Problem 16 - Algebra 1

Question

Find the product. $$(-8)(3)$$

Step-by-Step Solution

Answer

The product of -8 and 3 is -24.

Step 1: Identify the numbers

Identify the numbers to be multiplied which are -8 and 3.

Step 2: Multiply the numbers

Multiply the identified numbers. When a negative number is multiplied by a positive number, the result is usually negative. Thus, -8 multiplied by 3 equals to -24.

Key Concepts

Negative Numbers

Negative numbers are numbers with a minus sign (-) in front of them. They are essential in representing values less than zero. Learning about negative numbers often involves understanding that they behave differently when involved in operations like addition, subtraction, and multiplication.

Here are some key points to remember about negative numbers:

• Places below zero on a number line: Negative numbers are always on the left side of zero.
• Opposite of positive numbers: The opposite of +5 is -5.
• Multiplication Rules: When you multiply a negative number by a positive number, the product is negative.

In this exercise, -8 is a negative number, and it's important to remember that it will affect the sign of the result when multiplied.

Product

The product is the result you obtain when you multiply numbers together. Understanding how to find the product of numbers, especially when involving negatives, is important.

When calculating the product, it's important to apply consistent rules. For our specific problem,

• We have two numbers to multiply: -8 and 3.
• According to the rules of multiplication involving negative numbers, since one number is negative and the other is positive, the product will be negative.

This guideline shows that the product, in this case, is the value of \[(-8) imes 3 = -24\] demonstrating the rule that the product takes a negative sign when a negative is multiplied by a positive.

Step-by-Step Solution

The step-by-step solution method is a systematic approach to solving math problems. It breaks down the process into manageable parts, making it easier to follow and understand.

In the given exercise, the solution was handled in the following way:

• Step 1: Identify the numbers. Here, the numbers to be multiplied are noted: -8 and 3.
• Step 2: Multiply the numbers. By applying the rule that a negative times a positive equals a negative, the procedure simplifies the calculation: \[(-8) imes 3 = -24\]

These steps not only illustrate how to reach the solution, but also reinforce the fundamental rule of multiplying negative and positive numbers. It encourages systematic practice, helping solidify understanding through consistent application.