Problem 25 - Elementary Algebra Within Reach

Question

Solve the percent equation. What number is \(30 \%\) of 150 ?

Step-by-Step Solution

Answer

Therefore, \(30 \%\) of 150 is 45.

Step 1: Understand the Question

We are to calculate what number \(30 \% \) of 150 represents. In order to calculate this, we will translate the percentage into a decimal and then multiply by 150.

Step 2: Convert the Percentage to a Decimal

To convert the percentage to a decimal, we divide the percent by 100. Thus, \(30 \% = 30 / 100 = 0.30\)

Step 3: Multiply the Result by the Given Number

Now, we multiply 150 (the given number) by 0.30 (the decimal equivalent of the given percentage). That is, \(150 * 0.30 = 45\)

Key Concepts

Percentage Conversion Simplified

The first step in solving a percent equation is to convert the percent into a decimal. This is because calculations in math typically require numbers to be in decimal form, which is easier to use in arithmetic operations. To convert a percentage to a decimal:

• Divide the percentage by 100

For example, if you're asked to convert 30%, you simply calculate \(30 \div 100\).

This results in the decimal \(0.30\). Remember, the position of the decimal point is crucial—it affects the value significantly. This method works for all percentages and is a fundamental skill in making sense of percent problems.

Understanding Decimal Multiplication

Once you've converted the percentage to a decimal, the next major step involves multiplication. This step determines what portion the percentage represents of the total number given. When you multiply a number by a decimal:

• The product typically gives you a fraction of the original number.
• This helps you solve problems related to parts of a whole, such as in this exercise.

To illustrate, take 150 and multiply it by 0.30:\[150 \times 0.30 = 45\]Here, 150 is the total, and 0.30 represents 30%. Thus, by multiplying, you're determining what 30% of 150 is, which equals 45. This process is essential in everyday calculations involving discounts, interest rates, and scientific data.

Effective Problem Solving Steps

To solve percent-related problems effectively, it's helpful to use a structured approach like the one shown in the example. Here's how you can organize your steps:

• Read and Understand the Question: Clearly determine what the problem is asking you to find.
• Convert Percent to Decimal: Transform any percentages into decimals to simplify calculations.
• Perform the Calculation: Multiply the decimal by the total number involved to find your answer.

Following these steps ensures clarity and accuracy in your solution. In our exercise, realizing that we need to find 30% of 150 is the starting point. By systematically converting the percent and performing the multiplication, we solve the problem with confidence. This strategy aids not only in statlike exercises but also in real-life applications.