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\( \Large \frac{5-\left[ \frac{3}{4}+\{ 2\frac{1}{2}- \left(\frac{1}{2}+ \overline{ \frac{1}{6}-\frac{1}{7}}\right)\} \right]}{2}=? \)

A) \( \Large 1\frac{23}{168} \)
B) \( \Large 2\frac{23}{168} \)
C) \( \Large 3\frac{23}{168} \)
D) \( \Large 4\frac{23}{168} \)

Correct Answer:

A) \( \Large 1\frac{23}{168} \)

Description for Correct answer:
\( \Large ?=\frac{5-\left[ \frac{3}{4}+\{ \frac{5}{2}- \left(\frac{1}{2}+\overline{\frac{1}{6}-\frac{1}{7}}\right) \} \right]}{2} \)

=\( \Large \frac{5-\left[ \frac{3}{4}+\{ \frac{5}{2}- \left(\frac{1}{2}+\frac{7-6}{42}\right) \} \right]}{2} \)

=\( \Large \frac{5-\left[ \frac{3}{4}+\{ \frac{5}{2}- \left(\frac{21+1}{42}\right) \} \right]}{2} \)

=\( \Large \frac{5-\left[ \frac{3}{4}+\{ \frac{5}{2}-\frac{22}{42} \} \right]}{2} \)

=\( \Large \frac{5-\left[ \frac{3}{4}+\{ \frac{105-22}{42} \} \right]}{2} \)

=\( \Large \frac{5-\left[ \frac{3}{4}+\frac{83}{42} \right]}{2} = \frac{5-\left[ \frac{63+166}{84} \right]}{2} \)

=\( \Large \frac{5-\frac{229}{84}}{2} = \frac{\frac{420-229}{84}}{2} = \frac{\frac{191}{84}}{2} \)

=\( \Large \frac{191}{84 \times 2}=\frac{191}{168}=1\frac{23}{168} \)

Part of solved Simplification questions and answers : >> Elementary Mathematics >> Simplification

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Similar Questions

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