Question

Find four rational numbers between -3/2 and 5/3

Answer 1

Four rational numbers between
`-(3)/(2)` and
`(5)/(3)` are
`x_(1) = -(13)/(15)`,
`x_(2) = -(7)/(30)`,
`x_(3) = (2)/(5)` and
`x_(4) = (31)/(30)`.

Explanation:

First, we calculate the distance between
`-(3)/(2)` and
`(5)/(3)`:

`r = (5)/(3)-\left(-(3)/(2)\right)`

`r = (5)/(3)+(3)/(2)`

`r = (10+9)/(6)`

`r = (19)/(6)`

Then, we find four rational numbers by using the following formula:

`x = -(3)/(2)+\left((n)/(5))\cdot \left((19)/(6) \right)`

First number (
`n = 1`)

`x_(1) = -(13)/(15)`

Second number (
`n = 2`)

`x_(2) = -(7)/(30)`

Third number (
`n = 3`)

`x_(3) = (2)/(5)`

Fourth number (
`n = 4`)

`x_(4) = (31)/(30)`