Question

Identify the unknown amount as the percent, part, or whole. What number is \(7.5 \%\) of \(28 ?\)

Short answer

Answer: 2.1

Step-by-step solution

Understand the problem

We are given a percent (7.5%) and a whole (28). Our task is to find the part (the number that is 7.5% of 28).

Set up the equation

We can use the following equation to represent the problem: \(\text{Part} = \text{Percent} \times \text{Whole}\). In this case, the Percent is 7.5%, and the Whole is 28.

Convert the percent to a decimal

To work with the percentage, we'll first convert it to a decimal form. To do this, simply divide the percentage by 100: \(\frac{7.5}{100}\) = 0.075.

Solve the equation

Now, we can substitute our values for Percent and Whole into the equation and solve for the Part. $$\text{Part}=0.075 \times 28$$

Calculate the result

By multiplying 0.075 by 28, we get the Part: $$\text{Part}=2.1$$ So, the number that represents \(7.5 \%\) of 28 is 2.1.

Key concepts

Converting Percentages to Decimals

Understanding how to convert percentages to decimals is a fundamental skill in mathematics, especially when solving percent problems. To perform this conversion, simply divide the percentage by 100. This is because the word 'percent' itself means 'per hundred', so you are essentially finding out how many units you have per hundred units. For instance, to convert 7.5% to a decimal, divide 7.5 by 100, which gives you 0.075.

Why is this step important? It's because percentages are not only easier to interpret in this form, but also because decimals are necessary for various mathematical operations, such as multiplication or division, in further calculations.

• To convert a percentage to a decimal, divide by 100.
• 'Percent' means 'per hundred', so you're finding how many out of a hundred.
• Decimal form is needed for further mathematical operations.

Percent Equation

The percent equation is an incredibly useful tool for solving problems related to percentages. It is a simple formula: \[\begin{equation}\text{Part} = \text{Percent} \times \text{Whole}\end{equation}\]This formula allows you to find any of the three components (part, percent, whole) as long as you have the other two. When the percent is already known, as in the exercise, it's a matter of substituting the values into the equation after converting the percent to a decimal.

Using this equation ensures that you are systematically approaching the problem and reduces the risk of error. It's a versatile formula that can be adapted to find different values depending on the given information and what is being asked.

• The percent equation is a foundational formula for solving percent problems.
• It allows you to find one component (part, percent, whole) when you have the other two.
• Converting percent to decimal is a necessary step before using the equation.

Solving for Part in Percentage Problems

When dealing with percentage problems, you often need to find a 'part' of a 'whole' based on a given percent. This is a common real-world scenario, such as figuring out discounts during shopping or determining the concentration of a solution. Using the percent equation \[\begin{equation}\text{Part} = \text{Percent} \times \text{Whole}\end{equation}\]and knowing how to convert the percent to a decimal, the process becomes straightforward. You multiply the decimal form of the percent by the whole to get the part as we did to find that 7.5% of 28 is 2.1.

Remember, the order of operations is important: convert the percentage to a decimal first, then multiply by the whole. This step-by-step method will help you accurately determine the 'part' in percentage problems.

• 'Part' in percentage problems refers to a portion of the 'whole' that corresponds to a certain 'percent'.
• Use the percent equation after converting the percent to a decimal.
• The method is widely applicable in various real-world scenarios.