Question

List five rational numbers between -2 and -1.

Answer 1

Hint: The rational number between a and b is ${\displaystyle \frac{(a+b)}{2}}$, use this equation to find the rational numbers between the given two numbers.

Complete step-by-step answer:

Given, to find 5 rational numbers between -2 and -1.
As, we know, the rational number between a and b is given by, ${\displaystyle \frac{(a+b)}{2}}$
Hence, the rational number between -2 and -1 is ${\displaystyle \frac{(-2-1)}{2}}={\displaystyle \frac{-3}{2}}=-1.5$
Rational number between -2 and -3/2 is $\left[{\displaystyle \frac{-2+\left({\displaystyle \frac{-3}{2}}\right)}{2}}\right]={\displaystyle \frac{-7}{4}}=-1.75$
Rational number between -2 and -7/4 is $\left[{\displaystyle \frac{-2+\left({\displaystyle \frac{-7}{4}}\right)}{2}}\right]={\displaystyle \frac{-15}{8}}=-1.875$
Rational number between -2 and -15/8 is $\left[{\displaystyle \frac{-2+\left({\displaystyle \frac{-15}{8}}\right)}{2}}\right]={\displaystyle \frac{-31}{16}}=-1.9375$
Rational number between -31/16 and -1 is $\left[{\displaystyle \frac{\left({\displaystyle \frac{-31}{16}}\right)-1}{2}}\right]={\displaystyle \frac{-47}{32}}=-1.46875$

Therefore, five rational numbers between -2 and -1 are -1.75, -1.875, -1.9375, -1.46875, -1.5.

Note: Whenever such a type of question appears, i.e., it is asked to find a rational number between any two rational numbers, suppose x and y, the simplest approach is to divide their sum by 2, as mentioned in the question. Proceed step by step, obtain the value of (sum of the two no.)/2, then find the next rational number by dividing the sum of the first rational no. obtained in step 1 with the first number in the range, repeat it till you get all the required rational numbers.