Question

List three rational numbers between -2 over 5 , -2 over 7​

Answer 1

Given:

Two rational numbers are
`-(2)/(5)` and
`-(2)/(7)`.

To find:

The three rational numbers between the given two numbers.

Solution:

Two rational numbers are
`-(2)/(5)` and
`-(2)/(7)`. First we need to make denominators common.

`-(2)/(5)=-(2* 7)/(5* 7)`

`-(2)/(5)=-(14)/(35)`

and,

`-(2)/(7)=-(2* 5)/(7* 5)`

`-(2)/(7)=-(10)/(35)`

Now, we have same denominators. Numerators are -14 and -10.

So, three numbers between -14 and -10 are -11, -12 ,13.

`-14<-13<-12<-11<-10`

`(-14)/(35)<(-13)/(35)<(-12)/(35)<(-11)/(35)<(-10)/(35)`

`(-2)/(7)<(-13)/(35)<(-12)/(35)<(-11)/(35)<(-2)/(5)`

Therefore, the three rational numbers between
`-(2)/(5)` and
`-(2)/(7)` are
`(-13)/(35),(-12)/(35),(-11)/(35)`.