Percentages are an integral part of our daily lives, used in everything from calculating discounts to understanding election results. They represent a fraction of 100, providing a convenient way to express proportions and ratios. A fundamental understanding of percentages is crucial for navigating the world around us, whether we’re making financial decisions, analyzing data, or simply understanding everyday information. One common question that arises when working with percentages is: “21 is 75 percent of what number?” This seemingly simple question unlocks a deeper understanding of how percentages work and how to solve proportion problems.
This blog post will delve into the concept of percentages, explore the relationship between percentages and fractions, and guide you through the process of solving the problem “21 is 75 percent of what number?” We’ll also touch upon real-world applications of percentages to illustrate their importance in various contexts.
Understanding Percentages
A percentage is a numerical representation of a fraction out of 100. The symbol “%” represents “out of one hundred.” For example, 50% means 50 out of every 100, which can be expressed as the fraction 50/100 or the decimal 0.50.
Converting Percentages to Fractions and Decimals
Percentages can be easily converted to fractions and decimals. To convert a percentage to a fraction, divide the percentage by 100 and simplify the resulting fraction. For example, 75% is equivalent to 75/100, which simplifies to 3/4. To convert a percentage to a decimal, divide the percentage by 100. So, 75% is equal to 0.75.
Calculating Percentages
To calculate a percentage of a number, follow these steps:
- Convert the percentage to a decimal by dividing it by 100.
- Multiply the decimal by the number.
For example, to calculate 25% of 80:
- 25% divided by 100 is 0.25.
- 0.25 multiplied by 80 is 20.
Solving the Problem: 21 is 75 Percent of What Number?
Now, let’s address the specific problem: “21 is 75 percent of what number?” This is a proportion problem where we need to find the unknown number. We can represent this problem mathematically as: (See Also: Easy Math Questions And Answers? Solved!)
21 = 0.75 * x
Where ‘x’ is the unknown number.
To solve for ‘x’, we can use the following steps:
- Divide both sides of the equation by 0.75:
- 21 / 0.75 = x
Performing the calculation, we get:
x = 28
Therefore, 21 is 75 percent of 28. (See Also: How Much Is a Room Addition? Costs Revealed)
Real-World Applications of Percentages
Percentages play a vital role in various aspects of our lives. Here are some examples:
Finance
- Interest Rates: Banks use percentages to calculate interest rates on loans and savings accounts.
- Discounts: Retailers offer discounts on products, often expressed as percentages.
- Taxes: Governments levy taxes on income, goods, and services, typically as percentages.
Statistics
- Polling Data: Election polls use percentages to represent the proportion of voters supporting a particular candidate.
- Survey Results: Market research surveys often present data as percentages to show the distribution of opinions.
- Population Growth: Percentages are used to track changes in population size over time.
Other Applications
- Grades: Students’ academic performance is often measured using percentages.
- Nutritional Information: Food labels display the percentage of daily recommended intake for various nutrients.
- Sports Statistics: Percentages are used to calculate batting averages, winning percentages, and other performance metrics.
Conclusion
Percentages are a fundamental concept in mathematics and have widespread applications in various fields. Understanding how to work with percentages, including converting them to fractions and decimals, calculating percentages, and solving proportion problems, is essential for navigating the world around us. The problem “21 is 75 percent of what number?” serves as a practical example of how to apply these concepts. By breaking down the problem and using the appropriate formulas, we can arrive at the solution, which is 28.
As we’ve seen, percentages are not merely abstract mathematical constructs; they are powerful tools for analyzing data, making informed decisions, and understanding the world around us. Whether we’re dealing with financial transactions, statistical trends, or everyday occurrences, a grasp of percentages empowers us to interpret information accurately and effectively.
Frequently Asked Questions
What is the formula for calculating a percentage?
The formula for calculating a percentage is: (Part / Whole) * 100
How do I convert a percentage to a decimal?
To convert a percentage to a decimal, divide the percentage by 100.
How do I convert a decimal to a percentage?
To convert a decimal to a percentage, multiply the decimal by 100 and add the “%” symbol. (See Also: How Long Is the Math Tsi? A Comprehensive Guide)
What is the difference between a percentage and a fraction?
A percentage is a fraction out of 100, while a fraction represents a part of a whole. Both can express the same proportion, but percentages are typically used for representing proportions out of 100.
What is the meaning of “75 percent”?
“75 percent” means that 75 out of every 100 is represented. It can also be expressed as the fraction 3/4 or the decimal 0.75.