Question

Find two rational numbers between the following using average method
a) 2/3 and 13/14

Answer 1

2/3 = 28/42
13/14 = 39/42
Two rational no. between 28/42 and 39/42 are
29/42 and 30/42

Answer 2

Answer:

Step-by-step explanation:

Concept:

The concept of average method will be used to solve this question.

The mean technique states that dividing the sum of the two rational integers x and y by two yields the rational number that lies between them. Therefore, $\frac{a+b}{2}, \frac{a+\frac{a+b}{2}}{2}$ etc., will be the rational numbers between a and b. The simplest way to find a rational number between two numbers is to use this formula.

Given :

The two numbers are given in the question which are $\frac{2}{3}$ and $\frac{13}{14}$ .

To Find:

We have to find out the rational numbers between the given boundary.

Solution:

First we need to make the denominator of two numbers same.

$\frac{2}{3} =\frac{2 \times 14}{3 \times 14} =\frac{28}{42}$

The second number will be $\frac{13}{14} =\frac{13 \times 3}{14 \times 3} =\frac{39}{42}$ .

Here we have to use average method to get the rational numbers.

Then the  rational number between $\frac{28}{42}$ and $\frac{39}{42}$ is $\frac{(\frac{28}{42}+\frac{39}{42} ) }{2} =\frac{(\frac{67}{42} )}{2} =\frac{67}{84}$

The second rational number is $\frac{\frac{28}{42}+\frac{67}{84} }{2} =\frac{\frac{56+67}{84} }{2} =\frac{\frac{123}{84} }{2}=\frac{123}{168} =\frac{41}{56}$

The rational number are $\frac{67}{84}$ and $\frac{41}{56}$.

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