Math, asked by pranavcoll8, 1 month ago

3\frac{1}{4}\Bigg[ 9\frac{1}{6}+2\frac{1}{8}\div 3\frac{1}{4}+\bigg[ 9\frac{1}{6}-\bigg( 3\frac{1}{2}-8\frac{1}{6}+7\frac{1}{4}\bigg) \bigg]​

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Answered by 12thpáìn
198

\underline{\green{\sf{Questions}}}\\

  • {3\frac{1}{4}\Bigg[ 9\frac{1}{6}+2\frac{1}{8}\div 3\frac{1}{4}+\bigg[ 9\frac{1}{6}-\bigg( 3\frac{1}{2}-8\frac{1}{6}+7\frac{1}{4}\bigg) \bigg]}

\\\underline{\green{\sf{Step~By~Step~ Explanation}}}\\

{3\frac{1}{4}\Bigg[ 9\frac{1}{6}+2\frac{1}{8}\div 3\frac{1}{4}+\bigg[ 9\frac{1}{6}-\bigg( 3\frac{1}{2}-8\frac{1}{6}+7\frac{1}{4}\bigg) \bigg]}\\\\

\underline{  \green{\text{ Convert \:  these all improper fraction into Proper Fraction}}}\\

{ \sf\frac{13}{4}\Bigg[\frac{55}{6}+\frac{17}{8}\div \frac{13}{4}+\bigg[ \frac{55}{6}-\bigg( \frac{7}{2}-\frac{49}{6}+\frac{29}{4}\bigg) \bigg]}\\\\

\underline{  \green{\text{ taking \: lcm \: of \: 6 \: and \: 8 \: or \: 2 \: .6 \: and \: 4}}}

 \sf{LCM  \: of  \: 6 \:  and \:  8= 2 \underline{|6,8}} \\ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  3,4 \\ \sf{LCM  \: of  \: 6 \:  and \:  8=24 }\\

Or

\\\sf{LCM  \: of  \: 2 \:  and 6 \: and \:  \: \:  4= 2 \underline{|2,6,4}} \\ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:1 , 3,2 \\ \sf{LCM  \: of  \: 2 \: and \: 6 \:  \:  and \: 4 =2 \times 3 \times 2 } \\ \sf{LCM  \: of  \: 2 \: and \: 6 \:  \:  and \: 4 = \green{12} \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: }\\\\

{\implies \sf\frac{13}{4}\Bigg[\frac{4(54) + 6(17)}{24}\div \frac{13}{4}+\bigg[ \frac{55}{6}-\bigg( \frac{6(7) - 2(49) + 3(29)}{12}\bigg) \bigg]}

{ \sf\implies\frac{13}{4}\Bigg[\frac{216 + 102}{24}\div \frac{13}{4}+\bigg[ \frac{55}{6}-\bigg( \frac{42 - 98+ 87}{12}\bigg) \bigg]}

{ \implies\sf\frac{13}{4}\Bigg[\frac{114}{24}\div \frac{13}{4}+\bigg[ \frac{55}{6}-\bigg( \frac{42 - 11}{12}\bigg) \bigg]}

{ \implies\sf\frac{13}{4}\Bigg[\frac{114}{24}\div \frac{13}{4}+\bigg[ \frac{55}{6}-\frac{31}{12} \bigg]}

\sf{LCM  \: of  \: 6 \:  and \:  12= 12}

{\implies \sf\frac{13}{4}\Bigg[\frac{114}{24}\div \frac{13}{4}+\bigg[ \frac{2(55) - 31}{12} \bigg]}

{  ~~~~~~~~~\sf\implies\frac{13}{4}\Bigg[\frac{114}{24}\div \frac{13}{4}+\bigg[ \frac{110 - 31}{12} \bigg]}

{ ~~~~~~ \sf\implies\frac{13}{4}\Bigg[\frac{114}{24}\div \frac{13}{4}+ \frac{79}{12} \bigg]}

{ ~~~~~~ \sf\implies\frac{13}{4}\Bigg[\frac{114}{24}\div  \frac{39 + 79}{12} \bigg]}

{ ~~~~~~~ \sf\implies\frac{13}{4}\Bigg[\frac{114}{24}\div  \frac{114}{12} \bigg]}

{  ~~~~~~~~\sf\implies\frac{13}{4}\Bigg[\frac{114}{24}\div  \frac{12}{114} \bigg]}

{ ~~~~~~~~~~~~~\sf\implies\frac{13}{4} \times  \frac{1}{2}}

{ ~~~ ~~~~~~~~~\sf\implies\frac{13}{8} }

Hope It Helpful ❣️

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