Question

find four rational number between 3/7 and 5/7

Answer 1

multiply 3 in both fraction
3/7×3/3 , 5/7×3/3

9/21, 15/21

so rational numbers are,10/21. ,11/21 ,12/21. ,13/21

Answer 2

Answer:

$\frac{1}{2},\frac{4}{7},\frac{17}{28}$ and $\frac{9}{14}$.

Step-by-step explanation:

We are given that two rational numbers $\frac{3}{7}$ and $\frac{5}{7}$

We have to find four rational number between given two rational numbers

To find the four rational numbers we find mean value of rational  of two given rational number.

Let $a=\frac{3}{7},b=\frac{5}{7}$

Let x be the mean vlaue of two rational numbers.

Then,x=$\frac{\frac{3}{7}+\frac{5}{7}}{2}$

x=$\frac{\frac{3+5}{7}}{2}$

x=$\frac{8}{7\times2}=\frac{4}{7}$

x=$\frac{4}{7}$

Let y be the mean value of rational numbers $\frac{3}{7}$ and $\frac{4}{7}$

Then, y=$\frac{\frac{3}{7}+\frac{4}{7}}{2}$

y=$\frac{\frac{3+4}{7}}{2}$

y=$\frac{7}{7\times2}$

y=$\frac{1}{2}$

Let z be the mean value of two rational numbers $\frac{4}{7}$ and $\frac{5}{7}$

Then, z=$\frac{\frac{4}{7}+\frac{5}{7}}{2}$

z=$\frac{\frac{4+5}{7}}{2}$

z=$\frac{9}{7\times2}$

z=$\frac{9}{14}$

Let w be the mean value of two rational numbers $\frac{4}{7}$ and $\frac{9}{14}$

Then,w=$\frac{\frac{4}{7}+\frac{9}{14}}{2}$

w=$\frac{\frac{8+9}{14}}{2}$

w=$\frac{17}{2\times14}$

w=$\frac{17}{28}$

Hence, $\frac{1}{2},\frac{4}{7},\frac{17}{28} and \frac{9}{14}$ are four rational numbers between given two rational numbers $\frac{3}{7}$ and $\frac{5}{7}$.