Discussion
The value of
\[ \begin{aligned} &6\tfrac{2}{3} \div 2\tfrac{1}{2} \times 3\tfrac{3}{4} - 5\tfrac{1}{2} \times 4\tfrac{1}{4} \\ &+ 1\tfrac{2}{3}\left(\tfrac{7}{8} + \tfrac{3}{4} \times \tfrac{2}{3}\right) \end{aligned} \]
is
Answer: A
The value is \(-11\frac{1}{12}\).
Convert the mixed numbers to improper fractions and follow the order of operations, working left to right for ÷ and ×:
\[ \begin{aligned} \tfrac{20}{3} \div \tfrac{5}{2} \times \tfrac{15}{4} &= \tfrac{8}{3} \times \tfrac{15}{4} = 10 \\ \tfrac{11}{2} \times \tfrac{17}{4} &= \tfrac{187}{8} \\ \tfrac{5}{3}\left(\tfrac{7}{8} + \tfrac{1}{2}\right) &= \tfrac{5}{3} \times \tfrac{11}{8} = \tfrac{55}{24} \end{aligned} \]
\[ \begin{aligned} 10 - \tfrac{187}{8} + \tfrac{55}{24} &= \tfrac{240 - 561 + 55}{24} \\ &= -\tfrac{266}{24} = -11\tfrac{1}{12} \end{aligned} \]
The positive option \(11\frac{1}{12}\) loses the sign; the result is negative because the subtracted product, about 23.4, exceeds the other terms.
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