Question

Arrange the given rational numbers in ascending order:​
(i)\(\dfrac{7}{10} ,\dfrac{-11}{-30} ~\text{and}~\dfrac{5}{-15}\).

Answer 1

Given , rational numbers \(\dfrac{7}{10} ,\dfrac{-11}{-30} ~\text{and}~\dfrac{5}{-15}\)

Also \(\dfrac{-11}{-30} =\dfrac{11}{30}\) and \(\dfrac{5}{-15}=\dfrac{-5}{15}\)

\(\therefore\)LCM of \(10,30, 15\)

Factor of \(10 =5\times2\)
Factor of \(30 =5\times3\times2\)
Factor of \(15 =5\times3\)

\(\therefore\) LCM of \(10,30,15= 5\times3\times2 =30\).

Making Denominator of rational number equal to LCM i.e 30.

\(\dfrac{7}{10}=\dfrac{7\times3}{10\times3}= \dfrac{21}{30}\)
\(\dfrac{-5}{15}=\dfrac{-5\times2}{15\times2}= \dfrac{-10}{30}\)
and \(\dfrac{11}{30}\)

\(\because\) same denominator, the rational number with the greater numerator is greater .
So, \(\dfrac{21}{30} > \dfrac{11}{30} > \dfrac{-10}{30}\)

[\(\because\) denominator are same and \(21> 11>-10\)]

\(=\dfrac{7}{10}> \dfrac{11}{30} > \dfrac{5}{-15}\)

Hence, the ascending order is \(\dfrac{5}{-15} < \dfrac{-11}{-30}< \dfrac{7}{10}\).