Problem 54 - Algebra 2

Question

Find each percent. 99% of 500

Step-by-Step Solution

Answer

99% of 500 is 495.

Step 1: Understand the Problem

To find 99% of 500, we need to determine what number is 99% when 500 is the whole, or 100%.

Step 2: Convert Percent to Decimal

Percentages are based on 100, so 99% can be converted to a decimal by dividing by 100: \[99\% = \frac{99}{100} = 0.99\]

Step 3: Calculate 99% of 500

Now, multiply 500 by the decimal equivalent of 99%:\[99\% \text{ of } 500 = 0.99 \times 500 \]

Step 4: Perform the Multiplication

Calculate the product: \[0.99 \times 500 = 495\]

Step 5: Conclude the Calculation

Thus, 99% of 500 is 495.

Key Concepts

Convert Percent to Decimal

When working with percentages, it's often necessary to convert them into decimal form in order to perform calculations more easily. This process involves a simple yet crucial step. Every percentage can be viewed as a number out of 100 since "percent" means "per hundred." To convert a percentage to a decimal, divide the percentage by 100. For example, to convert 99% into a decimal, you would calculate:

• Divide 99 by 100.

In mathematical terms, this looks like:\[99\% = \frac{99}{100} = 0.99\]This conversion is important because it allows you to use the number in further mathematical operations, such as multiplication, which we'll explore next. Remember, converting from percentage to decimal is always done by dividing by 100.

Multiplication in Percent Problems

Once a percentage is converted to a decimal, you are ready to address specific percent problems that involve multiplication. These often come in the format of finding a percentage of a given number. For instance, to find 99% of 500, with the decimal conversion already done (99% equals 0.99), we multiply the decimal by the number.Here's how you handle this step:

• Take the decimal equivalent of the percentage (0.99).
• Multiply it by the total amount (500).

This is performed as:\[0.99 \times 500 = 495\]The result, 495 in this instance, represents the value of 99% of 500. Multiplication allows us to find part of a whole based on the given percentage, simplifying calculations in practical and mathematical contexts.

Mathematical Reasoning

Mathematical reasoning involves understanding and applying the steps and logic needed to solve a problem effectively. In percent calculations, like 99% of 500, reasoning involves the sequence of conversion and operations to reach the final result. Here’s a basic outline of the reasoning process used in the problem:

• Identify what the problem asks: What is 99% of 500?
• Convert the percentage into a decimal by dividing by 100 (99% becomes 0.99).
• Multiply the decimal by the whole (0.99 multiplied by 500).
• Interpret the product for your answer (495 is the value of 99% of 500).

This reasoning approach ensures that steps are logically followed, which is essential for solving both simple and complex mathematical problems. By practicing such reasoning, one improves not only problem-solving skills but also gains confidence in mathematical computations.