What Is 1 5 Of 90

What is 1/5 of 90? A Comprehensive Guide to Fractions and Their Applications

Finding a fraction of a number is a fundamental concept in mathematics with wide-ranging applications in everyday life, from calculating discounts to understanding proportions in various fields. This article will delve into the calculation of 1/5 of 90, explaining the process step-by-step and exploring the broader context of fractions and their practical uses.

Understanding Fractions

Before we tackle the specific problem, let's review the basics of fractions. A fraction represents a part of a whole. It's written in the form a/b, where 'a' is the numerator (the number of parts we have) and 'b' is the denominator (the total number of equal parts the whole is divided into).

For example, in the fraction 1/5, 1 is the numerator and 5 is the denominator. This represents one part out of five equal parts.

Calculating 1/5 of 90

To find 1/5 of 90, we need to perform a simple multiplication:

(1/5) * 90

There are two common methods to solve this:

Method 1: Direct Multiplication

We can multiply the numerator (1) by 90 and then divide the result by the denominator (5):

(1 * 90) / 5 = 90 / 5 = 18

Therefore, 1/5 of 90 is 18.

Method 2: Simplifying First

Alternatively, we can simplify the calculation before multiplying. Since 90 is divisible by 5, we can simplify the fraction first:

(1/5) * 90 = (1 * (90/5)) = 1 * 18 = 18

This method can be particularly useful when dealing with larger numbers or more complex fractions. It reduces the complexity of the calculation.

Real-World Applications of Fractions

Understanding fractions is crucial for numerous real-world applications. Here are a few examples:

1. Calculating Discounts and Sales Tax

Imagine a shirt costing $90 is on sale with a 1/5 discount. Using our knowledge of fractions, we can easily calculate the discount amount: (1/5) * $90 = $18. The discounted price would be $90 - $18 = $72. Similarly, calculating sales tax involves finding a fraction (e.g., 0.06 for a 6% tax) of the total price.

2. Recipe Scaling

Fractions are essential in cooking and baking. If a recipe calls for 1/5 of a cup of flour and you want to double the recipe, you simply multiply 1/5 by 2, resulting in 2/5 of a cup of flour. Adapting recipes involves constant fraction manipulation.

3. Sharing and Dividing Quantities

Dividing items or resources equally often involves fractions. If you have 90 candies and want to share them equally among 5 friends, each friend receives 1/5 of 90, which is 18 candies.

4. Understanding Proportions and Ratios

Fractions are fundamental to understanding proportions and ratios. For instance, if a map has a scale of 1:5, it means that 1 unit on the map represents 5 units in reality. This is a ratio expressed as a fraction (1/5). Many engineering and architectural designs rely on precise proportions expressed as fractions.

5. Financial Calculations

Fractions are ubiquitous in financial calculations, including calculating interest rates, shares of ownership, and profit margins. For example, calculating a 1/5 share of a $90,000 investment requires understanding the same fractional concept we've been discussing.

Beyond 1/5 of 90: Working with Different Fractions

The principles discussed here extend to calculating any fraction of any number. For example, to find 3/5 of 90, we would multiply:

(3/5) * 90 = (3 * 90) / 5 = 270 / 5 = 54

Or, simplifying first: (3 * (90/5)) = 3 * 18 = 54

Improper Fractions and Mixed Numbers

It's important to also understand improper fractions (where the numerator is larger than the denominator) and mixed numbers (a combination of a whole number and a fraction). For example, if we wanted to find 7/5 of 90, we'd get:

(7/5) * 90 = 630/5 = 126

This could also be expressed as a mixed number: 25 1/5

Conclusion: Mastering Fractions for a Better Understanding of the World

The simple calculation of 1/5 of 90 serves as a gateway to understanding the broader world of fractions and their applications. From everyday tasks like shopping and cooking to complex financial and scientific calculations, the ability to work with fractions is a valuable skill that enhances problem-solving capabilities and provides a more profound understanding of numerical relationships within our world. This foundational mathematical concept underpins many aspects of life, making a solid grasp of it incredibly beneficial. By practicing different examples and applying fractions to real-world scenarios, you can further build your confidence and proficiency in this essential area of mathematics.