Calculating Remaining String Length After Cut-Off A Step-by-Step Guide

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In this article, we will delve into a practical problem involving the calculation of remaining string length after a portion has been cut off. This type of problem often appears in mathematics and physics, and understanding how to solve it is crucial for developing problem-solving skills. We will break down the problem step by step, explaining the concepts and calculations involved. Our goal is to provide a comprehensive guide that will help you not only solve this specific problem but also tackle similar challenges in the future. By the end of this article, you will have a solid understanding of how to convert units, calculate percentages, and determine the remaining length of an object after a portion has been removed. So, let's embark on this mathematical journey together and enhance our problem-solving abilities.

H2: Problem Statement: Cutting a String

The problem we're tackling is as follows: A string is initially 3 1/2 meters long. 20% of the string is cut off and given to a friend. The question is: What is the length of the remaining string in centimeters?

This problem involves several steps, including converting mixed numbers to decimals, calculating percentages, and converting meters to centimeters. Let's break it down to understand each step clearly. We will explore the initial length of the string, the portion that was cut off, and finally, how to calculate the remaining length. Understanding each of these aspects is essential for arriving at the correct answer. This problem is a great example of how mathematics is used in everyday life, whether it's measuring materials for a project or calculating discounts while shopping.

H2: Step 1: Convert Mixed Number to Decimal

The first step in solving this problem is to convert the mixed number 3 1/2 meters into a decimal. This will make our calculations easier. A mixed number consists of a whole number and a fraction. In this case, we have 3 as the whole number and 1/2 as the fraction. To convert 3 1/2 to a decimal, we need to convert the fraction 1/2 to its decimal equivalent. We know that 1/2 is equal to 0.5. Therefore, 3 1/2 is equal to 3 + 0.5, which is 3.5 meters. This conversion is crucial because it allows us to perform calculations more efficiently using decimal values. Converting fractions to decimals is a fundamental skill in mathematics and is widely used in various applications. Now that we have the initial length of the string in decimal form, we can proceed to the next step of calculating the length that was cut off.

H2: Step 2: Calculate the Length Cut Off

Next, we need to calculate the length of the string that was cut off. We are given that 20% of the string was cut off. To find this length, we need to calculate 20% of 3.5 meters. To do this, we first convert the percentage to a decimal. 20% is equivalent to 20/100, which simplifies to 0.20. Now, we multiply the decimal equivalent of the percentage (0.20) by the total length of the string (3.5 meters). So, the calculation is 0.20 * 3.5 meters. This gives us 0.7 meters. This means that 0.7 meters of the string was cut off and given to the friend. Understanding how to calculate percentages is a vital skill in mathematics, with applications ranging from calculating discounts and taxes to analyzing data and statistics. Now that we know the length of the string that was cut off, we can move on to the next step of determining the remaining length.

H2: Step 3: Calculate the Remaining Length

Now that we know the initial length of the string (3.5 meters) and the length that was cut off (0.7 meters), we can calculate the remaining length. To do this, we simply subtract the length cut off from the initial length. So, the calculation is 3.5 meters - 0.7 meters. This gives us 2.8 meters. Therefore, the remaining length of the string is 2.8 meters. This step is a straightforward application of subtraction, a fundamental arithmetic operation. It's important to ensure that we are subtracting the correct values to arrive at the accurate remaining length. With the remaining length now calculated in meters, we proceed to the final step of converting it to centimeters, as required by the problem.

H2: Step 4: Convert Meters to Centimeters

The final step is to convert the remaining length from meters to centimeters. We know that 1 meter is equal to 100 centimeters. Therefore, to convert 2.8 meters to centimeters, we multiply 2.8 by 100. So, the calculation is 2.8 * 100 centimeters, which gives us 280 centimeters. This means that the remaining length of the string is 280 centimeters. Converting between different units of measurement is a crucial skill in mathematics and science, ensuring that we can express quantities in the most appropriate units for a given context. In this case, the problem specifically asked for the answer in centimeters, so this final conversion is essential for providing the correct answer. With the remaining length now calculated in centimeters, we have successfully completed all the steps required to solve the problem.

H2: Final Answer

Therefore, the length of the remaining string is 280 centimeters. Looking at the options provided:

a. 250m b. 260m c. 270m d. 280m

The correct answer is (d) 280 cm. This problem demonstrated several important mathematical concepts, including converting mixed numbers to decimals, calculating percentages, subtracting decimals, and converting between units of measurement. By breaking the problem down into smaller steps, we were able to solve it systematically and arrive at the correct answer. Understanding these concepts is crucial for success in mathematics and related fields. Furthermore, the ability to apply these concepts to real-world problems enhances our problem-solving skills and prepares us for various practical situations. We hope this step-by-step explanation has been helpful in understanding the solution to this problem. Remember, practice is key to mastering mathematical concepts, so keep solving problems and challenging yourself to improve your skills.

