42 Is What Percent Of 120

42 is What Percent of 120? A Comprehensive Guide to Percentage Calculations

Calculating percentages is a fundamental skill with widespread applications in various fields, from everyday budgeting and shopping to complex financial analysis and scientific research. Understanding how to solve percentage problems, such as "42 is what percent of 120?", is crucial for anyone aiming to improve their numerical literacy. This comprehensive guide will not only provide the solution but also delve into the underlying principles, offering multiple approaches and practical examples to solidify your understanding.

Understanding Percentages

Before tackling the specific problem, let's refresh our understanding of percentages. A percentage is a fraction expressed as a number out of 100. The symbol "%" represents "per cent," meaning "out of one hundred." Therefore, 50% is equivalent to 50/100, which simplifies to 1/2 or 0.5.

Method 1: The Proportion Method

This method leverages the concept of proportions to solve percentage problems. We can set up a proportion where one ratio represents the known values (42 and 120) and the other represents the unknown percentage (x%).

• Step 1: Set up the proportion:

  42/120 = x/100

• Step 2: Cross-multiply:

  42 * 100 = 120 * x

• Step 3: Solve for x:

  4200 = 120x x = 4200 / 120 x = 35

Therefore, 42 is 35% of 120.

Method 2: The Decimal Method

This method utilizes the decimal equivalent of a percentage. We can express the percentage as a decimal and then solve the equation.

• Step 1: Convert the percentage to a decimal:

  Let x represent the unknown percentage. We can write the problem as:

  42 = x * 120

• Step 2: Solve for x:

  x = 42 / 120 x = 0.35

• Step 3: Convert the decimal back to a percentage:

  To convert the decimal to a percentage, we multiply by 100:

  0.35 * 100 = 35%

Thus, 42 is 35% of 120.

Method 3: Using a Calculator

Most calculators have a percentage function that simplifies the calculation. Simply enter "42 ÷ 120 × 100" and the calculator will directly provide the answer: 35%.

Practical Applications: Real-World Examples

Percentage calculations are ubiquitous in daily life. Here are some examples showing how understanding this concept can be beneficial:

• Shopping Discounts: A store offers a 25% discount on an item originally priced at $80. To calculate the discount, you would find 25% of $80: 0.25 * $80 = $20. The discounted price would be $80 - $20 = $60.

• Tax Calculations: A sales tax of 6% is added to a purchase of $150. The tax amount is calculated as 0.06 * $150 = $9. The total cost including tax is $150 + $9 = $159.

• Grade Calculations: A student scores 45 out of 60 points on a test. To determine the percentage score, you would calculate (45/60) * 100 = 75%.

• Financial Investments: If you invest $1000 and it increases by 10%, your profit would be 0.10 * $1000 = $100, and your new balance would be $1100.

• Data Analysis: Percentages are extensively used to represent data in charts, graphs, and reports, making it easier to understand trends and patterns. For instance, a survey might reveal that 60% of respondents prefer a particular product.

Advanced Percentage Problems

While the problem "42 is what percent of 120?" is relatively straightforward, percentage calculations can become more complex. Understanding the fundamentals allows you to tackle more challenging scenarios:

• Finding the original value: If 30% of a number is 60, what is the original number? This requires solving the equation 0.30 * x = 60, where x is the original number. Dividing both sides by 0.30 gives x = 200.

• Percentage increase or decrease: If a value increases from 50 to 60, the percentage increase is calculated as [(60-50)/50] * 100 = 20%. Similarly, if a value decreases from 80 to 60, the percentage decrease is [(80-60)/80] * 100 = 25%.

• Compound interest: Compound interest involves calculating interest not only on the principal amount but also on accumulated interest. This requires a more complex formula.

Mastering Percentages: Tips and Practice

Mastering percentage calculations requires practice and a strong understanding of the underlying concepts. Here are some tips to improve your skills:

• Practice regularly: Solve various percentage problems regularly to build your confidence and fluency.

• Use different methods: Try solving problems using multiple methods (proportion, decimal, calculator) to enhance your understanding and identify the most efficient approach for each situation.

• Visualize the problem: Draw diagrams or use real-world examples to help visualize the problem and make it easier to understand.

• Break down complex problems: If facing a complex problem, break it down into smaller, more manageable steps.

• Check your answers: Always check your answers to ensure accuracy. You can do this by using a different method or working backward from your answer.

Conclusion: The Power of Percentage Calculations

Understanding how to calculate percentages is an invaluable skill with applications in numerous aspects of life. Whether it’s managing finances, interpreting data, or simply solving everyday problems, a firm grasp of percentage calculations empowers you to make informed decisions and navigate various quantitative challenges effectively. By mastering the different methods and practicing regularly, you can confidently tackle any percentage problem, from the simple to the more complex. Remember the core principle: a percentage is simply a fraction expressed out of 100, and with a bit of practice, you'll become proficient in handling percentage calculations. The answer to "42 is what percent of 120?" is definitively 35%, but the real takeaway is the broader understanding of percentage calculations and their pervasive usefulness.