The world of percentages can be intriguing and sometimes puzzling, especially when we are faced with questions like “What percent is 90 of 120?” This query may seem straightforward, but understanding the underlying mathematics and applying it correctly is crucial. In this article, we will delve into the concept of percentages, how to calculate them, and specifically, how to find what percent 90 is of 120.
Introduction to Percentages
Percentages are a way to express a value as a fraction of 100. The term “percent” means “per 100,” and it is denoted by the symbol %. Percentages are used in various aspects of life, including finance, statistics, and everyday calculations. They help in comparing quantities and understanding proportions. For instance, saying a shirt is on sale for 20% off is more intuitive than saying it’s on sale for 0.20 of its original price.
Calculating Percentages
To calculate a percentage, you need to know the part of the whole you are interested in and the whole itself. The formula for finding what percent one number is of another is: (part/whole) * 100. This formula is essential for solving problems like the one at hand: finding what percent 90 is of 120.
Applying the Formula
Using the formula mentioned above, we can calculate what percent 90 is of 120. Here, the part is 90, and the whole is 120. Plugging these values into the formula gives us: (90/120) * 100. Simplifying this, 90 divided by 120 equals 0.75. Then, multiplying 0.75 by 100 gives us 75. Therefore, 90 is 75% of 120.
Understanding the Concept
Understanding that 90 is 75% of 120 can be further reinforced by considering the concept of proportions. If you have 120 items and you take 90 of them, you have taken 75% of the total. This can be visualized on a number line or a pie chart, where 90 out of 120 units are shaded or marked, representing 75% of the whole.
Real-World Applications
Percentages have numerous real-world applications. For example, in finance, percentages are used to calculate interest rates, investment returns, and discounts. In education, percentages are used to grade exams and assignments. In health and fitness, percentages can be used to track progress in weight loss or muscle gain. Understanding how to calculate percentages, like finding what percent 90 is of 120, is essential for making informed decisions in these areas.
Percentage Increase and Decrease
Another important aspect of percentages is calculating increases and decreases. For instance, if a product’s price increases from $100 to $120, the increase can be calculated as ((120-100)/100) * 100 = 20%. Similarly, if the price decreases from $120 to $90, the decrease is ((120-90)/120) * 100 = 25%. These calculations are vital in understanding market trends, budgeting, and financial planning.
Conclusion
In conclusion, finding what percent 90 is of 120 involves a simple yet powerful formula: (part/whole) * 100. By applying this formula, we find that 90 is 75% of 120. This calculation is not just a mathematical exercise; it has practical implications in various fields. Understanding percentages and how to calculate them is crucial for navigating the world effectively, whether it’s in personal finance, education, or professional settings. By grasping these concepts, individuals can make more informed decisions and better analyze the world around them.
To further illustrate the practicality of percentage calculations, consider the following table that outlines the calculation of what percent 90 is of 120, along with a brief explanation:
| Part | Whole | Percentage | Calculation |
|---|---|---|---|
| 90 | 120 | 75% | (90/120) * 100 |
This calculation and the concept of percentages are fundamental to many aspects of life. By mastering these concepts, one can develop a stronger foundation in mathematics and a more nuanced understanding of the world. Whether it’s calculating discounts, understanding investment returns, or simply grasping the proportion of one quantity to another, the ability to work with percentages is invaluable. As such, the next time you encounter a question like “What percent is 90 of 120?”, you’ll be well-equipped to provide a precise and confident answer: 75%.
What is the concept of percentage and how does it apply to the problem of finding 90% of 120?
The concept of percentage is a way to express a value as a fraction of 100. It is often denoted by the symbol “%”. In the context of the problem, finding 90% of 120 means we need to calculate 90% of the value 120. To do this, we can use the formula: (percentage / 100) * number. This formula allows us to find the specified percentage of a given number. In this case, we will use the formula to find 90% of 120.
To apply the formula, we simply plug in the values: (90 / 100) * 120. This calculation can be simplified to 0.9 * 120. By multiplying 0.9 and 120, we get the result, which is the value that represents 90% of 120. This calculation is a straightforward application of the percentage formula and provides the solution to the problem. The result of this calculation will give us the answer we are looking for, which is the value that represents 90% of 120.
How do I calculate 90% of 120 using the percentage formula?
To calculate 90% of 120, we use the formula: (percentage / 100) * number. Plugging in the values, we get: (90 / 100) * 120. This can be simplified to 0.9 * 120. The next step is to perform the multiplication. Multiplying 0.9 by 120 gives us 108. Therefore, 90% of 120 is equal to 108. This calculation is a direct application of the percentage formula and provides the correct solution to the problem.
