What Is 5 Of 1200

What is 5% of 1200? A Comprehensive Guide to Percentages

Finding a percentage of a number is a fundamental skill in mathematics with wide-ranging applications in everyday life, from calculating discounts and taxes to understanding statistics and financial reports. This article will comprehensively explore how to calculate 5% of 1200, explaining the process step-by-step, exploring different calculation methods, and delving into the underlying mathematical principles. We'll also touch upon real-world applications to solidify your understanding. This guide is perfect for anyone, from students brushing up on their math skills to adults needing a refresher on percentage calculations.

Understanding Percentages

Before we delve into calculating 5% of 1200, let's briefly recap the concept of percentages. A percentage is a fraction expressed as a number out of 100. The symbol "%" represents "per hundred." For example, 5% means 5 out of 100, or 5/100, which is equivalent to the decimal 0.05. Understanding this fundamental relationship is crucial for calculating percentages.

Method 1: Converting Percentage to Decimal

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

Steps:

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

2. Multiply the decimal by the number: Now, we multiply the decimal (0.05) by 1200: 0.05 * 1200 = 60

Therefore, 5% of 1200 is $\boxed{60}$.

Method 2: Using Fractions

This method leverages the fractional representation of percentages. We express the percentage as a fraction and then perform the multiplication.

Steps:

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

2. Simplify the fraction (optional): The fraction 5/100 can be simplified to 1/20.

3. Multiply the fraction by the number: Now, we multiply the simplified fraction (1/20) by 1200: (1/20) * 1200 = 1200/20 = 60

Again, we find that 5% of 1200 is $\boxed{60}$.

Method 3: Proportion Method

This method uses the concept of proportions to solve for the unknown value. We set up a proportion where one ratio represents the percentage and the other represents the part and the whole.

Steps:

1. Set up the proportion: We set up a proportion: 5/100 = x/1200, where 'x' represents 5% of 1200.

2. Cross-multiply: We cross-multiply to solve for x: 5 * 1200 = 100 * x

3. Solve for x: 6000 = 100x => x = 6000/100 = 60

Thus, using the proportion method, we arrive at the same answer: 5% of 1200 is $\boxed{60}$.

Real-World Applications: Illustrative Examples

The calculation of percentages, like finding 5% of 1200, has numerous applications in daily life. Let's look at some illustrative examples:

• Sales Tax: If you buy an item costing 1200 dollars and the sales tax is 5%, you would pay an additional 60 dollars in tax (5% of 1200).

• Discounts: A store offers a 5% discount on an item priced at 1200 dollars. The discount amount would be 60 dollars, and you would pay 1140 dollars (1200 - 60).

• Interest Calculations: If you invest 1200 dollars and earn a 5% annual interest rate, you would earn 60 dollars in interest after one year.

• Commission: A salesperson earns a 5% commission on sales. If they sell 1200 dollars worth of goods, their commission would be 60 dollars.

• Tip Calculation: In some cultures, it’s customary to leave a tip for services. If you want to leave a 5% tip on a 1200 dollar bill, you'd leave a 60 dollar tip.

Expanding the Understanding: Calculating Other Percentages of 1200

The methods described above can easily be adapted to calculate other percentages of 1200. For example:

• 10% of 1200: 0.10 * 1200 = 120

• 25% of 1200: 0.25 * 1200 = 300

• 75% of 1200: 0.75 * 1200 = 900

Frequently Asked Questions (FAQ)

Q: What is the easiest way to calculate percentages?

A: The easiest method depends on your preference and the specific problem. The decimal method is generally considered the most straightforward for most people.

Q: Can I use a calculator to calculate percentages?

A: Yes, most calculators have a percentage function (%) that simplifies the process. You can input the calculation directly as 5% * 1200.

Q: How can I improve my understanding of percentages?

A: Practice is key! Work through various percentage problems, using different methods, to build your confidence and understanding. You can find plenty of practice problems online or in textbooks.

Q: Why is understanding percentages important?

A: Percentages are used extensively in everyday life, from shopping to finance to understanding statistics. A strong grasp of percentages is crucial for making informed decisions and navigating various aspects of daily life.

Conclusion

Calculating 5% of 1200, whether using decimals, fractions, or proportions, consistently yields the answer $\boxed{60}$. Mastering percentage calculations empowers you to handle various real-world scenarios with confidence. Remember to choose the method you find most comfortable and practice regularly to reinforce your skills. Understanding percentages is a valuable tool that will serve you well in numerous contexts. The ability to quickly and accurately calculate percentages enhances your problem-solving abilities and improves your overall mathematical proficiency. Don't hesitate to revisit this guide and explore the different methods to solidify your understanding of this crucial mathematical concept.