What Is 70 Of 1200

What is 70% of 1200? A Comprehensive Guide to Percentages and 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 statistics and financial data. This article will comprehensively address the question, "What is 70% of 1200?", explaining the process step-by-step, exploring different calculation methods, and delving into the underlying mathematical concepts. We'll also examine real-world applications and answer frequently asked questions about percentages.

Understanding Percentages

A percentage is a fraction or ratio expressed as a number out of 100. The symbol "%" represents "per cent," meaning "out of one hundred." Therefore, 70% means 70 out of 100, which can be written as the fraction 70/100 or the decimal 0.7. Understanding this basic concept is crucial for calculating percentages.

Method 1: Using Decimal Multiplication

The most straightforward method for calculating 70% of 1200 involves converting the percentage to a decimal and then multiplying it by the given number.

Steps:

1. Convert the percentage to a decimal: To convert 70% to a decimal, divide it by 100: 70 ÷ 100 = 0.7

2. Multiply the decimal by the number: Multiply the decimal (0.7) by the number you want to find the percentage of (1200): 0.7 x 1200 = 840

Therefore, 70% of 1200 is 840.

Method 2: Using Fraction Multiplication

Another approach involves converting the percentage to a fraction and then multiplying.

Steps:

1. Convert the percentage to a fraction: 70% can be written as the fraction 70/100. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 10: 70/100 = 7/10

2. Multiply the fraction by the number: Multiply the simplified fraction (7/10) by the number (1200): (7/10) x 1200 = 840

Therefore, 70% of 1200 is 840. This method reinforces the understanding of percentages as fractions.

Method 3: Using Proportions

A proportion is an equation stating that two ratios are equal. We can use proportions to solve percentage problems.

Steps:

1. Set up a proportion: We can set up a proportion as follows:

   70/100 = x/1200

   Where 'x' represents the unknown value (70% of 1200).

2. Cross-multiply: Cross-multiply the terms:

   70 x 1200 = 100x

3. Solve for x: Simplify and solve for 'x':

   84000 = 100x x = 84000 / 100 x = 840

Therefore, 70% of 1200 is 840. This method provides a more algebraic approach to solving percentage problems.

Real-World Applications

The ability to calculate percentages is crucial in many real-world scenarios. Here are a few examples:

• Sales and Discounts: If a store offers a 70% discount on an item priced at $1200, the discount amount would be $840 (70% of $1200), making the final price $360 ($1200 - $840).

• Taxes: If a sales tax rate is 7%, the tax on a $1200 item would be $84 (7% of $1200).

• Statistics and Data Analysis: Percentages are frequently used to represent proportions and trends in data sets. For example, if 70% of 1200 survey respondents answered "yes" to a question, it means 840 respondents answered "yes."

• Financial Calculations: Interest rates, investment returns, and loan repayments are often expressed as percentages. Understanding percentages helps in making informed financial decisions.

• Grade Calculations: Many academic systems use percentages to represent grades. If a student scores 840 out of 1200 points on an exam, their percentage score would be 70%.

Understanding the Concept of "Of" in Percentage Calculations

The word "of" in percentage problems signifies multiplication. When you see "70% of 1200," it means "70% multiplied by 1200." This understanding is essential for solving percentage problems accurately.

Advanced Percentage Calculations: Finding the Percentage

While this article primarily focuses on finding a percentage of a number, it's also useful to understand how to determine the percentage one number represents of another. For example, if you scored 840 out of 1200 on a test, to find the percentage, you would divide the score by the total points and multiply by 100:

(840/1200) x 100 = 70%

Frequently Asked Questions (FAQ)

• Q: What is the easiest way to calculate percentages?

  A: The easiest method is usually converting the percentage to a decimal and multiplying it by the number.

• Q: Can I use a calculator for percentage calculations?

  A: Yes, most calculators have a percentage function (%) that simplifies the calculation.

• Q: What if the percentage is not a whole number (e.g., 70.5%)?

  A: Follow the same methods, converting the percentage to a decimal (70.5% = 0.705) and multiplying.

• Q: What if I need to find the original number given a percentage and the result?

  A: This involves using the inverse operation of multiplication: division. For example, if 70% of a number is 840, then the original number is 840 / 0.7 = 1200.

• Q: Are there online percentage calculators?

  A: Yes, many websites offer free online percentage calculators to help you perform these calculations quickly and easily.

Conclusion

Calculating percentages is a valuable skill applicable in numerous situations. Understanding the different methods, from decimal multiplication to proportion setups, empowers you to tackle a wide range of percentage problems. Remember that the core concept is to express the percentage as a fraction or decimal and then perform the necessary multiplication. Mastering this skill will greatly enhance your mathematical abilities and provide a valuable tool for navigating many aspects of everyday life and professional endeavors. The answer to "What is 70% of 1200?" is definitively 840, calculated through various methods, each reinforcing the underlying principles of percentage calculation.