Percentages are an integral part of our daily lives, used in everything from calculating discounts and interest rates to understanding election results and statistical data. They provide a standardized way to express a part of a whole as a fraction of 100. Understanding how to calculate percentages is essential for navigating the world around us effectively. One common scenario involves determining what percentage one number represents of another. For example, “46 is what percent of 107?” This seemingly simple question has a straightforward solution that can be applied to a wide range of real-world problems.
Understanding Percentages
A percentage is a numerical representation of a fraction out of one hundred. The symbol “%” signifies “out of one hundred.” For instance, 50% means 50 out of every 100, which can be expressed as the fraction 50/100 or the decimal 0.50. Percentages are widely used in various fields, including finance, business, science, and everyday life.
Calculating Percentages
To calculate a percentage, we follow a simple formula:
(Part / Whole) x 100 = Percentage
Let’s break down this formula:
* **Part:** This is the specific value we want to express as a percentage.
* **Whole:** This is the total value or the reference point against which we are comparing the part.
* **Percentage:** This is the result of the calculation, representing the part as a fraction of the whole expressed as a percentage.
Solving “46 is What Percent of 107?”
Now, let’s apply this formula to our specific question: “46 is what percent of 107?”
- **Identify the Part and Whole:** In this case, the part is 46, and the whole is 107.
- **Plug the Values into the Formula:** (46 / 107) x 100 = Percentage
- **Calculate the Result:** (0.43) x 100 = 43%
Therefore, 46 is 43% of 107. (See Also: Find Two Positive Integers Whose Sum Is 16? Solutions)
Applications of Percentage Calculations
Percentage calculations are ubiquitous in various aspects of our lives. Here are some examples:
Finance
- **Interest Rates:** Banks calculate interest on loans and savings accounts as a percentage of the principal amount.
- **Discounts:** Retailers offer discounts on products as a percentage reduction from the original price.
- **Taxes:** Governments levy taxes on income, property, and goods as a percentage of their value.
Business
- **Profit Margins:** Businesses calculate profit margins as a percentage of revenue, indicating their profitability.
- **Market Share:** Companies analyze their market share as a percentage of the total market for their products or services.
- **Sales Growth:** Businesses track sales growth as a percentage increase or decrease over a period.
Science and Research
- **Statistical Analysis:** Scientists and researchers use percentages to express the frequency or proportion of occurrences in their data.
- **Experimental Results:** Percentage changes in variables are often reported in scientific experiments.
- **Population Demographics:** Percentages are used to describe population characteristics, such as age distribution, gender ratios, and ethnic makeup.
Real-World Examples
Let’s consider some real-world scenarios where understanding percentages is crucial:
Shopping
Imagine you find a shirt on sale for 20% off its original price of $50. To calculate the discount amount, you would multiply the original price by the discount percentage: $50 x 0.20 = $10. Therefore, the discount is $10, and the sale price of the shirt is $40.
Investing
If you invest $1,000 in a stock that increases in value by 15%, your investment would be worth $1,150. To calculate this, you would multiply the original investment by the percentage increase: $1,000 x 0.15 = $150.
Health and Fitness
If you aim to lose 10% of your body weight, you would need to determine 10% of your current weight. For example, if you weigh 180 pounds, losing 10% would mean losing 18 pounds (180 x 0.10 = 18). (See Also: How Difficult Is College Algebra? A Guide To Success)
Frequently Asked Questions
46 Is What Percent of 107?
What is the formula for calculating percentages?
The formula for calculating percentages is: (Part / Whole) x 100 = Percentage
How do I calculate 46% of 107?
To calculate 46% of 107, you would multiply 107 by 0.46 (which is 46 divided by 100). So, 107 x 0.46 = 49.02.
What is the meaning of percentage?
A percentage is a way of representing a part of a whole as a fraction of 100. The symbol “%” means “out of one hundred.”
Can you give me another example of a percentage calculation?
Sure! If you have a pizza cut into 8 slices and you eat 3 slices, what percentage of the pizza did you eat?
* The part is 3 slices.
* The whole is 8 slices.
* (3/8) x 100 = 37.5%
You ate 37.5% of the pizza.
How are percentages used in everyday life?
Percentages are used everywhere! Some common examples include: calculating discounts at the store, understanding interest rates on loans, tracking your progress towards a goal, and analyzing data in reports or surveys. (See Also: Difference Between Multiplication and Division? Mastering Math Basics)
Summary
Understanding percentages is a fundamental skill with wide-ranging applications in various aspects of our lives. We’ve explored the concept of percentages, the formula for calculating them, and how to solve the specific problem of “46 is what percent of 107?” We’ve also delved into real-world examples demonstrating the practical use of percentages in finance, business, science, and everyday scenarios.
From calculating discounts to tracking investment growth, percentages provide a concise and standardized way to express proportions and make informed decisions. By mastering the art of percentage calculations, we empower ourselves to navigate the complexities of the world around us with greater clarity and confidence.