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Simplify \(2 + 4\frac{1}{8} \times \frac{11}{4} - \frac{8}{11} + 4\frac{2}{11}\)...


Question

Simplify \(2 + 4\frac{1}{8} \times \frac{11}{4} - \frac{8}{11} + 4\frac{2}{11}\).

Options

A) \(61\frac{23}{416}\)

B) \(52\frac{23}{416}\)

C) \(10\frac{3}{416}\)

D) \(10\frac{29}{32}\)

The correct answer is D.

Explanation:

\(2 + 4\frac{1}{8} \times \frac{11}{4} - \frac{8}{11} + 4\frac{2}{11}\)

\(= 2 + \frac{33}{8} \times \frac{11}{4} - \frac{8}{11} + \frac{46}{11}\)

\(2 + \frac{33}{8} \times \frac{11}{4} - \frac{54}{11}\)

\(= 2 + \frac{33}{8} \times \frac{95}{44}\)

\(= 2 + \frac{3 \times 95}{8 \times 4}\)

\(= 2 + \frac{285}{32}\)

\(2 + 8 \frac{29}{32} = 10\frac{29}{32}\)


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Dicussion (1)

  • \(2 + 4\frac{1}{8} \times \frac{11}{4} - \frac{8}{11} + 4\frac{2}{11}\)

    \(= 2 + \frac{33}{8} \times \frac{11}{4} - \frac{8}{11} + \frac{46}{11}\)

    \(2 + \frac{33}{8} \times \frac{11}{4} - \frac{54}{11}\)

    \(= 2 + \frac{33}{8} \times \frac{95}{44}\)

    \(= 2 + \frac{3 \times 95}{8 \times 4}\)

    \(= 2 + \frac{285}{32}\)

    \(2 + 8 \frac{29}{32} = 10\frac{29}{32}\)

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