To solve the expression \( 6 \frac{2}{3} (6 \times 2 \div 6 \times 3) \), we first need to interpret the parts step by step.
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Convert \( 6 \frac{2}{3} \) to an improper fraction: \[ 6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3} \]
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Calculate \( 6 \times 2 \div 6 \times 3 \): First, we multiply and divide as follows: \[ 6 \times 2 = 12 \] Next, interpret \( \div 6 \times 3 \) as follows: \[ 12 \div 6 = 2 \quad (then \quad 2 \times 3 = 6) \] Thus, \( 6 \) represents the result of the operation.
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Combine the two parts: Now multiply \( \frac{20}{3} \) by \( 6 \): \[ \frac{20}{3} \times 6 = \frac{20 \times 6}{3} = \frac{120}{3} = 40 \]
Thus, the final result is \( \frac{40}{1} \) or just \( 40 \).