Question

Arrange the following rational numbers in ascending orders $\frac{-4}{9},\frac{5}{-12},\frac{-7}{18},\frac{2}{-3}$

Answer 1

Given rational numbers are $\frac{-4}{9},\frac{5}{-12},\frac{-7}{18},\frac{2}{-3}$

First of all, we express each rational number with a positive denominator.

We have,

$$\begin{gathered} \frac{5}{-12}=\frac{5\times (-1)}{-12\times (-1)}=\frac{-5}{12} \\ \frac{2}{-3}=\frac{2\times (-1)}{-3\times (-1)}=\frac{-2}{3} \end{gathered}$$

Thus, the given rational numbers are

$\frac{-4}{9},\frac{-5}{12},\frac{-7}{18},\frac{-2}{3}$

Now $LCM(9,12,18,3)=36$

Thus,

$$\begin{gathered} \frac{-4}{9}=\frac{-4\times 4}{9\times 4}=\frac{-16}{36} \\ \frac{-5}{12}=\frac{-5\times 3}{12\times 3}=\frac{-15}{36} \\ \frac{-7}{18}=\frac{-7\times 2}{18\times 2}=\frac{-14}{36} \\ \frac{-2}{3}=\frac{-2\times 12}{3\times 12}=\frac{-24}{36} \end{gathered}$$

Since,

$$\begin{gathered} \frac{24}{36}>\frac{16}{36}>\frac{15}{36}>\frac{14}{36} \\ \Rightarrow \frac{-24}{36}<\frac{-16}{36}<\frac{-15}{36}<\frac{-14}{36} \\ \Rightarrow \frac{-2}{3}<\frac{-4}{9}<\frac{-5}{12}<\frac{-7}{18} \end{gathered}$$

Hence, the ascending order of given rational numbers are

$\frac{2}{-3},\frac{-4}{9},\frac{5}{-12},\frac{-7}{18}$