To determine the sign of the product and compute \(-\frac{3}{8} \times -1 \frac{2}{3}\), we can follow these steps:
Step 1: Determine the signs of the factors
- The first factor is \(-\frac{3}{8}\) (negative).
- The second factor, \(-1 \frac{2}{3}\), is also negative because it has a negative sign in front.
Conclusion of Sign
Since both factors are negative, the product will be positive. Therefore, the response is: Positive - If the signs of the factors are the same, the product is positive.
Step 2: Compute the product in simplest form
To compute the product \(-\frac{3}{8} \times -1 \frac{2}{3}\), we first convert the mixed number \(-1 \frac{2}{3}\) to an improper fraction.
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Convert \(-1 \frac{2}{3}\) to an improper fraction:
- Multiply the whole number \(1\) by the denominator \(3\) and add the numerator \(2\): \[ 1 \times 3 + 2 = 3 + 2 = 5 \]
- Therefore, \(-1 \frac{2}{3} = -\frac{5}{3}\).
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Now, multiply the two fractions: \[ -\frac{3}{8} \times -\frac{5}{3} \] The negatives cancel out (because negative times negative is positive): \[ = \frac{3}{8} \times \frac{5}{3} \] When multiplying fractions, multiply the numerators and the denominators: \[ = \frac{3 \times 5}{8 \times 3} = \frac{15}{24} \]
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Simplify \(\frac{15}{24}\):
- Find the greatest common divisor (GCD) of \(15\) and \(24\), which is \(3\).
- Divide both numerator and denominator by \(3\): \[ = \frac{15 \div 3}{24 \div 3} = \frac{5}{8} \]
Final Answer
Thus, the product in simplest form is: 5 eighths (58).
So, the answers are:
- Determining the sign: Positive
- Determining the product in simplest form: 5 eighths (58).
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