Question

9. Find six rational numbers between -1/2 and 5/4..​..maths

Answer 1

$\textbf{Given:}$

$\dfrac{-1}{2}\;\text{and}\;\dfrac{5}{4}$

$\text{To find:}$

$\text{6 rational numbers between the given two rational numbers}$

$\textbf{Solutioin:}$

$\text{We apply average method to find 6 rational  numbers}$

$\text{Rational number between \frac{-1}{2} and \frac{5}{4} }$

$c_1=\dfrac{\frac{-1}{2}+\frac{5}{4}}{2}$

$c_1=\dfrac{\frac{-2+5}{4}}{2}$

$c_1=\dfrac{\frac{3}{4}}{2}$

$c_1=\dfrac{3}{8}$

$\text{Rational number between \frac{-1}{2} and \frac{3}{8} }$

$c_2=\dfrac{\frac{-1}{2}+\frac{3}{8}}{2}$

$c_2=\dfrac{\frac{-4+3}{8}}{2}$

$c_2=\dfrac{\frac{-1}{8}}{2}$

$\bf\c_2=\dfrac{-1}{16}$$c_2=\dfrac{-1}{16}$

$\text{Rational number between \frac{-1}{2} and \frac{-1}{16} }$

$c_3=\dfrac{\frac{-1}{2}+\frac{-1}{16}}{2}$

$c_3=\dfrac{\frac{-8-1}{16}}{2}$

$c_3=\dfrac{\frac{-9}{16}}{2}$

$\,c_3=\dfrac{-9}{32}$

$\text{Rational number between \frac{-1}{2} and \frac{-9}{32} }$

$c_4=\dfrac{\frac{-1}{2}+\frac{-9}{32}}{2}$

$c_4=\dfrac{\frac{-16-9}{32}}{2}$

$c_4=\dfrac{\frac{-25}{32}}{2}$

$\,c_4=\dfrac{-25}{64}$

$\text{Rational number between \frac{-1}{2} and \frac{-25}{64} }$

$c_5=\dfrac{\frac{-1}{2}+\frac{-25}{64}}{2}$

$c_5=\dfrac{\frac{-32-25}{64}}{2}$

$c_5=\dfrac{\frac{-57}{64}}{2}$

$\,c_5=\dfrac{-57}{128}$

$\text{Rational number between \frac{-1}{2} and \frac{-57}{128} }$

$c_6=\dfrac{\frac{-1}{2}+\frac{-57}{128}}{2}$

$c_6=\dfrac{\frac{-64-25}{128}}{2}$

$c_6=\dfrac{\frac{-89}{128}}{2}$

$\,c_6=\dfrac{-89}{256}$

Answer 2

$\textbf{Given:}$

$\dfrac{-1}{2}\;\text{and}\;\dfrac{5}{4}$

$\text{To find:}$

$\text{6 rational numbers between the given two rational numbers}$

$\textbf{Solutioin:}$

$\text{We apply average method to find 6 rational  numbers}$

$\text{Rational number between \frac{-1}{2} and \frac{5}{4} }$

$c_1=\dfrac{\frac{-1}{2}+\frac{5}{4}}{2}$

$c_1=\dfrac{\frac{-2+5}{4}}{2}$

$c_1=\dfrac{\frac{3}{4}}{2}$

$c_1=\dfrac{3}{8}$

$\text{Rational number between \frac{-1}{2} and \frac{3}{8} }$

$c_2=\dfrac{\frac{-1}{2}+\frac{3}{8}}{2}$

$c_2=\dfrac{\frac{-4+3}{8}}{2}$

$c_2=\dfrac{\frac{-1}{8}}{2}$

$\bf\c_2=\dfrac{-1}{16}$$c_2=\dfrac{-1}{16}$

$\text{Rational number between \frac{-1}{2} and \frac{-1}{16} }$

$c_3=\dfrac{\frac{-1}{2}+\frac{-1}{16}}{2}$

$c_3=\dfrac{\frac{-8-1}{16}}{2}$

$c_3=\dfrac{\frac{-9}{16}}{2}$

$\,c_3=\dfrac{-9}{32}$

$\text{Rational number between \frac{-1}{2} and \frac{-9}{32} }$

$c_4=\dfrac{\frac{-1}{2}+\frac{-9}{32}}{2}$

$c_4=\dfrac{\frac{-16-9}{32}}{2}$

$c_4=\dfrac{\frac{-25}{32}}{2}$

$\,c_4=\dfrac{-25}{64}$

$\text{Rational number between \frac{-1}{2} and \frac{-25}{64} }$

$c_5=\dfrac{\frac{-1}{2}+\frac{-25}{64}}{2}$

$c_5=\dfrac{\frac{-32-25}{64}}{2}$

$c_5=\dfrac{\frac{-57}{64}}{2}$

$\,c_5=\dfrac{-57}{128}$

$\text{Rational number between \frac{-1}{2} and \frac{-57}{128} }$

$c_6=\dfrac{\frac{-1}{2}+\frac{-57}{128}}{2}$

$c_6=\dfrac{\frac{-64-25}{128}}{2}$

$c_6=\dfrac{\frac{-89}{128}}{2}$

$\,c_6=\dfrac{-89}{256}$