Question

Arrange the rational numbers$\frac{-7}{10},\frac{5}{-8},\frac{2}{-3},\frac{-1}{4},\frac{-3}{5}$ in ascending order.

Answer 1

Given rational numbers are $\frac{-7}{10},\frac{5}{-8},\frac{2}{-3},\frac{-1}{4},\frac{-3}{5}.$
To arrange in any order, we make denominators of all rational numbers as same.
$\therefore$ LCM of 10, 8, 3, 4 and 5 is 120.
So,$\frac{-7\times 12}{10\times 12},\frac{5\times 15}{-8\times 15},\frac{2\times 40}{-3\times 40},\frac{-1\times 30}{4\times 30},\frac{-3\times 24}{5\times 24}=\frac{-84}{120},\frac{75}{-120},\frac{80}{-120},\frac{-30}{120},\frac{-72}{120}=\frac{-84}{120},\frac{-75}{120},\frac{-80}{120},\frac{-30}{120},\frac{-72}{120}$
Since, denominators are same so ascending order of numerators are - 84, -80, -75, -72, -30
Hence, $\frac{-84}{120}<\frac{-80}{120}<\frac{-75}{120}<\frac{-72}{120}<\frac{-30}{120}$
i.e. $\frac{-7}{10}<\frac{2}{-3}<\frac{5}{-8}<\frac{-3}{5}<\frac{-1}{4}$