Discussion
The value of \(8\frac{1}{4}\) of \(\frac{3}{4} + 6 \div [4 \times \{3 - (2 - \frac{1}{3})\}]\) is
Answer: B
The value is \(7\frac{5}{16}\).
Work the brackets from the inside out, then 'of', then division, then addition:
\[ \begin{aligned} 2 - \tfrac{1}{3} &= \tfrac{5}{3},\ \ 3 - \tfrac{5}{3} = \tfrac{4}{3} \\ 4 \times \tfrac{4}{3} &= \tfrac{16}{3},\ \ 6 \div \tfrac{16}{3} = \tfrac{9}{8} \\ \tfrac{33}{4} \times \tfrac{3}{4} &= \tfrac{99}{16} \end{aligned} \]
Adding, \(\frac{99}{16} + \frac{18}{16} = \frac{117}{16} = 7\frac{5}{16}\). All four options end in \(\frac{5}{16}\), so the question turns on the whole number; \(6\frac{5}{16}\) is \(\frac{99}{16}\) alone, forgetting to add the \(\frac{9}{8}\).
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