Question

Q: Find five retional number between 2\3 and 4\5

Answer 1

$\star \ {\underline{\underline{\frak \pink{To\;find:-}}}}$

• $\sf{Five\;rational\;number\;b/w\; \dfrac{2}{3} \;and\; \dfrac{4}{5}}$

$\star \ {\underline{\underline{\frak \pink{Solution:-}}}}$

$\star \; {\underline{\underline{\sf{Multiplying\; \dfrac{2}{3}\;by\;5\;on\;both\;numerator\;and\;denominator.}}}}$

$\longmapsto \sf{ \dfrac{2}{3} = \dfrac{2 \times 5}{3 \times 5}} \\ \\ \longmapsto \sf{ \dfrac{10}{15}}$

$\star{ \; \underline{\underline{\sf{Multiplying\; \dfrac{4}{5}\;by\;3\;on\;both\;numerator\;and\;denominator.}}}}$

$\longmapsto \sf{ \dfrac{4}{5} = \dfrac{4 \times 3}{5 \times 3}} \\ \\ \longmapsto \sf{ \dfrac{12}{15}}$

$\tiny{\underline{\underline{\sf{\blue{\dag\;we\;can\;find\;5\;rational\;number\;b/w\; \dfrac{2}{3}\;and\; \dfrac{4}{5}\;by\;multiplying\;them\;with\;5 + 1 = 6.}}}}}$

$\longmapsto \sf{ \dfrac{10}{15} \times \dfrac{6}{6}} \\ \\ \longmapsto \sf{ \dfrac{60}{90}}$

$\longmapsto \sf{ \dfrac{12}{15} \times \dfrac{6}{6}} \\ \\ \longmapsto \sf{ \dfrac{72}{90}}$

$\therefore {\underline{\underline{\sf{\purple{The\;five\;rational\;number\;are:-}}}}} \\ \\ \implies \sf{\boxed{ \dfrac{61}{90} , \dfrac{62}{90} , \dfrac{63}{90} , \dfrac{64}{90} , \dfrac{65}{90} , \dfrac{66}{90} , \dfrac{67}{90}}}$

$\rule{200}{2}$