Problem 4 - Algebra A Combined Function

Question

The number 87.2 is what percent of \(436 ?\)

Step-by-Step Solution

Answer

87.2 is 20% of 436.

Step 1: Understand the Problem

We need to find out what percent the number 87.2 is of 436. This means we will be comparing 87.2 to 436 to determine what portion 87.2 is, expressed as a percentage.

Step 2: Write the Percent Equation

The equation to find what percent one number (87.2) is of another number (436) is written as: \[ \text{Percent} = \left( \frac{87.2}{436} \right) \times 100 \]

Step 3: Calculate the Fraction

First, calculate the fraction \( \frac{87.2}{436} \). Divide 87.2 by 436 to get:\[ \frac{87.2}{436} \approx 0.2 \]

Step 4: Convert the Fraction to a Percentage

Now that we have the fraction, convert it to a percentage by multiplying by 100:\[ 0.2 \times 100 = 20 \]

Step 5: State the Final Answer

The result is 20, meaning 87.2 is 20% of 436.

Key Concepts

Understanding the Percent Equation

When you're tasked with finding what percent one number is of another, you're setting up a percent equation. This is a mathematical expression that shows the relationship between the portion or part of the whole number. The basic equation can be expressed as:\[\text{Percent} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\]This formula helps you determine the percentage by dividing the part by the total or whole, and then multiplying the result by 100. For example, to find what percent 87.2 is of 436, you use:\[\text{Percent} = \left( \frac{87.2}{436} \right) \times 100\]By following this structure, you can solve any similar percent-related problem with confidence and ease.

Fraction to Percentage Conversion

Converting a fraction to a percentage is a crucial skill in understanding percentages. It involves turning a smaller part in relation to a whole into a percentage.

• First, divide the numerator by the denominator to get a decimal.
• Next, multiply this decimal by 100 to convert it into a percentage.

In our example, we start with the fraction \[\frac{87.2}{436}\]The fraction converts to approximately 0.2 when 87.2 is divided by 436. To change this into a percentage:\[0.2 \times 100 = 20\]This shows that 87.2 is 20% of 436. This simple conversion is essential for turning many everyday fractions into percentages, making them easier to interpret and compare.

Mastering Numerical Comparison

Numerical comparison involves examining two or more numbers to determine their relationship. In the context of percentage calculations, it's about comparing the part to the whole to find out how significant or substantial the part is in relation to the whole.

• Identify the numbers you need to compare; here it's 87.2 and 436.
• Divide the smaller number by the larger one to evaluate its proportion.
• Use decimal approximation for clarity when necessary.

For instance, when you calculate \[\frac{87.2}{436}\approx 0.2\]you're essentially comparing 87.2 to 436, illustrating how 87.2 makes up a 20% portion of 436.

Basic Arithmetic Operations in Percentages

Conducting basic arithmetic operations is fundamental when dealing with percentages. Whether you are adding, subtracting, multiplying, or dividing, understanding how these operations relate to percentages is key.

• **Addition and Subtraction:** Frequently relate to finding increased or decreased percentages of numbers.
• **Multiplication:** Essential for converting fractions to percentages. Simply multiply a decimal by 100.
• **Division:** Used to convert a part into a fraction of a whole. Divide the part by the whole number.

In our example, we used division initially by calculating \[\frac{87.2}{436}\]and then used multiplication for conversion: \[0.2 \times 100 = 20\]These operations help you manipulate and understand percentages more directly in everyday math applications.