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Quantitative Aptitude Question on Number Systems

The arrangement of rational numbers −710,5−8,2−3\frac{-7}{10},\frac{5}{-8},\frac{2}{-3} in ascending order is

A

−710,5−8,2−3\frac{-7}{10},\frac{5}{-8},\frac{2}{-3}

B

5−8,−710,2−3\frac{5}{-8},\frac{-7}{10},\frac{2}{-3}

C

2−3,5−8,−710\frac{2}{-3},\frac{5}{-8},\frac{-7}{10}

D

−710,2−3,5−8\frac{-7}{10},\frac{2}{-3},\frac{5}{-8}

Answer

−710,2−3,5−8\frac{-7}{10},\frac{2}{-3},\frac{5}{-8}

Explanation

Solution

First write the rational numbers with positive denominator =−710,−58,23=\frac{-7}{10},\frac{-5}{8},\frac{2}{3}
LCM of denominators (LCM of 10, 8, 3 is 120)
−710=(−7×12)(10×12)=−84120\frac{-7}{10}=\frac{(-7\times12)}{(10\times12)}=\frac{-84}{120}
−58=(−5×15)(8×15)=−75120\frac{-5}{8}=\frac{(-5\times15)}{(8\times15)}=\frac{-75}{120}
−23=(2×40)(3×40)=−80120\frac{-2}{3}=\frac{(2\times40)}{(3\times40)}=\frac{-80}{120}
Comparing the numerators of these numbers, we get
−84<−80<−75-84<-80<-75
∴−84120<−80120<−75120;−710<−23<−58\therefore \frac{-84}{120}<\frac{-80}{120}<\frac{-75}{120};\frac{-7}{10}<\frac{-2}{3}<\frac{-5}{8}
The correct option is (D): −710,2−3,5−8\frac{-7}{10},\frac{2}{-3},\frac{5}{-8}