Question

The arrangement of rational numbers \(\frac{-7}{10},\frac{5}{-8},\frac{2}{-3}\) in ascending order is

• A. \(\frac{-7}{10},\frac{5}{-8},\frac{2}{-3}\)
• B. \(\frac{5}{-8},\frac{-7}{10},\frac{2}{-3}\)
• C. \(\frac{2}{-3},\frac{5}{-8},\frac{-7}{10}\)
• D. \(\frac{-7}{10},\frac{2}{-3},\frac{5}{-8}\)

Answer 1

The Correct Option is D

First write the rational numbers with positive denominator \(=\frac{-7}{10},\frac{-5}{8},\frac{2}{3}\)
LCM of denominators (LCM of 10, 8, 3 is 120)
\(\frac{-7}{10}=\frac{(-7\times12)}{(10\times12)}=\frac{-84}{120}\)
\(\frac{-5}{8}=\frac{(-5\times15)}{(8\times15)}=\frac{-75}{120}\)
\(\frac{-2}{3}=\frac{(2\times40)}{(3\times40)}=\frac{-80}{120}\)
Comparing the numerators of these numbers, we get
\(-84<-80<-75\)
\(\therefore \frac{-84}{120}<\frac{-80}{120}<\frac{-75}{120};\frac{-7}{10}<\frac{-2}{3}<\frac{-5}{8}\)
The correct option is (D): \(\frac{-7}{10},\frac{2}{-3},\frac{5}{-8}\)