Before we conclude, let's briefly revisit the key concepts we utilized to solve this problem. This will reinforce our understanding and ensure we can apply these concepts to similar problems in the future.

  1. Converting Mixed Numbers to Decimals: This is a fundamental skill for simplifying calculations. We converted 3 1/2 meters to 3.5 meters.
  2. Calculating Percentages: We determined 20% of 3.5 meters, which involved converting the percentage to a decimal and then multiplying.
  3. Subtracting Decimals: We subtracted the length cut off (0.7 meters) from the initial length (3.5 meters) to find the remaining length.
  4. Converting Units of Measurement: We converted meters to centimeters by multiplying by 100.

These concepts are not only crucial for solving mathematical problems but also have practical applications in everyday life. By mastering these skills, we become more confident and capable problem solvers. Remember, mathematics is not just about formulas and equations; it's about logical thinking and problem-solving. The more we practice and apply these concepts, the better we become at understanding and navigating the world around us. So, let's continue to explore and learn, and embrace the power of mathematics in our lives.

To further enhance our understanding and problem-solving abilities, let's discuss some common mistakes that students often make when tackling problems like this. Being aware of these pitfalls can help us avoid them and ensure we arrive at the correct solution.

  1. Incorrectly Converting Mixed Numbers: A common mistake is misinterpreting mixed numbers or making errors during the conversion to decimals. For example, confusing 3 1/2 with 3.12 or making a calculation error when converting the fraction part.
  2. Miscalculating Percentages: Errors in percentage calculations can lead to significant deviations in the final answer. For instance, forgetting to convert the percentage to a decimal before multiplying or making mistakes in the multiplication process itself.
  3. Errors in Subtraction: While subtraction may seem straightforward, errors can occur if the decimal points are not aligned correctly or if there are mistakes in the subtraction process.
  4. Forgetting to Convert Units: Failing to convert the final answer to the required units (in this case, centimeters) is a common oversight. It's crucial to pay attention to the units specified in the problem and ensure the answer is expressed accordingly.
  5. Misinterpreting the Problem: Sometimes, students may misinterpret the problem statement, leading to an incorrect approach. It's essential to read the problem carefully and understand what is being asked before attempting to solve it.

By being mindful of these common mistakes and taking steps to avoid them, we can improve our accuracy and problem-solving skills. Remember, attention to detail and careful execution are key to success in mathematics. Let's strive to learn from these potential pitfalls and become more confident and capable problem solvers.

To solidify your understanding of the concepts discussed, let's explore some practice problems similar to the one we solved. Working through these problems will help you apply the skills you've learned and build your confidence in tackling such challenges.

  1. Problem 1: A rope is 5 1/4 meters long. 30% of the rope is cut off. What is the length of the remaining rope in centimeters?
  2. Problem 2: A ribbon is 2.8 meters long. If 45% of the ribbon is used, what is the length of the remaining ribbon in centimeters?
  3. Problem 3: A wire is 7 3/4 meters long. 25% of the wire is removed. What is the length of the remaining wire in centimeters?

These problems are designed to test your understanding of the concepts we've covered, including converting mixed numbers to decimals, calculating percentages, subtracting decimals, and converting units of measurement. Take your time to work through each problem step by step, and don't hesitate to refer back to the explanations and examples we've discussed. Practice is essential for mastering mathematical skills, and the more problems you solve, the more confident and proficient you'll become. So, let's put our knowledge to the test and continue to grow as problem solvers. Remember, the journey of learning mathematics is a continuous one, and every problem we solve brings us one step closer to mastery.

In conclusion, we have successfully tackled a problem involving the calculation of remaining string length after a portion was cut off. We broke down the problem into manageable steps, including converting mixed numbers to decimals, calculating percentages, subtracting decimals, and converting units of measurement. By understanding and applying these concepts, we were able to arrive at the correct answer: 280 centimeters. This problem serves as a practical example of how mathematics is used in everyday situations, from measuring materials for a project to calculating quantities in various contexts.

Throughout this article, we emphasized the importance of step-by-step problem-solving, careful execution, and attention to detail. We also discussed common mistakes to avoid and provided practice problems to solidify your understanding. Remember, the key to mastering mathematical skills is consistent practice and a willingness to learn from mistakes. By embracing challenges and persevering through difficulties, you can develop your problem-solving abilities and achieve your mathematical goals. We hope this article has been helpful and informative, and we encourage you to continue exploring the fascinating world of mathematics. Keep practicing, keep learning, and keep growing as a problem solver. The possibilities are endless, and with dedication and effort, you can achieve anything you set your mind to.