Question

Please anyone give me the answer​

Answer 1

Required Answer :

QUESTION :-

$\boxed{\sf{\red{ 3 \dfrac{2}{3} - \bigg[ 4 + \bigg\{ 2 \dfrac{1}{2} - \bigg( 2 \times 1 \dfrac{1}{3} \div 1 \dfrac{1}{9} + 1 \bigg) \bigg\} \bigg] }}}$

FINAL ANSWER :-

$\sf{= \dfrac{9}{2} - \bigg[ 4 + \bigg\{ \dfrac{5}{2} - \bigg( 2 \times \dfrac{4}{3} \div \dfrac{10}{9} + 1 \bigg) \bigg\} \bigg] }$

$\sf{= \dfrac{9}{2} - \bigg[ 4 + \bigg\{ \dfrac{5}{2} - \bigg( 2 × \dfrac{4}{3} × \dfrac{9}{10} + 1 \bigg) \bigg\} \bigg]}$

$\sf{= \dfrac{9}{2} - \bigg[ 4 + \bigg\{ \dfrac{5}{2} - \bigg( 2 × \dfrac{\bcancel{4}^{2}}{\cancel{3}} × \dfrac{\cancel{9}^{3}}{\bcancel{10}^{5}} + 1 \bigg) \bigg\} \bigg] }$

$\sf{= \dfrac{9}{2} - \bigg[ 4 + \bigg\{ \dfrac{5}{2} - \bigg( \dfrac{12}{5} + 1 \bigg) \bigg\} \bigg] }$

$\sf{= \dfrac{9}{2} - \bigg[ 4 + \bigg\{ \dfrac{5}{2} - \bigg( \dfrac{ 12 + 5 }{5} \bigg) \bigg\} \bigg] }$

$\sf{= \dfrac{9}{2} - \bigg[ 4 + \bigg\{ \dfrac{5}{2} - \dfrac{17}{5} \bigg\} \bigg] }$

$\sf{= \dfrac{9}{2} - \bigg[ 4 + \bigg\{ \dfrac{ 25 - 34 }{10} \bigg\} \bigg]}$

$\sf{= \dfrac{9}{2} - \bigg[ 4 + \bigg\{ - \dfrac{9}{10}\bigg \} \bigg] }$

$\sf{ = \dfrac{9}{2} - \bigg[ 4 - \dfrac{9}{10} \bigg] }$

$\sf{ = \dfrac{9}{2} - \bigg[ \dfrac{40 - 9}{10} \bigg] }$

$\sf{= \dfrac{9}{2} - \dfrac{31}{10} }$

$\sf{= \dfrac{ 45 - 31 }{10}}$

$\sf{= \bigg\langle \dfrac{\cancel{14}}{\cancel{10}} \bigg\rangle }$

$= \sf{\bigg\langle \dfrac{7}{5} \bigg\rangle }$

$= \boxed{\sf{\green{ 1 \dfrac{2}{5} }}}$

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• Rules applicable in simplification

ㅤㅤ➪ B O D M A S ( serially )

• ( + ) × ( - ) = ( - )

• ( - ) × ( + ) = ( - )

• ( + ) × ( + ) = ( + )

• ( - ) × ( - ) = ( + )

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Answer 2

${\maltese \: \: {\underline{{ \large{ \text{A}}}{\sf{nswer} }}\:: }}$

$\quad : \to \: \bf\dfrac{17}{30}.$

$\\ {\maltese \: \: {\underline{{ \large{\text{E}}}{\sf{xplanation} }}\:: }}$

$\quad \bullet \: \: \tt{Express \: 2\times \left(\frac{4}{3}\right) \: as \: a \: single \: fraction.}$

$\quad \bullet \: \: \tt{Multiply \: 2 \: and \: 4 \: to \: get \: 8.}$

$\quad \bullet \: \: \tt{Divide \: \frac{8}{3} \: by \: \frac{10}{9} \: by \: multiplying \: \frac{8}{3} \: by \: the \: reciprocal \: of \: \frac{10}{9}.}$

$\quad \bullet \: \: \tt{Multiply \: \frac{8}{3} \: times \: \frac{9}{10} \: by \: multiplying \: numerator \: times \: numerator \: and \: denominator \: times \: denominator.}$

$\quad \bullet \: \: \tt{Do \: the \: multiplications \: in \: the \: fraction \: \frac{8\times 9}{3\times 10}.}$

$\quad \bullet \: \: \tt{Reduce \: the \: fraction \: \frac{72}{30} \: to \: lowest \: terms \: by \: extracting \: and \: canceling \: out \: 6.}$

$\quad \bullet \: \: \tt{Convert \: 1 \: to \: fraction \: \frac{5}{5}.}$

$\quad \bullet \: \: \tt{Since \: \frac{12}{5} \: and \: \frac{5}{5} \: have \: the \: same \: denominator, \: add \: them \: by \: adding \: their \: numerators.}$

