Question

find three rational number between - 4/ 5 and - 6 / 7

Answer 1

$\textbf{Given numbers are \frac{-4}{5} and \frac{-6}{7} }$

$\text{We apply average method to find rational numbers between them}$

$\text{Take a=\frac{-4}{5} and b=\frac{-6}{7} }$

$\text{Rational number between a and b is c_1 }$

$=\frac{a+b}{2}$

$=\frac{\frac{-4}{5}+(\frac{-6}{7})}{2}$

$=\frac{\frac{-28-30}{35}}{2}$

$=\frac{\frac{-58}{35}}{2}$

$=\frac{-29}{35}$

$\text{Rational number between a and c_1 is c_2 }$

$=\frac{a+c_1}{2}$

$=\frac{\frac{-4}{5}+(\frac{-29}{35})}{2}$

$=\frac{\frac{-28-29}{35}}{2}$

$=\frac{\frac{-57}{35}}{2}$

$=\frac{-57}{70}$

$\text{Rational number between c_1 and b is c_3 }$

$=\frac{c_1+b}{2}$

$=\frac{\frac{-29}{35}+\frac{-6}{7}}{2}$

$=\frac{\frac{-29-30}{35}}{2}$

$=\frac{\frac{-59}{35}}{2}$

$=\frac{-59}{70}$

$\therefore\textbf{The three rational numbers between \frac{-4}{5} and \frac{-6}{7} are \frac{-57}{70},\frac{-29}{35} and \frac{-59}{35} }$

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Insert two rational number between 2/5 and 5/7

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