Problem 51 - Algebra 2

Question

Find each percent. 95% of 400

Step-by-Step Solution

Answer

95% of 400 is 380.

Step 1: Understand the Problem

We need to find 95% of the number 400. This means we are calculating 95 percent of 400, which involves understanding that 'percent' means 'per hundred'. Therefore, we want to find 95 out of every 100 parts of the number 400.

Step 2: Convert Percentage to Decimal

To calculate percentages, we need to convert the percentage into a decimal form. Since 95% means 95 per 100, we can convert this to a decimal by dividing 95 by 100, which results in 0.95.

Step 3: Multiply to Find the Result

Now that we have the decimal equivalent of 95% as 0.95, we multiply this decimal by 400 to find 95% of 400. \[ 0.95 \times 400 = 380 \]

Step 4: Verify the Calculation

Check the calculation by considering the logical consistency: multiplying 0.95 by 400 gives us 380. This means that we have taken 95 out of every 100 parts of 400, which matches our original requirement.

Key Concepts

Converting Percentages to Decimals

When you come across a percentage, remember that it's simply a fraction out of 100. Converting percentages to decimals is a crucial first step in many mathematical calculations, including finding percentages of numbers.Here's how you can do it:

• Remove the percent sign (%).
• Divide the percentage value by 100.

For example, to convert 95% into a decimal, you divide 95 by 100: \[ 95 \div 100 = 0.95 \]It's as easy as moving the decimal point two places to the left. This conversion is essential because working with decimals makes calculations, like multiplication, more straightforward.

Multiplication

Multiplication is a fundamental math operation essential for solving various problems, including our task of finding 95% of 400. Once you have converted a percentage to a decimal, you multiply it by the number you're interested in. This process involves adding the original number to itself a specified number of times. In the context of percentages, however, it represents multiplying by a part of the whole.To find 95% of 400:

• Start with the decimal 0.95.
• Multiply by the number 400.

The calculation looks like this:\[ 0.95 \times 400 = 380 \]This means that 95% of 400 is 380. Multiplication in this context allows us to apply the decimal equivalent of a percentage to a whole number to get the desired part.

Basic Arithmetic Operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. In working with percentages, we often rely on multiplication and division. Here's a quick overview:

• Addition: Summing two or more numbers.
• Subtraction: Finding the difference between two numbers.
• Multiplication: Combining equal groups, which is particularly useful when handling percentages after converting them to decimals.
• Division: Splitting a number into equal parts, essential for converting percentages to decimals.

In the process of calculating percentages, we typically use conversion (a form of division) to turn the percentage into a decimal before using multiplication to find the desired amount. By mastering these operations, solving problems involving percentages becomes much more manageable.