Question

Arrange the rational numbers `(-7)/10, 5/(-8), 2/(-3), (-1)/4, (-3)/5` in ascending order.

Answer 1

Given rational numbers are `(-7)/10, 5/(-8), 2/(-3), (-1)/4, (-3)/5`

To arrange in any order, we make denominators of all rational numbers as same.

∴ LCM of 10, 8, 3, 4 and 5 is 120

So, `(-7 xx 12)/(10 xx 12), (5 xx 15)/(-8 xx 15), (2 xx 40)/(-3 xx 40), (-1 xx 30)/(4 xx 30), (-3 xx 24)/(5 xx 24)`

= `(-84)/120, 75/(-120), 80/(-120), (-30)/120, (-72)/120`

= `(-84)/120, (-75)/120, (-80)/120, (-30)/120, (-72)/120`

Since, denominators are same, so ascending order of numerators are –84, –80, –75, –72, –30

Hence, `(-84)/120 < (-80)/120 < (-75)/120 < (-72)/120 < (-30)/120`

i.e. `(-7)/10 < 2/(-3) < 5/(-8) < (-3)/5 < (-1)/4`