Problem 1 - Prealgebra

Question

Solve each of the following problems. What number is \(25 \%\) of \(32 ?\)

Step-by-Step Solution

Answer

25% of 32 is 8.

Step 1: Understand the question

We need to find a number that represents 25% of 32. This means we take 25% of the whole, which is 32, and find the corresponding amount.

Step 2: Convert Percentage to Decimal

To calculate a percentage of a number, first convert the percentage to a decimal. For 25%, divide 25 by 100, getting 0.25.

Step 3: Multiply to find the percentage

Now, multiply the decimal form of the percentage by the number. Calculate \(0.25 \times 32\) to find 25% of 32.

Step 4: Calculate the result

Perform the multiplication: \(0.25 \times 32 = 8\). So, 25% of 32 is 8.

Key Concepts

Percentage Calculation

Percentage calculation helps us determine how a given number compares to a whole, represented by 100%. The most common scenario is finding out what part a percentage is of a particular number. For example, when asked what 25% of 32 is, we want to know which number is 25% of 32. Here are the steps to consider:

• Identify the whole: In this example, the whole is represented by the number 32.
• Select the percentage you want to find: In this case, it's 25%.
• Perform the calculations to find out what that percentage equals as a part of the whole.

This approach simplifies the process of translating percentages into real-world numbers, making it more relatable and easier to understand. Breaking the question down into manageable steps allows for accurate calculation and understanding of percentage as a part of real values.

Converting Percentages to Decimals

Converting percentages to decimals is a crucial step in solving problems that involve percentages. The key to this conversion is understanding the relationship between percentages and numbers in decimal form. To convert a percentage into a decimal:

• Recall that 'percent' means 'per hundred.' For example, 25% means 25 per 100.
• Divide the percentage value by 100. This conversion shifts the decimal point two places to the left, effectively turning the percentage into a decimal.

In practice, for 25%, this means taking 25 ÷ 100, which equals 0.25. Practicing this step is important, as it simplifies the calculation process in math problems dealing with percentages. Performing this process allows you to handle more complex calculations with ease, as most further calculations in percentage problems use their decimal form.

Multiplying Decimals

Multiplying decimals may seem tricky, but it follows the same core principles as basic multiplication. The key is managing the place value—or the position of the decimal point—in the final answer. When multiplying decimals such as in this case of finding 25% of 32:

• First, multiply the numbers as if they were whole numbers. For example, multiply 25 by 32.
• Count the total decimal places in both factors. Here, 0.25 has two decimal places, while 32 is a whole number, having none.
• Move the decimal place to the left in your product result to match the total number of decimal spaces in the original problem.

So, for multiplying 0.25 by 32, you notice 0.25 is the decimal representation of 25%, and your multiplication results in 8. Understanding decimal multiplication is key for problems involving percentage operations, ensuring you get accurate results regardless of the decimal nature of the numbers involved.