Question

find five rational number between 2/5 and 2/7

Answer 1

Given:

Two Values   $\dfrac{2}{5} \ \textrm{and} \ \dfrac{2}{7}$

To Find:

Five rational numbers between $\dfrac{2}{5} \ \textrm{and} \ \dfrac{2}{7}$.

Solution:

To find the rational number between any two quantities we need to take LCM and arrange the number like this:

Multiply by cross denominator to each number,we get:

$\dfrac{2\times 7}{5\times 7} \ \textrm{and} \ \dfrac{2\times 5}{7\times 5}$

$\Rightarrow \dfrac{14}{35} \ \textrm{and} \ \dfrac{10}{35}$

Now for finding the rational number between the given values, we need to find the number for adding in previous value numerator to get new rational number as:

n = number of rational numbers to be find = 5

$\dfrac{14-10}{n+1} \\\Rightarrow \dfrac{14-10}{5+1}\\\Rightarrow \dfrac{4}{6}\\\Rightarrow 0.67$

Therefore we need to add 0.67 in previous value numerator to find the 5 rational number between $\dfrac{2}{5} \ \txtrm{and} \ \dfrac{2}{7}$:

$\dfrac{2}{5}, \dfrac{2+0.67}{35}, \dfrac{2+0.67+0.67}{35}, \dfrac{2+0.67+0.67+0.67}{35}, \dfrac{2+0.67+0.67+0.67+0.67}{35},$$\dfrac{2+0.67+0.67+0.67+0.67+0.67}{35}, \dfrac{2}{7}$

$\Rightarrow \dfrac{2}{5}, \dfrac{2.67}{35}, \dfrac{3.34}{35}, \dfrac{4.01}{35}, \dfrac{4.68}{35}, \dfrac{5.35}{35}, \dfrac{2}{7}$

$\textbf{ Therefore the five rational number between} \dfrac{2}{5} \ \textrm{and} \ \dfrac{2}{7}\ \textrm{are} \dfrac{2}{5}, \dfrac{2.67}{35}, \dfrac{3.34}{35}, \dfrac{4.01}{35}, \dfrac{4.68}{35}, \dfrac{5.35}{35}, \dfrac{2}{7}.$