What Is 15 Of 90

What is 15 of 90? Understanding Fractions, Percentages, and Ratios

This article delves into the seemingly simple question, "What is 15 of 90?", but expands it to explore the broader concepts of fractions, percentages, and ratios. Understanding these mathematical relationships is crucial in various aspects of life, from everyday calculations to complex scientific analyses. We'll uncover multiple ways to interpret and solve this problem, providing a solid foundation for tackling similar scenarios.

Introduction: Different Perspectives on "15 of 90"

The phrase "15 of 90" can be interpreted in several ways, depending on the context. It could represent a fraction (15/90), a percentage (what percentage is 15 of 90?), or a ratio (15:90). Each interpretation offers a unique approach to understanding the relationship between 15 and 90. We will explore each approach in detail, emphasizing the underlying mathematical principles.

1. Understanding the Fraction: 15/90

The most straightforward interpretation of "15 of 90" is the fraction 15/90. This fraction represents the portion of 90 that is equal to 15. To simplify this fraction, we need to find the greatest common divisor (GCD) of both the numerator (15) and the denominator (90).

The GCD of 15 and 90 is 15. Dividing both the numerator and the denominator by 15 gives us:

15 ÷ 15 = 1 90 ÷ 15 = 6

Therefore, the simplified fraction is 1/6. This means that 15 is one-sixth of 90.

2. Calculating the Percentage: What Percentage is 15 of 90?

To express 15 as a percentage of 90, we need to determine what proportion 15 represents out of 90, and then multiply that proportion by 100%. The formula is:

(Part / Whole) * 100%

In this case:

(15 / 90) * 100% = 0.1666... * 100% = 16.67% (approximately)

Therefore, 15 is approximately 16.67% of 90. The recurring decimal 0.1666... is often rounded to two decimal places for practical purposes.

3. Exploring the Ratio: 15:90

A ratio expresses the relationship between two numbers. The ratio 15:90 signifies that for every 15 units of one quantity, there are 90 units of another quantity. Like the fraction, we can simplify this ratio by dividing both sides by their GCD (15):

15 ÷ 15 = 1 90 ÷ 15 = 6

The simplified ratio is 1:6. This indicates a 1 to 6 relationship between the two quantities.

4. Real-World Applications: Putting it into Practice

These mathematical concepts – fractions, percentages, and ratios – are fundamental to many real-world scenarios. Let's consider a few examples:

• Baking: A recipe calls for 90 grams of flour, and you only want to make one-sixth of the recipe. Using the simplified fraction (1/6), you would use 15 grams of flour (90 grams * 1/6 = 15 grams).

• Sales: A store offers a 16.67% discount on an item originally priced at $90. The discount amount would be $15 ($90 * 0.1667 ≈ $15).

• Surveys: If 15 out of 90 respondents to a survey answered "yes" to a particular question, the ratio of "yes" responses to the total responses is 1:6. This demonstrates a preference for the "no" answer.

5. Expanding the Understanding: Proportions and Problem Solving

Understanding "15 of 90" allows us to delve into the broader concept of proportions. A proportion is a statement that two ratios are equal. We can express the relationship between 15 and 90 as a proportion:

15/90 = x/y

Where 'x' and 'y' represent other quantities that maintain the same ratio. Solving for 'x' or 'y' involves cross-multiplication and can be used to solve various real-world problems involving proportional relationships. For example:

If 15 apples cost $3, how much would 90 apples cost?

We can set up the proportion:

15/3 = 90/x

Cross-multiplying:

15x = 270

x = 270/15 = $18

Therefore, 90 apples would cost $18.

6. Advanced Concepts: Working with Decimals and Percentages

Beyond the basics, we can explore more complex calculations involving decimals and percentages. For instance, we might need to calculate the percentage increase or decrease between two values, or work with compound percentages. Understanding the fundamental relationship between 15 and 90 provides a strong foundation for tackling these more advanced calculations.

7. Frequently Asked Questions (FAQ)

• Q: Can I express 15/90 as a decimal? A: Yes, 15/90 simplifies to 1/6, which is approximately 0.1667 as a decimal.

• Q: How do I convert a percentage to a fraction? A: Divide the percentage by 100 and simplify the resulting fraction. For example, 16.67% becomes 16.67/100 which simplifies to approximately 1/6.

• Q: What is the difference between a ratio and a fraction? A: While both ratios and fractions express the relationship between two numbers, ratios are often used to compare different quantities, while fractions represent a part of a whole.

• Q: Are there other ways to simplify 15/90 besides dividing by 15? A: Yes, you could divide by 3, then 5, achieving the same result (1/6). However, dividing by the GCD is the most efficient method.

8. Conclusion: Mastering the Fundamentals

The question "What is 15 of 90?" serves as a springboard to explore fundamental mathematical concepts such as fractions, percentages, ratios, and proportions. Understanding these concepts is essential for various applications in daily life, academic studies, and professional fields. By mastering these foundational skills, you build a strong base for tackling more complex mathematical problems and enhance your problem-solving abilities. Remember, practice is key to solidifying your understanding and gaining confidence in your mathematical skills. The more you work with these concepts, the more intuitive they become. So, continue to explore, experiment, and apply these mathematical tools to various situations – you'll be surprised at how often they prove useful!