15 Is What Percent Of 120

15 is What Percent of 120? A Comprehensive Guide to Percentage Calculations

Understanding percentages is a fundamental skill in various aspects of life, from calculating discounts and taxes to analyzing data and understanding statistics. This comprehensive guide will delve into the question, "15 is what percent of 120?", providing a step-by-step solution, exploring different calculation methods, and offering real-world applications to solidify your understanding. We’ll also cover the underlying concepts and explore related percentage problems.

Understanding Percentages

A percentage is a fraction or ratio expressed as a number out of 100. The symbol "%" represents "percent," meaning "per hundred." For example, 50% means 50 out of 100, which is equivalent to ½ or 0.5.

Percentages are incredibly useful for:

• Comparing proportions: Expressing values as percentages allows for easy comparison of different quantities, even if they are based on different total amounts.
• Analyzing data: Percentages are frequently used in data analysis to present trends, changes, and proportions in a clear and concise manner.
• Financial calculations: Interest rates, discounts, taxes, and profit margins are all commonly expressed as percentages.

Calculating "15 is What Percent of 120?"

There are several ways to solve this problem:

Method 1: Using the Percentage Formula

The fundamental formula for calculating percentages is:

(Part / Whole) x 100% = Percentage

In our case:

• Part: 15
• Whole: 120

Substituting these values into the formula:

(15 / 120) x 100% = 12.5%

Therefore, 15 is 12.5% of 120.

Method 2: Setting up a Proportion

Another way to approach this is by setting up a proportion:

15/120 = x/100

Here, 'x' represents the percentage we want to find. To solve for 'x', cross-multiply:

15 * 100 = 120 * x

1500 = 120x

x = 1500 / 120

x = 12.5

Therefore, x = 12.5%

Method 3: Using Decimal Conversion

We can also solve this by first converting the fraction to a decimal and then multiplying by 100%:

15/120 = 0.125

0.125 x 100% = 12.5%

Real-World Applications

Understanding percentage calculations is crucial in numerous real-world scenarios. Here are some examples:

• Discounts: If a store offers a 20% discount on an item priced at $120, the discount amount is (20/100) * $120 = $24. The final price would be $120 - $24 = $96.

• Taxes: If a sales tax is 6%, the tax amount on a $120 purchase is (6/100) * $120 = $7.20. The total cost including tax would be $120 + $7.20 = $127.20.

• Grade Calculation: If you scored 15 out of 20 on a test, your percentage score would be (15/20) * 100% = 75%.

• Investment Returns: If you invested $120 and your investment grew by $15, your return on investment (ROI) would be (15/120) * 100% = 12.5%.

• Data Analysis: Imagine you're analyzing sales figures. If your total sales for the year were $120,000 and sales in one particular month were $15,000, that month's sales represent (15000/120000) * 100% = 12.5% of your annual sales.

Expanding on Percentage Problems

Let's explore some related percentage problems to further solidify your understanding:

Problem 1: What is 25% of 120?

Using the formula: (25/100) * 120 = 30

Problem 2: 15 is 15% of what number?

Let 'x' be the number. We can set up the equation:

15 = (15/100) * x

Solving for x:

x = (15 * 100) / 15

x = 100

Problem 3: If 120 is increased by 12.5%, what is the new value?

The increase is (12.5/100) * 120 = 15

The new value is 120 + 15 = 135

Problem 4: If 120 is decreased by 20%, what is the new value?

The decrease is (20/100) * 120 = 24

The new value is 120 - 24 = 96

Mastering Percentage Calculations

Consistent practice is key to mastering percentage calculations. Start with simple problems and gradually progress to more complex scenarios. Using different methods to solve the same problem will reinforce your understanding and help you identify the most efficient approach for each situation.

Conclusion

The answer to "15 is what percent of 120?" is 12.5%. This seemingly simple question highlights the importance of understanding percentage calculations, a skill applicable across various disciplines and everyday life. By understanding the different methods presented and practicing their application, you'll enhance your numerical literacy and confidently tackle percentage-related problems. Remember to always double-check your work and choose the method that feels most intuitive and efficient for you. The more you practice, the easier and faster these calculations will become.