$\quad \bullet \: \: \tt{Add \: 12 \: and \: 5 \: to \: get \: 17.}$

$\quad \bullet \: \: \tt{Least \: common \: multiple \: of \: 2 \: and \: 5 \: is \: 10. \: Convert \: \frac{5}{2} \: and \: \frac{17}{5} \: to \: fractions \: with \: denominator \: 10.}$

$\quad \bullet \: \: \tt{Since \: \frac{25}{10} \: and \: \frac{34}{10} \: have \: the \: same \: denominator, \: subtract \: them \: by \: subtracting \: their \: numerators.}$

$\quad \bullet \: \: \tt{Subtract \: 34 \: from \: 25 \: to \: get \: -9.}$

$\quad \bullet \: \: \tt{Convert \: 4 \: to \: fraction \: \frac{40}{10}.}$

$\quad \bullet \: \: \tt{Since \: \frac{40}{10} \: and \: \frac{9}{10} \: have \: the \: same \: denominator, \: subtract \: them \: by \: subtracting \: their \: numerators.}$

$\quad \bullet \: \: \tt{Subtract \: 9 \: from \: 40 \: to \: get \: 31.}$

$\quad \bullet \: \: \tt{Least \: common \: multiple \: of \: 3 \: and \: 10 \: is \: 30. \: Convert \: \frac{11}{3} \: and \: \frac{31}{10} \: to \: fractions \: with \: denominator \: 30.}$

$\quad \bullet \: \: \tt{Since \: \frac{110}{30} \: and \: \frac{93}{30} \: have \: the \: same \: denominator, \: subtract \: them \: by \: subtracting \: their \: numerators.}$

$\quad \bullet \: \: \tt{Subtract \: 93 \: from \: 110 \: to \: get \: 17.}$

$\\ {\maltese \: \: {\underline{{ \large{\text{C}}}{\sf{alculation} }}\:: }}$

$:\longmapsto \tt \:\:\frac{ 11 }{ 3 } -(4+( \frac{ 5 }{ 2 } -(2 \times \frac{ 4 }{ 3 } \div \frac{ 10 }{ 9 } +1))) \\\\\ \: :\longmapsto \tt \:\: \frac{11}{3}-\left(4+\frac{5}{2}-\left(\frac{\frac{2\times 4}{3}}{\frac{10}{9}}+1\right)\right) \\\\\ \: :\longmapsto \tt \:\:\frac{11}{3}-\left(4+\frac{5}{2}-\left(\frac{\frac{8}{3}}{\frac{10}{9}}+1\right)\right) \\\\\ \: :\longmapsto \tt \:\:\frac{11}{3}-\left(4+\frac{5}{2}-\left(\frac{8}{3}\times \left(\frac{9}{10}\right)+1\right)\right) \\\\\ \: :\longmapsto \tt \:\:\frac{11}{3}-\left(4+\frac{5}{2}-\left(\frac{8\times 9}{3\times 10}+1\right)\right) \\\\\ \: :\longmapsto \tt \:\:\frac{11}{3}-\left(4+\frac{5}{2}-\left(\frac{72}{30}+1\right)\right) \\\\\ \: :\longmapsto \tt \:\:\frac{11}{3}-\left(4+\frac{5}{2}-\left(\frac{12}{5}+1\right)\right) \\\\\ \: :\longmapsto \tt \:\: \frac{11}{3}-\left(4+\frac{5}{2}-\left(\frac{12}{5}+\frac{5}{5}\right)\right) \\\\\ \: :\longmapsto \tt \:\:\frac{11}{3}-\left(4+\frac{5}{2}-\frac{12+5}{5}\right) \\\\\ \: :\longmapsto \tt \:\: \frac{11}{3}-\left(4+\frac{5}{2}-\frac{17}{5}\right) \\\\\ \: :\longmapsto \tt \:\:\frac{11}{3}-\left(4+\frac{25}{10}-\frac{34}{10}\right) \\\\\ \: :\longmapsto \tt \:\: \frac{11}{3}-\left(4+\frac{25-34}{10}\right) \\\\\ \: :\longmapsto \tt \:\: \frac{11}{3}-\left(4-\frac{9}{10}\right) \\\\\ \: :\longmapsto \tt \:\: \frac{11}{3}-\left(\frac{40}{10}-\frac{9}{10}\right) \\\\\ \: :\longmapsto \tt \:\:\frac{11}{3}-\frac{40-9}{10} \\\\\ \: :\longmapsto \tt \:\: \frac{110}{30}-\frac{93}{30} \\\\\ \: :\longmapsto \tt \:\: \frac{110-93}{30} \\\\\ \: \underline{\boxed{: \implies \purple {\frak{\frac{17}{30} } } }} \: \: \bigstar$

.°. The value of the given equation is ¹⁷⁄₃₀.

$\\{\maltese \: \: {\underline{{ \large{ \text{N}}}{\sf{ote} }}\:: }}$

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