Problem 15 - Elementary and Intermediate Algebra

Question

Multiply. $$ 8 \cdot(-3) $$

Step-by-Step Solution

Answer

-24

Step 1: Identify the Numbers

Identify the two numbers in the multiplication problem. Here, we need to multiply 8 and -3.

Step 2: Understand the Sign Rules

Recall the rule for multiplying positive and negative numbers. The product of a positive number and a negative number is always negative.

Step 3: Perform the Multiplication

Multiply the absolute values of the numbers: 8 multiplied by 3 is 24.

Step 4: Apply the Sign

Since we are multiplying a positive number (8) and a negative number (-3), the result is negative. Thus, the final answer is -24.

Key Concepts

multiplication rules

Understanding the rules of multiplication is essential to mastering the concept. Here are some key rules to remember:

• If you multiply two positive numbers, the result is always positive (e.g., 5 * 4 = 20).
• If you multiply two negative numbers, the result is always positive (e.g., -5 * -4 = 20).
• If you multiply a positive number by a negative number, the result is always negative (e.g., 8 * -3 = -24).

These rules form the foundation of multiplication and are critical when working with both positive and negative numbers. Remember these rules to help solve multiplication problems efficiently.

positive and negative numbers

Positive and negative numbers are fundamental concepts in mathematics. Here are essential points to remember:

• Positive numbers are greater than zero, such as 1, 2, and 3.
• Negative numbers are less than zero, such as -1, -2, and -3.
• Zero is neutral, neither positive nor negative.

When working with these numbers, remember:

• Adding two positive numbers results in a positive number.
• Adding two negative numbers results in a negative number.
• Adding a positive number and a negative number can result in either a positive or negative number, depending on their sizes.
• Subtracting a negative number is the same as adding its positive counterpart.

Understanding these properties helps in many mathematical operations, including multiplication.

absolute value

The absolute value of a number is its distance from zero on the number line, without considering direction. Here are some important points about absolute value:

• The absolute value of a positive number is the number itself (e.g., |5| = 5).
• The absolute value of a negative number is its positive counterpart (e.g., |-5| = 5).
• The absolute value of zero is zero (|0| = 0).

Absolute value is represented by two vertical bars around the number, e.g., \( |x| \). This concept is useful in multiplication, especially when dealing with negative numbers. For instance, when multiplying 8 and -3, we first consider the absolute values to get 8 * 3 = 24. Then, we apply the sign rule (positive times negative) to get -24. Understanding absolute value aids in simplifying and accurately solving multiplication problems.