Question

Arrange the following rational numbers in ascending order.

$\frac{17}{-30},\frac{-11}{20},\frac{7}{-15},\frac{-3}{10}$

Answer 1

Given rational numbers

$\frac{17}{-30},\frac{-11}{20},\frac{7}{-15},\frac{-3}{10}$

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

We have $\frac{7}{-15}=\frac{7\times (-1)}{-15\times (-1)}=\frac{-7}{15}$

$\frac{17}{-30}=\frac{17\times (-1)}{-30\times (-1)}=\frac{-17}{30}$

Thus, Given rational numbers are

$\frac{17}{-30},\frac{-11}{20},\frac{7}{-15},\frac{-3}{10}$

Now $LCM(10,15,20,30)=60$

$$\begin{gathered} \frac{-3}{10}=\frac{-3\times 6}{10\times 6}=\frac{-18}{60} \\ \frac{-7}{15}=\frac{-7\times 4}{15\times 4}=\frac{-28}{60} \\ \frac{-11}{20}=\frac{-11\times 3}{20\times 3}=\frac{-33}{60} \\ \frac{-17}{30}=\frac{-17\times 2}{30\times 2}=\frac{-34}{60} \end{gathered}$$

Since,

$$\begin{gathered} \frac{34}{60}>\frac{33}{60}>\frac{28}{60}>\frac{18}{60} \\ \Rightarrow \frac{-34}{60}<\frac{-33}{60}<\frac{-28}{60}<\frac{-18}{60} \\ \Rightarrow \frac{-17}{30}<\frac{-11}{20}<\frac{-7}{15}<\frac{-3}{10} \end{gathered}$$

Hence, the ascending order of given numbers are

$\frac{17}{-30},\frac{-11}{20},\frac{7}{-15},\frac{-3}{10}$