To multiply \(1 \frac{2}{3}\) by \(\frac{3}{4}\), follow these steps:
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Convert \(1 \frac{2}{3}\) to an improper fraction. \[ 1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{5}{3} \]
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Now multiply \(\frac{5}{3}\) by \(\frac{3}{4}\): \[ \frac{5}{3} \times \frac{3}{4} = \frac{5 \times 3}{3 \times 4} = \frac{15}{12} \]
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Simplify \(\frac{15}{12}\). The greatest common divisor of 15 and 12 is 3: \[ \frac{15 \div 3}{12 \div 3} = \frac{5}{4} \]
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Convert \(\frac{5}{4}\) back to a mixed number: \[ \frac{5}{4} = 1 \frac{1}{4} \]
So, \(1 \frac{2}{3} \times \frac{3}{4} = 1 \frac{1}{4}\).