Problem 13 - Prealgebra

Question

Solve each problem using the percent equation. 9 is what percent of \(25 ?\)

Step-by-Step Solution

Answer

9 is 36% of 25.

Step 1: Identify the Components

First, we need to identify the parts of the problem that fit into the percent equation. The problem states that 9 is some percent of 25. The number 9 is the part, 25 is the whole, and we are looking for the percent.

Step 2: Write the Percent Equation

The general percent equation is: \( \text{Part} = \text{Percent} \times \text{Whole} \). Here, our equation becomes: \( 9 = P \times 25 \), where \( P \) represents the percent in decimal form.

Step 3: Solve for Percent

We need to isolate \( P \) in the equation \( 9 = P \times 25 \). Divide both sides by 25 to solve for \( P \): \( P = \frac{9}{25} \).

Step 4: Convert Decimal to Percent

The fraction \( \frac{9}{25} \) as a decimal is 0.36. To convert a decimal to a percent, multiply by 100. Thus, \( 0.36 \times 100 = 36 \).

Key Concepts

Identifying Parts of a Percent Problem

When you're given a percent problem, the first step is to determine the key components: the part, the whole, and the percent. Consider the statement "9 is what percent of 25?" Here, the **part** is the number you're trying to find the percentage for, which is 9 in this case. The **whole** is the larger number in relation to which you're finding the percentage, which is 25 here. Finally, the missing element that you're solving for is the **percent**. This is the value that will express the relationship between the part and the whole in percentage terms.

• **Part**: This is the number you're comparing to the whole (9).
• **Whole**: This is the total or the number you're comparing against (25).
• **Percent**: This is what you're trying to find out.

By identifying these components, you set up the problem to use the percent equation. We can express this as: **Part = Percent × Whole**. Here, you will arrange it as: **9 = P × 25**, where **P** is the percent in its decimal form. Separating these parts helps to correctly solve for the unknown.

Percent as a Decimal

Understanding how percents relate to decimals is essential in solving percent problems. Percent means "per hundred," so when you see a percentage, it's showing you how many parts out of a hundred something is. To work with percents in mathematical equations, you often need to convert them into decimals first.
Percents can easily be turned into decimals by dividing the percent value by 100. For example, converting 36% into a decimal involves simply placing the percent over 100, resulting in 0.36. This is because 36% is essentially 36 out of 100, which simplifies to 0.36 as a decimal.
Why do we do this? Decimal form makes it easier to handle calculations, especially in equations like **Part = Percent × Whole**. Here, the percent in decimal form (**P**) can be multiplied directly by the whole to reveal the part.

Converting Decimals to Percents

After solving an equation and getting your answer as a decimal, it's often necessary to convert it back into a percent to interpret the result in the problem's context. This is a common step in percent problems that helps in understanding the answer in a familiar percent format.
To convert a decimal to a percent, you multiply the decimal by 100. This shifts the decimal point two places to the right. In our example, after dividing 9 by 25, we got 0.36 as the decimal. Multiplying 0.36 by 100 gives you 36. Thus,

• Decimal: 0.36
• Percent: 36%

By doing this, you clearly see that 9 is 36% of 25. This conversion step provides a clear way to express your results in percentage, which is often easier to understand and interpret.