Question

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

Answer 1

Ignoring the signs and making the denominators equal.

$\frac{1}{3}=\frac{1\times 3}{3\times 3}=\frac{3}{9}$
$\frac{2}{9}=\frac{2\times 1}{9\times 1}=\frac{2}{9}$
$\frac{4}{3}=\frac{4\times 3}{3\times 3}=\frac{12}{9}$


$\frac{2}{9}<\frac{3}{9}<\frac{12}{9}$
$\Rightarrow \frac{-2}{9}>\frac{-3}{9}>\frac{-12}{9}$
$\Rightarrow \frac{-2}{9}>\frac{-1}{3}>\frac{-4}{3}$


Ascending order: $\frac{-4}{3}$, $\frac{-1}{3}$, and $\frac{-2}{9}$