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

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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).

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