What Is 5 Of 225

What is 5% of 225? A Comprehensive Guide to Percentage Calculations

Finding a percentage of a number is a fundamental skill in mathematics with widespread applications in everyday life, from calculating discounts and sales tax to understanding financial reports and statistical data. This comprehensive guide will walk you through how to calculate 5% of 225, explaining the process step-by-step and delving into the underlying mathematical concepts. We'll also explore different methods for calculating percentages and touch upon real-world scenarios where this type of calculation proves useful. By the end, you'll not only know the answer but also possess a solid understanding of percentage calculations.

Understanding Percentages

A percentage is a fraction expressed as a number out of 100. The symbol "%" represents "per cent," meaning "out of one hundred." So, 5% means 5 out of 100, which can be written as the fraction 5/100 or the decimal 0.05. Calculating a percentage of a number essentially means finding that proportional part of the number.

Method 1: Using Decimal Conversion

This is arguably the most straightforward method. We convert the percentage to its decimal equivalent and then multiply it by the number.

Steps:

1. Convert the percentage to a decimal: To convert 5% to a decimal, divide it by 100: 5% ÷ 100 = 0.05

2. Multiply the decimal by the number: Multiply the decimal (0.05) by 225: 0.05 x 225 = 11.25

Therefore, 5% of 225 is $\boxed{11.25}$

Method 2: Using Fraction Conversion

This method uses the fractional representation of the percentage.

Steps:

1. Convert the percentage to a fraction: 5% can be written as the fraction 5/100.

2. Simplify the fraction (if possible): The fraction 5/100 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5: 5/100 = 1/20

3. Multiply the fraction by the number: Multiply the simplified fraction (1/20) by 225: (1/20) x 225 = 225/20

4. Simplify the resulting fraction (if necessary) or convert to a decimal: 225/20 simplifies to 11.25.

Therefore, 5% of 225 is $\boxed{11.25}$

Method 3: Using Proportion

This method utilizes the concept of ratios and proportions.

Steps:

1. Set up a proportion: We can set up a proportion to represent the problem: 5/100 = x/225, where 'x' represents 5% of 225.

2. Cross-multiply: Cross-multiply the terms in the proportion: 5 x 225 = 100 x

3. Solve for x: 1125 = 100x. Divide both sides by 100: x = 1125/100 = 11.25

Therefore, 5% of 225 is $\boxed{11.25}$

Understanding the Result in Context

The answer, 11.25, represents 5% of the total value of 225. This means that if you have 225 of something, 5% of that amount is 11.25. This is a valuable piece of information in various practical applications.

Real-World Applications

Percentage calculations are ubiquitous in daily life. Here are a few examples where understanding how to calculate 5% of 225 (or any percentage of any number) could be helpful:

• Sales and Discounts: Imagine a store offering a 5% discount on an item priced at $225. The discount amount would be $11.25, making the final price $213.75.

• Taxes: If a 5% sales tax is applied to a $225 purchase, the tax amount would be $11.25.

• Tips: Calculating a 5% tip on a $225 restaurant bill would yield a tip of $11.25.

• Commission: A salesperson earning a 5% commission on a $225 sale would receive $11.25.

• Finance and Investment: Understanding percentage changes in investments, interest rates, or loan payments relies on these fundamental calculations. For instance, if an investment of $225 increases by 5%, the increase would be $11.25.

Further Exploration of Percentage Calculations

The methods described above provide a solid foundation for calculating percentages. However, you can expand your understanding by exploring these concepts:

• Calculating other percentages: The same principles apply when calculating any other percentage of a number. Simply replace the 5% with the desired percentage and follow the same steps.

• Calculating the percentage one number represents of another: You can use the same principles to find what percentage one number represents of another. For example, to find what percentage 11.25 represents of 225, you would divide 11.25 by 225 and multiply by 100, resulting in 5%.

• Using calculators and spreadsheets: Calculators and spreadsheet software (like Microsoft Excel or Google Sheets) have built-in functions for calculating percentages, simplifying the process considerably. Familiarizing yourself with these tools can significantly improve your efficiency.

• Understanding compound interest: Compound interest involves calculating interest on the principal amount plus accumulated interest. This concept builds upon the fundamental understanding of percentage calculations.

• Percentage increase and decrease: Understanding how to calculate percentage increases and decreases is essential in various contexts, including analyzing trends and growth rates.

Frequently Asked Questions (FAQ)

Q1: What if the percentage is not a whole number, for example, 5.5%?

A1: The process remains the same. Convert 5.5% to its decimal equivalent (0.055) and multiply it by the number (225). 5.5% of 225 = 0.055 x 225 = 12.375

Q2: Can I use a calculator to solve this problem?

A2: Absolutely! Most calculators have a percentage function (%) that simplifies the calculation. You would typically enter 225 x 5 %, and the calculator will directly provide the answer: 11.25

Q3: How do I find what percentage one number is of another?

A3: To find what percentage number 'a' is of number 'b', you divide 'a' by 'b' and then multiply by 100. For example, to find what percentage 11.25 is of 225, you would calculate (11.25 / 225) x 100 = 5%.

Q4: Are there any online resources that can help me practice percentage calculations?

A4: Many websites and educational platforms offer practice exercises and interactive tutorials on percentage calculations.

Conclusion

Calculating 5% of 225 is a straightforward process that utilizes fundamental mathematical concepts. By mastering the methods outlined above – using decimal conversion, fraction conversion, or proportion – you can confidently tackle similar percentage calculations in various real-world situations. Remember that understanding percentages is a crucial skill with far-reaching applications in finance, business, science, and everyday life. Practice these methods, explore further applications, and you'll quickly develop a strong grasp of this essential mathematical concept. The answer, as we've consistently shown, is $\boxed{11.25}$.