To determine the sign of the product \(-\frac{3}{8} \times -1 \frac{2}{3}\), we first need to analyze the signs of each factor.
- The first factor is \(-\frac{3}{8}\), which is negative.
- The second factor is \(-1 \frac{2}{3}\). We can convert this mixed number into an improper fraction: \[ -1 \frac{2}{3} = -\left(1 + \frac{2}{3}\right) = -\left(\frac{3}{3} + \frac{2}{3}\right) = -\frac{5}{3} \] So, the second factor is also negative.
Now we have the two factors:
- First factor: Negative \(-\frac{3}{8}\)
- Second factor: Negative \(-\frac{5}{3}\)
According to the rules for the sign of the product:
- Positive: if the signs of the factors are the same
- Negative: if the signs of the factors are different
In this case, both factors are negative. Since the signs of the factors are the same (both negative), the product will be positive.
Therefore, the sign of the product \(-\frac{3}{8} \times -1 \frac{2}{3}\) is positive.
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