To multiply \( \frac{2}{3} \) by \( 1 \frac{1}{4} \), we first need to convert the mixed number \( 1 \frac{1}{4} \) into an improper fraction.
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Convert \( 1 \frac{1}{4} \): \[ 1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \]
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Now multiply \( \frac{2}{3} \) by \( \frac{5}{4} \): \[ \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12} \]
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Next, simplify \( \frac{10}{12} \):
- Find the greatest common divisor (GCD) of 10 and 12, which is 2.
- Divide both the numerator and the denominator by 2: \[ \frac{10 \div 2}{12 \div 2} = \frac{5}{6} \]
Thus, the answer in simplest form is \( \frac{5}{6} \).