Problem 25 - Elementary and Intermediate Algebra

Question

Multiply. $$ 4.5 \cdot(-28) $$

Step-by-Step Solution

Answer

-126

Step 1: Understand the Problem

To solve the problem, you need to multiply 4.5 by -28. This involves a positive number and a negative number, which yields a negative result.

Step 2: Multiply the Absolute Values

First, multiply the absolute values of the numbers. So, calculate 4.5 times 28.

Step 3: Perform the Multiplication

\(4.5 \times 28 = 126\)

Step 4: Apply the Sign Rule

Since we are multiplying a positive number by a negative number, the result will be negative. Therefore, the result of \(4.5 \times (-28)\) will be \(-126\).

Key Concepts

absolute values

When dealing with multiplication of numbers, absolute values play an important role. The absolute value of a number represents its distance from zero, regardless of its sign. To find the absolute value of any number, you simply ignore its sign.

For example:

• The absolute value of 4.5 is 4.5.
• The absolute value of -28 is 28.

Understanding absolute values simplifies the calculation process. When faced with a multiplication problem, first consider the absolute values of the given numbers. In our example, you will multiply 4.5 and 28.

sign rule in multiplication

An important rule in multiplication involves determining the sign of the product. Here's a simple way to remember it:

• Positive × Positive = Positive
• Positive × Negative = Negative
• Negative × Positive = Negative
• Negative × Negative = Positive

This sign rule dictates the sign of the result. In our exercise:

Multiplying 4.5 (a positive number) by -28 (a negative number) results in a negative product. This is because a positive times a negative is always negative.

The result is negative as per the rule.

multiplication process

The multiplication process is straightforward but requires careful steps:

• First, identify the absolute values of the numbers involved.
• Next, multiply these absolute values.
• Finally, apply the sign rule to determine the final sign of the product.

Let's break down the multiplication of 4.5 and -28 in our exercise:

• Step 1: Find the absolute values: 4.5 and 28.
• Step 2: Multiply the absolute values: 4.5 × 28 = 126.
• Step 3: Apply the sign rule: Since the original problem involves multiplying a positive by a negative, the result is negative.
• Final Result: -126.