To multiply the two fractions \( 2 \frac{5}{6} \) and \( \frac{3}{4} \), we first convert the mixed number \( 2 \frac{5}{6} \) into an improper fraction.
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Convert \( 2 \frac{5}{6} \): \[ 2 \frac{5}{6} = 2 \times 6 + 5 = 12 + 5 = 17 \quad \text{(So, it becomes \( \frac{17}{6} \))} \]
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Now we multiply \( \frac{17}{6} \) by \( \frac{3}{4} \): \[ \frac{17}{6} \times \frac{3}{4} = \frac{17 \times 3}{6 \times 4} = \frac{51}{24} \]
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Now we simplify \( \frac{51}{24} \) if possible. The greatest common divisor (GCD) of 51 and 24 is 3. \[ \frac{51 \div 3}{24 \div 3} = \frac{17}{8} \]
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Finally, we can convert \( \frac{17}{8} \) back to a mixed number: \[ \frac{17}{8} = 2 \frac{1}{8} \quad \text{(because \( 17 \div 8 = 2 \) with a remainder of 1)} \]
Thus, the product of \( 2 \frac{5}{6} \) and \( \frac{3}{4} \) is \( \frac{17}{8} \) or \( 2 \frac{1}{8} \).