12.5 Is 8 Of What Number

12.5 is 8% of What Number? A Comprehensive Guide to Percentage Calculations

Understanding percentages is a fundamental skill in many aspects of life, from calculating discounts and taxes to analyzing data and making financial decisions. This article delves into the solution of the problem "12.5 is 8% of what number?", exploring the different methods to arrive at the answer and providing a broader understanding of percentage calculations. We'll break down the process step-by-step, making it accessible to everyone, regardless of their mathematical background.

Understanding the Problem: Deconstructing "12.5 is 8% of What Number?"

The question "12.5 is 8% of what number?" presents a classic percentage problem. We're given a part (12.5), a percentage (8%), and we need to find the whole number (the unknown). This type of problem requires us to work backward from the percentage to find the original value.

This problem is frequently encountered in various contexts:

• Financial calculations: Determining the original price before a discount.
• Data analysis: Finding the total based on a percentage representation.
• Statistical interpretations: Calculating the whole population based on a sample percentage.

Method 1: Using the Percentage Formula

The most straightforward approach involves using the basic percentage formula:

Part = Percentage × Whole

In our problem:

• Part = 12.5
• Percentage = 8% = 0.08 (remember to convert the percentage to a decimal by dividing by 100)
• Whole = x (this is the unknown we need to find)

Substituting these values into the formula gives us:

12.5 = 0.08x

To solve for 'x', we divide both sides of the equation by 0.08:

x = 12.5 / 0.08

x = 156.25

Therefore, 12.5 is 8% of 156.25.

Method 2: Setting up a Proportion

Another effective method involves setting up a proportion. A proportion is an equation stating that two ratios are equal. We can represent the problem as:

8/100 = 12.5/x

This proportion reads: "8 is to 100 as 12.5 is to x."

To solve for x, we cross-multiply:

8x = 12.5 * 100

8x = 1250

x = 1250 / 8

x = 156.25

Again, we arrive at the same answer: 12.5 is 8% of 156.25.

Method 3: Working with Fractions

Percentages can also be expressed as fractions. 8% can be written as 8/100, which simplifies to 2/25. We can then set up an equation:

(2/25) * x = 12.5

To solve for x, we multiply both sides by the reciprocal of 2/25, which is 25/2:

x = 12.5 * (25/2)

x = 156.25

This method confirms our previous results: 12.5 is 8% of 156.25.

Verifying the Answer

It's always a good practice to verify your answer. Let's check if 8% of 156.25 is indeed 12.5:

0.08 * 156.25 = 12.5

The calculation confirms our solution is correct.

Expanding the Understanding: Working with Different Percentages and Values

The methods described above can be applied to solve any percentage problem where you know the part and the percentage, and need to find the whole. Let's consider a few examples:

Example 1: 20 is 25% of what number?

Using the formula: 20 = 0.25x => x = 20 / 0.25 = 80

Example 2: 50 is 10% of what number?

Using the proportion method: 10/100 = 50/x => 10x = 5000 => x = 500

Practical Applications of Percentage Calculations

Percentage calculations are essential in numerous real-world scenarios:

• Sales and discounts: Calculating the original price of an item after a discount. For example, if a shirt is on sale for $25 after a 20% discount, you can use the methods above to determine the original price.
• Tax calculations: Determining the total amount payable after adding sales tax.
• Financial investments: Calculating returns on investments, interest earned, and compound interest.
• Statistical analysis: Interpreting survey results, understanding population demographics, and analyzing data trends.

Beyond the Basics: Advanced Percentage Problems

While the problem "12.5 is 8% of what number?" provides a foundation in percentage calculations, more complex problems may involve multiple percentages, consecutive discounts, or percentage increases over time. These problems often require a multi-step approach, combining the fundamental principles discussed above.

Tips for Success in Percentage Calculations

• Convert percentages to decimals: Always convert percentages to their decimal equivalents (by dividing by 100) before performing calculations.
• Use consistent units: Ensure that all values are expressed in the same units.
• Check your work: Always verify your answer to ensure accuracy.
• Practice regularly: The more you practice percentage calculations, the more comfortable and proficient you will become.

Conclusion: Mastering the Art of Percentage Calculations

Understanding and mastering percentage calculations is crucial for navigating various aspects of daily life and professional endeavors. The problem "12.5 is 8% of what number?" serves as an excellent illustration of the fundamental principles involved. By applying the methods discussed—using the percentage formula, proportions, or fractions—you can effectively solve this and similar problems. Consistent practice and a clear understanding of the underlying concepts will empower you to confidently tackle any percentage-related challenge. Remember, the key is to break down the problem into manageable steps and to always verify your answer.