Math, asked by anveshsingh058, 5 months ago

Please anyone give me the answer​

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Answered by BRAINLYxKIKI
19

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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Answered by Mister36O
16

{\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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