What Is 15 Of 90

What is 15/90? Unlocking the Power of Fractions and Percentages

Understanding fractions and percentages is a fundamental skill in mathematics, applicable across numerous fields from everyday budgeting to advanced scientific calculations. This article delves into the seemingly simple question, "What is 15/90?", but expands far beyond a mere numerical answer. We'll explore the different methods for solving this fraction, its equivalent percentage and decimal form, and the broader conceptual understanding of fractions and their real-world applications. This in-depth explanation will equip you with a solid foundation in working with fractions, allowing you to tackle more complex problems with confidence.

Understanding Fractions: A Foundation

A fraction represents a part of a whole. It consists of two numbers: the numerator (the top number) and the denominator (the bottom number). In the fraction 15/90, 15 is the numerator, and 90 is the denominator. The fraction indicates that we have 15 parts out of a total of 90 equal parts.

Before we calculate 15/90, let's refresh some basic principles of fraction simplification:

• Common Factors: A crucial concept in simplifying fractions is identifying common factors between the numerator and denominator. A common factor is a number that divides both the numerator and denominator without leaving a remainder.
• Greatest Common Factor (GCF): The GCF is the largest number that divides both the numerator and the denominator evenly. Finding the GCF is essential for simplifying a fraction to its lowest terms.
• Simplifying Fractions: To simplify a fraction, we divide both the numerator and the denominator by their GCF. This results in an equivalent fraction that is easier to understand and work with.

Calculating 15/90: Step-by-Step

Now, let's determine the value of 15/90. We can solve this using a few different approaches:

Method 1: Direct Simplification using the GCF

The first and most efficient method involves finding the GCF of 15 and 90.

1. List the factors of 15: 1, 3, 5, 15
2. List the factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
3. Identify the GCF: The greatest common factor of 15 and 90 is 15.

Now, divide both the numerator and the denominator by the GCF (15):

15 ÷ 15 = 1 90 ÷ 15 = 6

Therefore, 15/90 simplifies to 1/6.

Method 2: Stepwise Simplification

If you don't immediately see the GCF, you can simplify the fraction step-by-step by dividing by any common factor you find. For instance:

1. Divide both numerator and denominator by 5: 15/90 = 3/18
2. Divide both numerator and denominator by 3: 3/18 = 1/6

This method achieves the same result (1/6) but might require more steps.

Method 3: Conversion to Decimal

Another approach is to convert the fraction to a decimal. To do this, divide the numerator (15) by the denominator (90):

15 ÷ 90 = 0.166666... (this is a repeating decimal)

This decimal, 0.16666..., is equivalent to 1/6.

Method 4: Using Percentage

To express 15/90 as a percentage, we can first simplify the fraction to 1/6 and then convert it:

1/6 = (1 ÷ 6) * 100% ≈ 16.67%

Therefore, 15/90 is approximately 16.67%. The percentage value is approximate because the decimal representation of 1/6 is a repeating decimal.

Real-World Applications of Fractions and Percentages

Understanding fractions and percentages is crucial for numerous aspects of daily life:

• Financial Literacy: Calculating discounts, interest rates, taxes, and budgeting all require working with fractions and percentages. For instance, understanding that a 20% discount means paying 80% of the original price is essential for smart shopping.
• Cooking and Baking: Recipes often use fractions to specify ingredient quantities, such as 1/2 cup of sugar or 2/3 cup of flour.
• Science and Engineering: Fractions and percentages are fundamental in many scientific calculations, including measurements, data analysis, and probability.
• Data Analysis and Statistics: Representing data proportions using fractions and percentages is essential for understanding trends and patterns. For example, a survey result might show that 15/90 respondents (or 16.67%) prefer a particular product.
• Probability and Statistics: In probability, fractions and percentages represent the likelihood of an event happening.

Understanding these mathematical concepts empowers you to make informed decisions and solve problems efficiently in various real-world situations.

Beyond the Basics: Further Exploration of Fractions

While this article focuses primarily on the calculation of 15/90, let's delve deeper into the broader world of fractions:

• Improper Fractions and Mixed Numbers: An improper fraction has a numerator greater than or equal to the denominator (e.g., 90/15). A mixed number combines a whole number and a fraction (e.g., 6). Improper fractions can be converted to mixed numbers and vice versa.
• Adding and Subtracting Fractions: To add or subtract fractions, they must have a common denominator. If they don't, you need to find a common denominator by finding the least common multiple (LCM) of the denominators.
• Multiplying and Dividing Fractions: Multiplying fractions involves multiplying the numerators and denominators separately. Dividing fractions involves inverting the second fraction (reciprocal) and then multiplying.

Frequently Asked Questions (FAQs)

Q: Can I simplify a fraction by dividing the numerator and denominator by any number?

A: Yes, but only if the number divides both the numerator and denominator evenly (without leaving a remainder). The most efficient simplification uses the greatest common factor (GCF).

Q: What if I don't know how to find the GCF?

A: You can use a method called prime factorization. Break down both the numerator and denominator into their prime factors, then find the common factors and multiply them to find the GCF. For example:

15 = 3 x 5 90 = 2 x 3 x 3 x 5

The common factors are 3 and 5, so the GCF is 3 x 5 = 15.

Q: Are there any online calculators to help with fraction simplification?

A: Yes, many online calculators can simplify fractions. However, understanding the underlying principles is crucial for building a strong mathematical foundation.

Q: Why is it important to simplify fractions to their lowest terms?

A: Simplifying fractions makes them easier to understand and work with. It also provides a more concise and efficient representation of the quantity.

Conclusion: Mastering Fractions for a Brighter Future

In conclusion, 15/90 simplifies to 1/6, which is approximately 0.1667 or 16.67%. This seemingly simple calculation provides a springboard to understanding the fundamental concepts of fractions, percentages, and their extensive applications in various fields. By mastering these concepts, you equip yourself with a powerful toolset for problem-solving and decision-making across numerous aspects of life, from everyday tasks to complex professional endeavors. Remember, the journey to mathematical proficiency is a continuous process of learning, practicing, and applying your knowledge. Embrace the challenge, and the rewards will be substantial.