Question

Arrange the following rational numbers in ascending order.

$\frac{-3}{4},\frac{5}{-12},\frac{-7}{16},\frac{9}{-24}$

Answer 1

Given rational numbers are

$\frac{-3}{4},\frac{5}{-12},\frac{-7}{16},\frac{9}{-24}$

First of all, we express each of the given numbers with a positive denominator.

We have $\frac{5}{-12}=\frac{5\times (-1)}{-12\times (-1)}=\frac{-5}{12}$

$\frac{9}{-24}=\frac{9\times (-1)}{-24\times (-1)}=\frac{-9}{24}$

Therefore, given rational numbers are $\frac{-3}{4},\frac{-5}{12},\frac{-7}{16},\frac{-9}{24}$

Now, $LCM(4,12,16,24)=48$

Thus,

$$\begin{gathered} \frac{-3}{4}=\frac{-3\times 12}{4\times 12}=\frac{-36}{48} \\ \frac{-5}{12}=\frac{-5\times 4}{12\times 4}=\frac{-20}{48} \\ \frac{-7}{16}=\frac{-7\times 3}{16\times 3}=\frac{-21}{48} \\ \frac{-9}{24}=\frac{-9\times 2}{24\times 2}=\frac{-18}{48} \end{gathered}$$

Since, $\frac{36}{48}>\frac{21}{48}>\frac{20}{48}>\frac{16}{48}$

Therefore, $\frac{-36}{48}<\frac{-21}{48}<\frac{-20}{48}<\frac{-18}{48}$$\Rightarrow \frac{-3}{4}<\frac{-7}{16}<\frac{-5}{12}<\frac{-9}{24}$

Hence, the given rational numbers in their ascending orders are

$\frac{-3}{4},\frac{-7}{16},\frac{5}{-12},\frac{9}{-24}$