Question

The rational numbers with a denominator of 3 that lie between -1 and 1 inclusive

Answer 1

We need to find the rational numbers between -1 and 1 whose denominator is 3.

We know that a rational number can be written in the form:

`(p)/(q),\text{ p and q are integers, q }\\e0`

Observe that the number -1 can be written as:

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

Similarly, 1 can be written as:

`1=(3)/(3)`

The integers between -3 and 3 are: -2,-1,0,1,2

Therefore, the rational numbers with a denominator of 3 that lie between -1 and 1 inclusive are:

`(-3)/(3),(-2)/(3),(-1)/(3),(0)/(3),(1)/(3),(2)/(3),(3)/(3),`