Question

List five rational numbers between `-1/2  "and"  2/3`.

Answer 1

`-1/2  "and"  2/3`

Here, writing `-1/2  "and"  2/3` as rational numbers with the same denominator:

`(-1)/2 = (-1xx3)/(2xx3)=(-3)/6` and

`2/3 =(2xx2)/(3xx2)= 4/6`

`(-3)/6 < (-2)/6 < (-1)/6 < 0< 1/6 < 2/6 < 3/6 < 4/6`

`(-1)/2 < (-1)/3 < (-1)/6 <0< 1/6 <1/3 <1/2<2/3`

Therefore, there are five rational numbers between the rational numbers`(-1)/2  "and"  2/3`

`(-1)/3, (-1)/6, 0, 1/6, 1/3`