Question

Which of the following rational numbers is the greatest?

Options

• `(-17)/24`

• `(-13)/16`

• `7/(-8)`

• `(-31)/32`

Answer 1

`(-17)/24`

Explanation;

Hint:

L.C.M of 24, 16, 8, 32 = 8 × 2 × 3 × 2 = 96

`(-17)/24 = (-17 xx 4)/(24 xx 4) = (-68)/96`

`(-13)/16 = (-13 xx 6)/(16 xx 6) = (-78)/96`

`7/(-8) = (-7 xx 12)/(8 xx 12) = (-84)/96`

`(-31)/32 = (-31 xx 3)/(32 xx 3) = (-93)/96`

`(-93)/96 < (-84)/96 < (-78)/96 < (-68)/96`

`(-31)/32 < 7/(-8) < (-13)/16 < (-17)/24`

∴ `(-17)/24` is the greatest number