Question

Arrange the following rational numbers in ascending and descending order

`(-5)/12, (-11)/8, (-15)/24, (-7)/(-9), 12/36`

Answer 1

`(-5)/12, (-11)/8, (-15)/24, (-7)/(-9), 12/36`

L.C.M of 12, 8, 24, 9, 36 is 4 × 3 × 2 × 3 = 72

Hint:

`(-5)/12 = (-5 xx 6)/(12 xx 6) = (-30)/72`

`(-11)/8 = (-11 xx 9)/(8 xx 9) = (-99)/72`

`(-15)/24 = (-15 xx 3)/(24 xx 3) = (-45)/72`

`(-7)/(-9) = (7 xx 8)/(9 xx 8) = 56/72`

`12/36 = (12 xx 2)/(36 xx 2) = 24/72`

Now comparing the numerators – 30, – 99, − 45, 56, 24 we get 56 > 24 > – 30 > – 45 > – 99

i.e. `56/72 > 24/72 > (-30)/72 > (-45)/72 > (-99)/72` and so `(-7)/(-9) > 12/36 > (-5)/12 > (-15)/24 > (-11)/8`

∴ Descending order `(-7)/(-9) > 12/36 > (-5)/12 > (-15)/24 > (-11)/8`

Ascending order `(-11)/8 < (-15)/24 < (-5)/12 < 12/36 < (-7)/(-9)`