Question

insert two rational numbers between 2/5 and 5/7 PLEASE ANSWER MY QUESTION I WILL MARK U AS BRANLIEST​

Answer 1

Answer:

two rational no. between 2/5 and 5/7

2/5×7/7=14/35

5/7×5/5=25/35

so answer is 15/35 and 16/35

Answer 2

Two rational numbers between $\frac{2}{5} \text { and } \frac{5}{7} \text { are } \frac{39}{70} \text { and }\frac{67}{140}$

Concept used:

• The method used to find two rational numbers: Mid value method
• If p and q be two rational numbers then $\frac{p + q}{2}$ is between p and q such that p < $\frac{p + q}{2}$ < q
• By the repeated use of the above property, we can say that there are infinitely many rational numbers between two rational numbers.

Given: Two rational numbers $\frac{2}{5} \text { and } \frac{5}{7}$

To find: 2 rational numbers between $\frac{2}{5} \text { and } \frac{5}{7}$

Solution:

Step1: First rational number between $\frac{2}{5} \text { and } \frac{5}{7}$:

$\frac{1}{2} (\frac{2}{5} +\frac{5}{7}) = \frac{1}{2} (\frac{2 \times 7}{5 \times 7} +\frac{5\times 5}{7\times 5})$

$= \frac{1}{2} (\frac{14}{35} +\frac{25}{35})$

$= \frac{1}{2} (\frac{14 + 25}{35} )$

$= \frac{1}{2} (\frac{39}{35} )$

$= \frac{39}{70}$

Step 2: Second rational number between $\frac{2}{5} \text { and } \frac{39}{70}$ :

$\begin{array}{l}\frac{1}{2}\left(\frac{2}{5}+\frac{39}{70}\right) =\frac{1}{2}\left(\frac{2\times14}{5\times14}+\frac{39\times1}{70\times1}\right)\\\\=\frac{1}{2}\left(\frac{28}{70}+\frac{39}{70}\right)\\\\=\frac{1}{2}\left(\frac{28+39}{70}\right)\\\\=\frac{1}{2}\left(\frac{67}{70}\right)\\\\=\frac{67}{140}\end{array}$

Hence two rational numbers between  $\frac{2}{5} \text { and } \frac{5}{7} \text { are } \frac{39}{70} \text { and }\frac{67}{140}$

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