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If '+' means '÷', '÷' means '-', '-' means '×' and '×' means '+' then

12 + 6 + 3 - 2 × 8 = ?

  • A.\(8\tfrac{1}{3}\)
  • B.\(9\tfrac{1}{3}\)
  • C.\(9\tfrac{1}{4}\)
  • D.\(9\tfrac{1}{2}\)

Answer: B

The value is \(9\tfrac{1}{3}\).

Replace each sign by its meaning: '+' becomes '÷', '-' becomes '×' and '×' becomes '+'. The expression becomes

\[ 12 \div 6 \div 3 \times 2 + 8 \]

Working left to right for division and multiplication, then adding:

\[ \begin{aligned} 12 \div 6 &= 2,\quad 2 \div 3 = \tfrac{2}{3} \\ \tfrac{2}{3} \times 2 &= \tfrac{4}{3} \\ \tfrac{4}{3} + 8 &= 9\tfrac{1}{3} \end{aligned} \]

\(8\tfrac{1}{3}\) is one less than the correct value, and none of the other options results from applying the substitutions and then the usual order of operations.

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