Problem 12 - Beginning and Intermediate Algebra

Question

Find each product. \(-8(5)\)

Step-by-Step Solution

Answer

The product of -8(5) is -40.

Step 1: Identify the terms

In this exercise, you need to identify the two numbers you are multiplying. The given numbers are -8 and 5.

Step 2: Understand the concept of multiplication with negative numbers

Recall the rule that when you multiply a negative number by a positive number, the product is always negative. So, the product of -8 and 5 will be negative.

Step 3: Perform the multiplication

Multiply the absolute values of the numbers. Ignore the negative sign for now and multiply 8 by 5, which gives you 40.

Step 4: Apply the sign to the product

Since we know the product of a negative number and a positive number is negative, apply the negative sign to 40. Thus, the product of -8 and 5 is -40.

Key Concepts

Negative Numbers

Negative numbers represent values less than zero. They are commonly used to express loss, debt, or temperature below freezing, among other concepts.

Negative numbers are represented with a minus sign (-) in front of them. For example, -3 means three units less than zero. They are crucial in mathematics to perform various operations and solve real-world problems.

Understanding negative numbers helps in many areas, such as balancing equations and comprehending concepts like elevation below sea level or financial deficits.

Multiplication Rules

Multiplying numbers involves combining equal groups. The rules for multiplication, especially with negative numbers, are essential for getting the correct results:

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars around the number, like this: \( | x | \).

For instance, \( | -8 | = 8 \) and \( | 8 | = 8 \). The absolute value function strips the sign, focusing solely on magnitude.

Understanding absolute value is crucial when performing operations like multiplication, especially with negative numbers. For example, when multiplying -8 by 5, we first find the absolute values and multiply them: \ | -8 | = 8 \ and \ | 5 | = 5 \.

By multiplying these absolute values, we get 40. Then, we apply the correct sign according to multiplication rules, yielding -40 in the given exercise.

• It helps simplify problems.
• Allows easier handling of operations with negative values.
• Provides clarity on the magnitude and size of numbers.