Question

Find any five rational numbers between – 1 and – 2 

Answer 1

Converting to rational numbers, – 1 = `-10/11` and – 2 = `- 20/10`

So five rational numbers between – 2 and – 1 are `- 11/10, - 12/10, - 13/10, - 14/10, - 15/10`.

Other Method:

A rational number between – 1 and – 2

= `1/2 [-1 - 2]`

= `1/2[- 3]`

= `- 3/2`

A rational number between – 1 and `-3/2` 

= `1/2 [-1 - 3/2]`

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

= `- 5/4`

A rational number between – 1 and `-5/4` 

= `1/2 [-1 - 5/4]`

= `1/2 ((-4 - 5)/4)`

= `- 9/8`

A rational number between – 1 and `-9/8` 

= `1/2 [-1 - 9/8]`

= `1/2 ((-8 - 9)/8)`

= `- 17/16`

A rational number between – 1 and `-17/16` 

= `1/2 [-1 - 17/16]`

= `1/2 ((-16 - 17)/16)`

= `1/2 ((-33)/16)`

= `(-33)/32`

The five rational numbers are `-3/2, -5/4, -9/8, -17/16,` and `(-33)/32`