To calculate the product of \(-\frac{3}{8}\) and \(-1 \frac{2}{3}\), we first need to convert the mixed number \(-1 \frac{2}{3}\) into an improper fraction.
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Convert \(-1 \frac{2}{3}\) to an improper fraction: \[ -1 \frac{2}{3} = -\left( 1 \times 3 + 2 \right)/3 = -\frac{5}{3} \]
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Now, multiply \(-\frac{3}{8}\) by \(-\frac{5}{3}\): \[ -\frac{3}{8} \times -\frac{5}{3} = \frac{3 \times 5}{8 \times 3} \]
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Simplify: \[ = \frac{15}{24} \]
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We can simplify \(\frac{15}{24}\) by finding the greatest common divisor (GCD) of 15 and 24, which is 3: \[ = \frac{15 \div 3}{24 \div 3} = \frac{5}{8} \]
Thus, the product in its simplest form is \(\frac{5}{8}\).
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