Arrange the following in ascending order:
$\frac{3}{10} ,\frac{17}{-30} ,\ \frac{7}{15} ,\frac{-11}{20}$

Given :

Given numbers are $\frac{3}{10} ,\frac{17}{-30} =\frac{-17}{30},\ \frac{7}{15} ,\frac{-11}{20}$.

To find :

We have to arrange the given numbers in ascending order.

Solution :

To arrange the given numbers in ascending order we have to first find the LCM of the denominators.  

LCM of 10,30,15 and 20 is,

$ \begin{array}{l}
10=2\times 5\
30=2\times 3\times 5\
15=3\times 5\
20=2\times 2\times 5\
\end{array}$

LCM of 10,30,15 and 20 = $2\times 2\times 3\times 5$=60

Therefore,

$\frac{3}{10}=\frac{3\times6}{10\times6}=\frac{18}{60}$

$\frac{-17}{30}=\frac{-17\times2}{30\times2}=\frac{-34}{60}$

$\frac{7}{15}=\frac{7\times4}{15\times4}=\frac{28}{60}$

$\frac{-11}{20}=\frac{-11\times3}{20\times3}=\frac{-33}{60}$

Comparing the numerators,

$-34<-33<18<28$

This implies,

$\frac{-34}{60}<\frac{-33}{60}<\frac{18}{60}<\frac{28}{60}$

Therefore,

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

The given numbers arranged in the ascending order is $\frac{17}{-30} ,\frac{-11}{20}, \frac{3}{10} ,\frac{7}{15}$.

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Updated on: 10-Oct-2022

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