Question

Without evaluating the expression, explain why your answer is positive or negative.

(4)(-3) (27)(-6)(-52)(-41)(-90) (33)

Options:
Option 1: The answer is positive because there are an even number of negative factors.
Option 2: The answer is positive because there are an odd number of negative factors.
Option 3: The answer is negative because there are an even number of negative factors.
Option 4: The answer is negative because there are an odd number of negative factors.

Answer 1

The expression has five negative factors, which is an odd number of negative factors. According to the multiplication rules for signs, an odd number of negative factors results in a negative product. Thus, the answer is negative.

Step-by-step explanation:

To determine whether the product of several numbers is positive or negative, we need to consider the multiplication rules related to signs. Rule 6 states that the product of two negative numbers is positive. Rule 7 explains that the product of numbers with opposite signs is negative.

Looking at the expression (4)(-3)(27)(-6)(-52)(-41)(-90)(33), let's count the number of negative factors:

• -3
• -6
• -52
• -41
• -90

There are five negative factors, which is an odd number. Since the multiplication of two negative numbers yields a positive result, when there is an odd number of negative factors, the end product will be negative. This is because with each pair of negatives multiplying to a positive, one negative factor remains without a pair, resulting in a negative product.

Therefore, the correct option is:

Option 4: The answer is negative because there are an odd number of negative factors.