Question

Arrange the given rational numbers in ascending order :
$\frac{4}{-9},\frac{-5}{12}\text{and}\frac{2}{-3}$

Answer 1

Step 1 : Finding LCM of denominators of given number

Given, rational numbers ar $\frac{4}{-9},\frac{-5}{12}\text{and}\frac{2}{-3}$

Where, $\frac{4}{-9}=\frac{-4}{9}and\frac{-5}{12}and\frac{2}{-3}=\frac{-2}{3}$

Where, $\frac{4}{-9}=\frac{-4}{9}and\frac{-5}{12}and\frac{2}{-3}=\frac{-2}{3}$

Factors of $9=3\times 3$.

Factors of $12=3\times 4$.

Factors of $3=3\times 1$.

Now, LCM of 9, 12, 3 $=3\times 3\times 4=36$.

Step 2 : Making denominators of rational number equal to LCM i.e., 36

$\frac{-4}{9}=\frac{-4\times 4}{9\times 4}=\frac{-16}{36}$

$\frac{-5}{12}=\frac{-5\times 3}{12\times 3}=\frac{-15}{36}$

$\frac{-2}{3}=\frac{-2\times 12}{3\times 12}=\frac{-24}{36}$

Step 3 : Compare $\frac{-16}{36},\frac{-15}{36}and\frac{-24}{36}$

$\because$ For same denominator, the rational number with the greater numerator is greater.

$\therefore \frac{-15}{36}>\frac{-16}{36}>\frac{-24}{36}[\because \text{denominator are same and}$
$-15>-16>-24]$

$\Rightarrow \frac{-24}{36}<\frac{-16}{36}<\frac{-15}{36}$

$\Rightarrow \frac{-2}{3}<\frac{-4}{9}<\frac{-5}{12}$

$\Rightarrow \frac{2}{-3}<\frac{4}{-9}<\frac{-5}{12}$

Hence, the required ascending order is $\frac{2}{-3}<\frac{4}{-9}<\frac{-5}{12}$.