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Q.

[[1]] is the four rational numbers between 1 and 2.

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Detailed Solution

We are asked to find the rational numbers between 1 and 2.
First let us find the rational numbers between 0 and 1.
We know that a number that is represented in the form

\frac{p}{q}

where, q≠0 is called a rational number.
We know that increasing the denominator of 1 to more than 1 then the number lie between 0 and 1
By using the above two condition we get the rational numbers that lie between 0 and 1 as

\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}

We know that if we add a number n
to rational numbers between 0 and 1 then the resultant numbers will lie between n
and n+1
We are asked to find the rational numbers between 1 and 2
So, let us add 1 to the above rational numbers between 0 and 1 then we get

\Rightarrow \frac{1}{2} + 1 = \frac{3}{2}

\Rightarrow \frac{1}{3} + 1 = \frac{4}{3}

\Rightarrow \frac{1}{4} + 1 = \frac{5}{4}

\Rightarrow \frac{1}{5} + 1 = \frac{6}{5}

Therefore we can conclude that the rational numbers between 1 and 2 are given as

\frac{3}{2}, \frac{4}{3}, \frac{5}{4}, \frac{6}{5}

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