Question

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]​

Answer 1

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

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

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

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

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

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

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

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

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 ❣️