Problem 120 - Beginning and Intermediate Algebra

Question

Write a numerical expression for each phrase, and simplify the expression. \(30 \%\) of the product of -8 and 5

Step-by-Step Solution

Answer

-12

Step 1: Identify the product

First, identify the product of -8 and 5. Multiply these two numbers: i.e., the product of -8 and 5 = \(-8 \times 5 = -40\)

Step 2: Calculate 30% of the product

Next, find 30% of the product calculated in Step 1. To calculate the percentage of a number, multiply the number by the percentage expressed as a decimal: 30% of \(-40 = -40 \times 0.30\)

Step 3: Simplify the expression

Now, perform the multiplication to simplify the expression: \(-40 \times 0.30 = -12\)

Key Concepts

Percentage Calculation

Calculating a percentage of a number is a valuable mathematical skill. To do this, you must first convert the percentage to a decimal.
You can convert a percentage to a decimal by dividing it by 100. For example, 30% becomes 0.30.

You then multiply the decimal by the number you need the percentage of. In this case, we are finding 30% of -40.
The formula is: \text{Percentage Calculation} = \text{Original Number} \times \text{Percentage as a Decimal}
So, 30% of -40 is calculated as follows: \(-40 \times 0.30 = -12\).
Understanding how to calculate percentages helps you solve a variety of real-world problems, like finding discounts, interest rates, and more.

Multiplication

Multiplication is a basic arithmetic operation that combines equal groups. It's symbolized by a star \((*)\) or a cross \((\times)\).
When you multiply two numbers, you are essentially adding a number to itself multiple times. For example, \(4 \times 3\) means adding 4 three times: 4 + 4 + 4 = 12.

In our example, we had to find the product of -8 and 5. Multiplying involves a few simple rules when it comes to signs:

• Positive \(\times\) Positive = Positive
• Negative \(\times\) Negative = Positive
• Positive \(\times\) Negative = Negative
• Negative \(\times\) Positive = Negative

Following these rules, -8 multiplied by 5 is \(-8 \times 5 = -40\). This is because a negative multiplied by a positive number results in a negative product.

Simplifying Expressions

Simplifying expressions makes them easier to work with. The goal is to rewrite an expression in its simplest form. This often involves performing the indicated operations, like addition, subtraction, multiplication, and division.
Let's look at our example step-by-step.
First, we needed to find the product of -8 and 5. This gave us -40.
Next, we calculated 30% of this product. We did this by multiplying -40 by 0.30 to get -12.
Simplifying an expression can involve:

• Combining like terms
• Performing basic arithmetic operations
• Applying algebraic identities

In this case, our operations were straightforward: multiplication and percentage calculation.
By understanding these steps, you can tackle a wide variety of math problems with ease.