To determine which expressions have positive products, we need to consider the signs of each expression. The product of numbers is positive if it contains an even number of negative factors (including zero, which doesn't contribute to the product).
Let's analyze each option:
A: \[ (-5)(0.2)(-9) \]
- Negative numbers: 2 (−5 and −9)
- Positive numbers: 1 (0.2)
- Even count of negatives (2), so the product is positive.
B: \[ \left(\frac{2}{3}\right)\left(\frac{3}{2}\right)\left(-\frac{1}{2}\right) \]
- Negative numbers: 1 (−1/2)
- Positive numbers: 2 (2/3 and 3/2)
- Odd count of negatives (1), so the product is negative.
C: \[ (6)(-3)(8)(-7) \]
- Negative numbers: 2 (−3 and −7)
- Positive numbers: 2 (6 and 8)
- Even count of negatives (2), so the product is positive.
D: \[ (-4\frac{1}{3})(-\frac{1}{4})(-5\frac{1}{2})(-\frac{7}{9}) \]
- Negative numbers: 4 (all are negative)
- Positive numbers: 0
- Even count of negatives (4), so the product is positive.
E: \[ (5)(-10)(345)(2) \]
- Negative numbers: 1 (−10)
- Positive numbers: 3 (5, 345, and 2)
- Odd count of negatives (1), so the product is negative.
F: \[ (-1.2)(-3.5)(2.7)(-0.8) \]
- Negative numbers: 3 (−1.2, −3.5, −0.8)
- Positive numbers: 1 (2.7)
- Odd count of negatives (3), so the product is negative.
Based on this analysis, the expressions that have positive products are:
A, C, D.
1 answer