Question

Find five rational numbers between 1 and 2 by using mean method.​

Answer 1

Answer:

Given two numbers 1 and 2

We need to find a rational number between 1 and 2

Solution Let the two given numbers be a and b respectively a= 1 and b=2

We know that the rational number between a and b is given by (a + b)/2

So the rational number between 1 and 2 = (1+2)/2 = 3/2

Then, Rational number between 1 and 3/2 =[1+(3/2)]/2 = 5/4

Then Rational number between 1 and 5/4 =[1+(5/4)]/2 = 9/8

Then Rational number between 3/2 and 2 =[(3/2) + 2]/2 = 7/4

Then Rational number between 7/4 and 2 =[(7/4) + 2]/2 = 15/8 Hence the five rational numbers between 1 and 2 are 3/2, 5/4, 7/4, 9/8, and 15/8

Answer 2

Given: The mean method.​

To find: Five rational numbers between 1 and 2.

Solution:

• According to the mean method, the extreme values are first added and the, the sum obtained is divided by 2.
• This gives the number that lies exactlt between the two extreme digits.
• So, in the given question, to find the mean of 1 and 2, the following calculations are done,

        $\frac{1 + 2}{2} = 1.5$

• Hence, 1.5 is a rational number inserted between 1 and 2 using mean method.
• Then, the mean of 1 and 1.5, and of 1.5 and 2 is calculated as,

        $\frac{1 + 1.5}{2} = 1.25$

        $\frac{1.5+2}{2} = 1.75$

• Then, the mean of any two consecutive means is calculated in order to get rational number,

        $\frac{1+1.25}{2} = 1.125$

        $\frac{1.75+2}{2} = 1.875$

Therefore, 1.5, 1.25, 1.75, 1.125 and 1.185 are the five rational numbers between 1 and 2 by using mean method.