Question

5 Rational numbers between 2/3 and 3/4 ...
pls someone answer it in steps​

Answer 1

$\huge{\mathcal{\blue{\underline{SOLUTION:-}}}}$

$\sf{First\;we\;find\;LCM}\\\\ \sf{So\;LCM\;of\;3\;and\;4\;is\;12}\\ \\ \sf{So\;we\;rewrite\;these\;two\;fractions\;as:}$

$\sf{\frac{2\times 4}{3\times 4}\;and\;\frac{3\times 3}{4\times 3}}\\ \\ \\ \sf{\frac{28}{12}\;and\;\frac{9}{12}}$

$\sf{So\;basically\;we\;are\;trying\;to\;find\;five\;rational\;numbers\;between\; \frac{8}{12}\;and\;\frac{9}{12}.}$

$\sf{Which\;we\;can\;do\;as\;shown\;below:}$

$\sf{\frac{8}{12}=\frac{8\times 6}{12\times 6}=\frac{48}{72}\;and\;\frac{9}{12}=\frac{9\times 6}{12\times 6}=\frac{54}{72}}$

$\sf{It\;can\;be\;observed\;that,}$

$\sf{\frac{48}{72}<\frac{49}{72}<\frac{50}{72}<\frac{51}{72}<\frac{52}{72}<\frac{53}{72}}$

$\sf{So,}$

$\sf{\red{\frac{49}{72},\;\frac{50}{72},\;\frac{51}{72},\;\frac{52}{72}\;and\;\frac{53}{72}\;are\;5\;rational\;no.\;between\;\frac{2}{3}\;and\;\frac{3}{4}.}}$