Question

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

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

Answer 1

The expression (4)(-3)(27)(-6)(-52)(-41)(-90)(33) will have a negative result because there is an odd number of negative numbers being multiplied together.

Step-by-step explanation:

The expression given is (4)(-3)(27)(-6)(-52)(-41)(-90)(33). To determine the sign of the product without evaluating the expression, we need to consider the rules of multiplication for the signs of numbers. According to the rules:

• When two positive numbers are multiplied together, the result is positive.
• When two negative numbers are multiplied together, the result is positive.
• When numbers with opposite signs are multiplied, the result is negative.

In the expression, there are five negative numbers and three positive numbers. Multiplying the numbers together in pairs:

1. The product of two negative numbers is positive (e.g., (-3) x (-6) = +18).
2. However, multiplying this result by another negative number will make the product negative (e.g., +18 x (-52) = -936).
3. This pattern continues until all numbers have been multiplied.

Since we have an odd number of negative numbers (five), the overall product will be negative. There are four instances where a pair of negative numbers are multiplied, resulting in a positive, but the one remaining negative number will make the final product negative.