Question

Find any 4 rational number between -1/2 and -1/3

Answer 1

Given:

The two numbers are
`-(1)/(2)` and
`-(1)/(3)`.

To find:

The 4 rational numbers between the given numbers.

Solution:

We have,

`-(1)/(2)` and
`-(1)/(3)`

First we need to make common denominators. So multiply and divide the first fraction by 3 and second fraction by 2.

`-(1* 3)/(2* 3)=-(3)/(6)`

`-(1* 2)/(3* 2)=-(2)/(6)`

We need to find 4 rational numbers between the given numbers. So, multiply and divide both fractions by five, (4+1=5).

`-(3* 5)/(6* 5)=-(15)/(30)`

`-(2* 5)/(6* 5)=-(10)/(30)`

Now, the four numbers between -15 to -10 are -14, -13, -12, -11.

`-15<-14<-13<-12<-11<-10`

`-(15)/(30)<-(14)/(30)<-(13)/(30)<-(12)/(30)<-(11)/(30)<-(10)/(30)`

`-(1)/(2)<-(14)/(30)<-(13)/(30)<-(12)/(30)<-(11)/(30)<-(1)/(3)`

Therefore, the 4 rational number between the given numbers are
`-(14)/(30),\ -(13)/(30),\ -(12)/(30)\ -(11)/(30)`.