{3}$= (-4 × 3)/(3 × 3) = $\frac{-12}{9}$

$\frac{-12}{9}$ < $\frac{-3}{9}$ < $\frac{-2}{9}$

⇒ $\frac{-4}{3}$ < $\frac{-1}{3}$ < $\frac{-2}{9}$