1.

Fraction lies between 3/4 and 4/5​

Answer»

Given :

\sf \leadsto \:{\textit{\textsf{First\:<klux>FRACTION</klux>}}} : \dfrac{3}{4}.

\sf \leadsto \:{\textit{\textsf{Second\:fraction}}} : \dfrac{4}{5}.\\\\

Exigency To FIND : We have to find the fraction which LIES between the given fractions.

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❍ Let's Consider the REQUIRED fraction be X .

\\\dag\:\:\sf{ As,\:We\:know\:that\::}\\ \\ \qquad\qquad \maltese \: \bf Formula\:for\:between \: fraction\:: \\\\

\begin{gathered}\qquad \dag\:\:\Bigg\lgroup \sf{Required \: Fraction\:: \frac{1}{2} \bigg(1st \: frac. \: + \: 2nd \: frac. }\Bigg\rgroup \\\\\end{gathered}

⠀⠀⠀⠀⠀⠀\begin{gathered}\underline {\frak{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\\end{gathered}

\begin{gathered}:\implies \sf{x\:: \: \frac{1}{2} \bigg(1st \: frac. \: + \: 2nd \: frac. \bigg) }\end{gathered}

\begin{gathered}:\implies \sf{x\:: \: \frac{1}{2}\left(\frac{15}{20}+\frac{16}{20}\right) }\end{gathered}

\begin{gathered}:\implies \sf{x\:: \: \frac{1}{2}\times \left(\frac{15+16}{20}\right) }\end{gathered}

\begin{gathered}:\implies \sf{x\:: \: \frac{1}{2}\times \left(\dfrac{31}{20}\right) }\end{gathered}

\begin{gathered}\qquad :\implies \frak{\underline{\purple{\:x\::\: \dfrac{31}{40} }} }\:\:\bigstar \\\end{gathered}

Therefore,

⠀⠀⠀⠀⠀ \begin{gathered}\therefore {\underline{ \mathrm {\: Required \: fraction\:is\:\bf{\dfrac{31}{40}}}.}}\\\end{gathered}

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