Question

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2÷(1/2)-(1/2)÷2+(1/2)(2+1/2)



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Answer 1

Question :

Find the value of :

$\sf 2 \div \dfrac{1}{2} - \dfrac{1}{2} \div 2 + \dfrac{1}{2} \bigg(2 + \dfrac{1}{2} \bigg)$

Solution :

Here, we will use BODMAS concept .

B → Bracket

O → Of

D → Division

M → Multiplication

A → Addition

S → Subtraction

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Calculation :

$\longmapsto\sf 2 \div \dfrac{1}{2} - \dfrac{1}{2} \div 2 + \dfrac{1}{2} \bigg(2 + \dfrac{1}{2} \bigg) \\\\ \\ \longmapsto\sf 2 \div \dfrac{1}{2} - \dfrac{1}{2} \div 2 + \dfrac{1}{2} \bigg( \dfrac{4 + 1}{2} \bigg) \\\\ \\ \longmapsto\sf 2 \div \dfrac{1}{2} - \dfrac{1}{2} \div 2 + \dfrac{1}{2} \times \dfrac{5}{2} \\\\ \\ \longmapsto\sf 2 \times 2 - \dfrac{1}{2} \times \dfrac{1}{2} + \dfrac{5}{4} \\\\ \\ \longmapsto\sf 4 - \dfrac{1}{4} + \dfrac{5}{4} \\\\ \\ \longmapsto\sf \dfrac{16 - 1 + 5}{4}$

$\longmapsto\sf \dfrac{20}{4} \\\\ \\ \longmapsto\Large\underline{\boxed{\mathfrak{5 }}} \ \bigstar$

$\therefore \underline{\textsf{Required value of given expression = {\boxed{\textbf{ 5 }}}}}$

Answer 2

Required answer -

★ Find the value of the following -

${\tt{\longrightarrow 2 \div \dfrac{1}{2} - \dfrac{1}{2} \div 2 + \dfrac{1}{2} \bigg(2 + \dfrac{1}{2} \bigg)}}$

★ Let's solve this question...!

${\sf{:\implies 2 \div \dfrac{1}{2} - \dfrac{1}{2} \div 2 + \dfrac{1}{2} \bigg(2 + \dfrac{1}{2} \bigg)}}$

To solve this problem we have to use procedure of BODMAS !..

$\: \: \: \: \: \: \: \:{\bf{\leadsto B \: denotes \: Brackets}}$

$\: \: \: \: \: \: \: \:{\bf{\leadsto O \: denotes \: Off}}$

$\: \: \: \: \: \: \: \:{\bf{\leadsto D \: denotes \: Division}}$

$\: \: \: \: \: \: \: \:{\bf{\leadsto M \: denotes \: Multiplication}}$

$\: \: \: \: \: \: \: \:{\bf{\leadsto A \: denotes \: Additional}}$

$\: \: \: \: \: \: \: \:{\bf{\leadsto S \: denotes \: Subtraction}}$

~ When we have to use BODMAS then we have to work according to the denotation always like first solve brackets, then off (×) then others respectively...!

★ Let's do it...!

${\sf{:\implies 2 \div \dfrac{1}{2} - \dfrac{1}{2} \div 2 + \dfrac{1}{2} \bigg(2 + \dfrac{1}{2} \bigg)}}$

• Let's take LCM first of those digits that are in small bracket..!

${\sf{:\implies 2 \div \dfrac{1}{2} - \dfrac{1}{2} \div 2 + \dfrac{1}{2} \bigg(\dfrac{4+1}{2} \bigg)}}$

• Now let's solve the bracket..!

${\sf{:\implies 2 \div \dfrac{1}{2} - \dfrac{1}{2} \div 2 + \dfrac{1}{2} \bigg(\dfrac{5}{2} \bigg)}}$

• Now let's open brackets..!

${\sf{:\implies 2 \div \dfrac{1}{2} - \dfrac{1}{2} \div 2 + \dfrac{1}{2} \times \dfrac{5}{2}}}$

• Remember we have to work according to BODMAS so now have to solve for division...!

${\sf{:\implies 2 \times 2 - \dfrac{1}{2} \times \dfrac{1}{2} + \dfrac{5}{4}}}$

${\sf{:\implies 4 - \dfrac{1}{2} \times \dfrac{1}{2} + \dfrac{5}{4}}}$

${\sf{:\implies 4 - \dfrac{1}{4} + \dfrac{5}{4}}}$

${\sf{:\implies 4 - \dfrac{5}{4}}}$

${\sf{:\implies \dfrac{20}{4}}}$

${\sf{:\implies 5}}$

${\small{\boxed{\bf{\bigstar{Henceforth, \: 5 \: is \: the \: value \: of \: the \: given \: question}}}}}$