Final answer:
The product that is negative is Option d: (-3/8) (-5/7) (-1/4), because the rule is that multiplying two numbers with the same sign results in a positive product, and multiplying numbers with different signs results in a negative product.
Step-by-step explanation:
The student is asking which product of given numbers is negative. To answer this, we apply the rule that multiplying numbers with different signs results in a negative product, while multiplying numbers with the same sign results in a positive product.
Reviewing the options provided, we can determine that:
- Option a: (-3/8) (-5/7) (1/4) has two negative and one positive number. Two negatives make a positive, so the overall product is positive.
- Option b: (3/8) (-5/7) (-1/4) has two negatives and one positive, which means the overall product is positive.
- Option c: (3/8) (5/7) (1/4) has all positive numbers, so the product will be positive.
- Option d: (-3/8) (-5/7) (-1/4) has three negative numbers. The first two negatives make a positive, but when this positive is multiplied by the negative 1/4, the overall product becomes negative.
Therefore, the product that is negative is Option d.