Question

Find three rational numbers between -3 and 5.

Answer 1

Hint: We take a smaller interval than the given interval that exists in the given interval. Write the rational number that exists in the interval by dividing the sum of end points of the interval by 2.
* A rational number is a number that can be represented in the form of \[\dfrac{p}{q}\] where ‘p’ is the numerator and ‘q’ is the denominator.

Complete step-by-step solution:
We have to write three rational numbers between -3 and 5
Let us contract the interval and we find three rational numbers between 1 and 2 (say)
Since 1 and 2 lie between -3 and 5 then the rational numbers between 1 and 2 will also be in between -3 and 5
Rational number between 1 and 2 is \[\dfrac{{1 + 2}}{2} = \dfrac{3}{2}\]...............… (1)
Let us take another small interval lying between -3 and 5, say 2 and 3
Since 2 and 3 lie between -3 and 5 then the rational numbers between 2 and 3 will also be in between -3 and 5
Rational number between 2 and 3 is \[\dfrac{{2 + 3}}{2} = \dfrac{5}{2}\]...............… (2)
Let us take another small interval lying between -3 and 5, say -2 and -1
Since -2 and -1 lie between -3 and 5 then the rational numbers between -2 and -1 will also be in between -3 and 5
Rational number between -2 and -1 is \[\dfrac{{ - 2 - 1}}{2} = \dfrac{{ - 3}}{2}\].............… (3)

\[\therefore \]Three rational numbers between -3 and 5 are \[\dfrac{3}{2};\dfrac{5}{2};\dfrac{{ - 3}}{2}\]

Note: Students many times make mistake of writing the values of integers directly as rational numbers i.e. \[\dfrac{2}{1},\dfrac{3}{1}...\], keep in mind the denominator should contain value other than 1 to make it a rational number.