Question

find three irrational numbers between 2/3 and 6/7​

Answer 1

$\bf\purple{\underline{\boxed{Question}}}$

$\:$

$\small\tt{Find\:three\: irrational\:number\:between\:}\\{\small\tt{\frac{2}{3}}\:and\:{\frac{6}{7}}}$

$\:$

$\bf\purple{\underline{\boxed{Solution}}}$

$\:$

✏

$\small\tt{\frac{2}{3}}\:and\:{\frac{6}{7}}$

$\:$

$\small\tt{let\:first\:make\: the\: denominator\:}\\{\small\tt{ into\:like\:fraction}}$

$\:$

$\small\tt{so\:for\:that\:we\:\:have \:to\:multiply}\\{\small\tt{numerator\:and\: denominator\:of\:{\frac{2}{3}}\:by\:7}}$

$\:$

$\small\tt{We\:get\:,}$

$\:$

$\small\tt{\frac{2\times 7}{3\times7}}=\:{\frac{14}{21}}$

$\:$

$\small\tt{Similarly,}$

$\:$

$\small\tt{so\:for\:that\:we\:have to multiply}\\{\small\tt{numerator\:and\: denominator\:of\:{\frac{6}{7}}\:by\:3}}$

$\:$

$\small\tt{We\:get\:,}$

$\:$

$\small\tt{\frac{6\times3}{7\times3}}=\:{\frac{18}{21}}$

$\:$

$\small\tt{Now,}\\{\small\tt{we\:get\:fraction\:into\:like\:fraction}}$

$\:$

$\small\tt{So,The\: irrational\:number\:between\:}\\{\small\tt{These\:two\:like\:fraction\:are}}$

$\:$

$\small\tt\red{{\frac{14}{21}},{\frac{15}{21}},{\frac{16}{21}},{\frac{17}{21}},{\frac{18}{21}}}$

$\:$

$\bf\purple{\underline{\boxed{Thanks}}}$