Problem 124 - Introductory Algebra for College Students

Question

Explain how to determine the sign of a product that involves more than two numbers.

Step-by-Step Solution

Answer

To determine the sign of a product involving more than two numbers, count the number of negative numbers in the product. If the count is even (or zero), the product is positive. If the count is odd, the product is negative.

Step 1: Understanding the Multiplication Rule for Positive and Negative Numbers

Start by explaining the basic rule: The product of two positive numbers or two negative numbers is always positive, and the product of a positive number and a negative number is always negative. This applies no matter the value of the numbers involved.

Step 2: Determining the Sign When More Than Two Numbers Are Involved

When more than two numbers are being multiplied, the sign of the product can be determined by the number of negative factors: If the number of negative numbers is even (including zero), the product will be positive. If the number of negative numbers is odd, the product will be negative.

Step 3: Practical Application

Put the above principles into practice. For instance, if the numbers are -2,3,-4, the product is \( -2 \times 3 \times -4 = 24 \). There are two negative numbers(-2 and -4), an even count, so the product is positive.