The calculation can be further broken down into simpler steps for clarity. First, we convert the percentage to a decimal by dividing by 100: 90 / 100 = 0.9. Then, we multiply this decimal by the given number: 0.9 * 120 = 108. By following these steps, we can easily calculate 90% of 120 and arrive at the correct answer. This method can be applied to find any percentage of a given number, making it a useful tool for solving a wide range of problems.
What are the real-world applications of calculating percentages, such as finding 90% of 120?
Calculating percentages has numerous real-world applications across various fields, including finance, business, and education. For instance, in finance, percentages are used to calculate interest rates, investment returns, and discounts. In business, percentages are used to determine profit margins, sales growth, and market share. In education, percentages are used to calculate grades, test scores, and student progress. The ability to calculate percentages, such as finding 90% of 120, is an essential skill that can be applied to many everyday situations.
The application of percentage calculations can be seen in many aspects of life. For example, a store may offer a 10% discount on a product that originally costs $120. To find the discount amount, we calculate 10% of 120, which is $12. The new price of the product would then be $120 – $12 = $108. This is just one example of how percentage calculations can be used in real-world scenarios. By understanding how to calculate percentages, individuals can make informed decisions and solve problems in a variety of contexts.
How does the calculation of 90% of 120 relate to other mathematical concepts, such as fractions and decimals?
The calculation of 90% of 120 is closely related to other mathematical concepts, such as fractions and decimals. Percentages can be expressed as fractions or decimals, and vice versa. In the case of 90% of 120, we can express 90% as a fraction (90/100) or a decimal (0.9). This relationship between percentages, fractions, and decimals allows us to convert between these different forms and solve problems using the most convenient method. By understanding these relationships, individuals can develop a deeper understanding of mathematical concepts and improve their problem-solving skills.
The connection between percentages, fractions, and decimals is fundamental to many mathematical operations. For instance, to find 90% of 120, we can convert the percentage to a decimal (0.9) and then multiply by 120. Alternatively, we can express 90% as a fraction (90/100) and multiply by 120. Both methods will yield the same result, which is 108. By recognizing the relationships between these mathematical concepts, individuals can approach problems from different angles and develop a more comprehensive understanding of mathematics.
What are some common mistakes to avoid when calculating percentages, such as finding 90% of 120?
When calculating percentages, such as finding 90% of 120, there are several common mistakes to avoid. One of the most common mistakes is forgetting to convert the percentage to a decimal or fraction before multiplying by the given number. Another mistake is to multiply the percentage by the number without dividing by 100 first. Additionally, individuals may confuse the order of operations, such as multiplying before dividing, which can lead to incorrect results. By being aware of these potential mistakes, individuals can take steps to avoid them and ensure accurate calculations.
To avoid these mistakes, it is essential to follow the correct order of operations and to double-check calculations. When calculating 90% of 120, individuals should first convert the percentage to a decimal (0.9) and then multiply by 120. This will ensure that the calculation is performed correctly and the result is accurate. By taking the time to review calculations and avoid common mistakes, individuals can build confidence in their mathematical skills and develop a stronger understanding of percentage calculations.
How can I use technology, such as calculators or spreadsheets, to calculate percentages like 90% of 120?
Technology, such as calculators or spreadsheets, can be a powerful tool for calculating percentages like 90% of 120. Most calculators have a percentage function that allows users to easily calculate percentages. In a spreadsheet, such as Microsoft Excel, users can use formulas to calculate percentages. For example, to find 90% of 120 in Excel, users can enter the formula “=0.9*120” and the spreadsheet will display the result. By using technology to calculate percentages, individuals can save time and reduce the risk of errors.
Using technology to calculate percentages can also help individuals to explore and analyze data more efficiently. For instance, in a spreadsheet, users can create formulas to calculate percentages for multiple values and then use charts and graphs to visualize the results. This can be particularly useful in business or finance, where percentages are used to analyze trends and make informed decisions. By leveraging technology to calculate percentages, individuals can streamline their workflow and gain deeper insights into their data.
How can I check my answer to ensure that I have correctly calculated 90% of 120?
To check the answer to the calculation of 90% of 120, individuals can use several methods. One approach is to estimate the result and then compare it to the calculated answer. For example, if we estimate that 90% of 120 is close to 100, we can then compare this estimate to the calculated result of 108. Another method is to use a different calculation method, such as converting the percentage to a fraction and then multiplying by the given number. By using multiple methods to check the answer, individuals can verify that their calculation is correct.
Another way to check the answer is to use the reverse calculation. For instance, if we have calculated that 90% of 120 is 108, we can then calculate 100% of the result (108) and check if it equals 120. If 108 is indeed 90% of 120, then 120 should be 100% of 108 / 0.9. By performing this reverse calculation, individuals can confirm that their original answer is correct and build confidence in their mathematical skills. By taking the time to check answers, individuals can ensure accuracy and develop a more robust understanding of percentage calculations.