Answer :

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:

[tex]\frac{p}{q},\text{ p and q are integers, q }\ne0[/tex]

Observe that the number -1 can be written as:

[tex]-1=\frac{-3}{3}[/tex]

Similarly, 1 can be written as:

[tex]1=\frac{3}{3}[/tex]

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:

[tex]\frac{-3}{3},\frac{-2}{3},\frac{-1}{3},\frac{0}{3},\frac{1}{3},\frac{2}{3},\frac{3}{3},[/tex]

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