Simplify:\(\frac{{4 + \frac{1}{2}\;of\;{{10}^2}\; \div \sqrt {243 + 382\;} \times {2^{10}}\;}}{{\left( {60\% \;of\;400 \div 8} \right) \div 10\;}}\)
Solution
Correct Answer: Option C
Follow BODMAS rule to solve this question, as per the order given below,
Step-1-Parts of an equation enclosed in 'Brackets' must be solved first,
Step-2-Any mathematical 'Of' or 'Exponent' must be solved next,
Step-3-Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,
Step-4-Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.
The given expression is:\(\frac{{4 + \frac{1}{2}\;of\;{{10}^2}\; \div \sqrt {243 + 382\;} \times {2^{10}}\;}}{{\left( {60\% \;of\;400 \div 8} \right) \div 10}}\)
\(= \;\frac{{4\; + \;\frac{1}{2}\;of\;{{10}^2}\; \div \;\sqrt {625\;} \; \times \;{2^{10}}\;}}{{\left( {60\% \;of\;400 \div 8} \right) \div 10}}\)
\(= \;\frac{{4\; + \;\frac{1}{2}\; \times \;100\; \div 25\; \times 1024\;}}{{\left( {240 \div 8} \right) \div 10}}\)
\(= \;\frac{{4\; + \;50\; \div 25\; \times \;1024}}{{30 \div 10}}\)
\(= \;\frac{{4\; + \;2\; \times \;1024}}{3}\)
\(= \;\frac{{4\; + \;2048}}{3}\)
\(= \;\frac{{\;2052}}{3}\)
= 684
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