What Percent Of 90 Is 15

What Percent of 90 is 15? A Comprehensive Guide to Percentage Calculations

Finding what percentage one number represents of another is a fundamental skill in mathematics, applicable across numerous fields from finance and statistics to everyday life. This article will delve deep into calculating what percentage 15 represents of 90, explaining the process in detail, providing multiple approaches, and exploring related concepts to solidify your understanding. We'll move beyond a simple answer and equip you with the knowledge to tackle similar percentage problems confidently.

Understanding Percentages:

Before we tackle the specific problem, let's refresh our understanding of percentages. A percentage is simply a fraction expressed as a part of 100. The symbol "%" represents "per hundred" or "out of 100". For example, 50% means 50 out of 100, which is equivalent to the fraction 50/100 or the decimal 0.5.

Method 1: The Proportion Method

This method uses the concept of proportions to solve the problem. We can set up a proportion:

• Part/Whole = Percentage/100

In our case:

• Part = 15
• Whole = 90
• Percentage = x (what we want to find)

Substituting these values into the proportion:

15/90 = x/100

To solve for x, we can cross-multiply:

15 * 100 = 90 * x

1500 = 90x

Now, divide both sides by 90:

x = 1500 / 90

x = 16.67 (approximately)

Therefore, 15 is approximately 16.67% of 90.

Method 2: The Decimal Method

This method involves converting the fraction to a decimal and then multiplying by 100 to express it as a percentage.

First, we express the relationship as a fraction:

15/90

Next, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 15:

15/90 = 1/6

Now, convert the fraction to a decimal by dividing the numerator by the denominator:

1 ÷ 6 ≈ 0.1667

Finally, multiply the decimal by 100 to express it as a percentage:

0.1667 * 100 ≈ 16.67%

So, again, we find that 15 is approximately 16.67% of 90.

Method 3: Using a Calculator

Most calculators have a percentage function. Simply divide 15 by 90 and then multiply the result by 100:

(15 ÷ 90) * 100 ≈ 16.67%

This method offers the quickest solution, but understanding the underlying principles (as explained in Methods 1 and 2) is crucial for problem-solving beyond simple calculator inputs.

Understanding the Result: 16.67%

The result, 16.67%, tells us that 15 represents approximately one-sixth (1/6) of 90. This percentage is a recurring decimal, meaning the digits "67" repeat infinitely. For practical purposes, rounding to two decimal places (16.67%) is usually sufficient.

Real-World Applications:

Understanding percentage calculations is crucial in various real-world scenarios:

• Finance: Calculating interest rates, discounts, profit margins, and tax rates. For example, if an item is discounted by 16.67%, and the original price is $90, the discount amount would be $15.
• Statistics: Determining percentages in data analysis, surveys, and polls. If 15 out of 90 respondents answered "yes" to a question, the percentage of "yes" responses would be 16.67%.
• Everyday Life: Calculating tips, sales tax, and portion sizes. Imagine splitting a $90 bill equally among 6 people; each person would pay $15, which represents 16.67% of the total bill.

Expanding Your Understanding: Related Percentage Problems

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

• Finding the whole: If 20% of a number is 18, what is the number?
• Finding the part: What is 35% of 120?
• Finding the percentage increase or decrease: A price increased from $80 to $100. What is the percentage increase?

These types of problems utilize similar principles to those explained above but require a slight adjustment in the approach. Solving these problems will strengthen your grasp of percentage calculations.

Advanced Percentage Concepts:

As you delve deeper into mathematics, you’ll encounter more complex percentage concepts such as:

• Compound interest: Interest calculated on both the principal amount and accumulated interest.
• Percentage change: Calculating the percentage increase or decrease between two values.
• Percentage points: Representing the absolute difference between two percentages, not a relative change.

Mastering the fundamentals of percentage calculations, as demonstrated in this article, lays a solid foundation for understanding these more advanced concepts.

Conclusion:

Determining what percent of 90 is 15 involves understanding the core principles of percentages and applying appropriate calculation methods. Whether you use the proportion method, the decimal method, or a calculator, the result remains consistent: 15 is approximately 16.67% of 90. This seemingly simple calculation has far-reaching applications in various aspects of life, highlighting the importance of mastering this fundamental mathematical skill. By understanding the different methods and practicing related problems, you can confidently tackle percentage calculations in any context. Remember to always check your work and consider the context of the problem to ensure your answer is logical and meaningful.