Picnic Contribution Calculation Total Amount Collected By 67 Students
Introduction: The Class Picnic Fund
In this article, we will explore a common arithmetic problem involving calculating the total amount collected for an event. Our specific scenario involves a class of students planning a picnic and each contributing a fixed amount. This is a practical example of multiplication, a fundamental operation in mathematics. We aim to provide a comprehensive explanation that is easy to understand, catering to students, parents, and educators alike. Let’s dive into the details of how to calculate the total contributions for the class picnic.
Problem Statement: Gathering Funds for a Class Outing
The core question we address is: If all 67 students in Class 4 of a school planned a picnic, and each student contributed ₹125, how much total amount was collected? This problem exemplifies a real-world application of basic arithmetic. To solve this, we need to determine the total sum amassed from individual contributions. Understanding this problem requires grasping the concept of multiplication as repeated addition. Each student’s contribution adds to the total, and when the contributions are uniform, we can use multiplication as a shortcut to calculate the sum efficiently. The amount each student contributed is ₹125, and there are 67 students. Therefore, to find the total amount collected, we need to multiply these two numbers. This calculation will give us the total funds available for the picnic. This kind of problem is essential for students to learn as it bridges the gap between theoretical math and everyday financial situations. It helps in developing their number sense and problem-solving skills, which are crucial for various aspects of life. Furthermore, understanding how to calculate total contributions is vital in many practical scenarios, such as fundraising events, group outings, or even managing household expenses. By breaking down the problem into simple steps and providing a clear explanation, we aim to make this concept accessible to all learners. The ability to solve such problems empowers students to handle similar situations confidently in the future. So, let's proceed with the detailed solution to uncover the total amount collected for the picnic.
Method 1: Multiplication - The Efficient Approach
To efficiently calculate the total amount collected, we employ the method of multiplication. Multiplication is a fundamental arithmetic operation that simplifies the process of adding the same number multiple times. In this scenario, we are adding ₹125 sixty-seven times, which represents each student’s contribution. Instead of manually adding ₹125 sixty-seven times, we can multiply ₹125 by 67 to arrive at the total amount collected. This approach is not only faster but also less prone to errors. To perform the multiplication, we set up the problem as follows: 125 multiplied by 67. The calculation involves multiplying each digit of 67 (which are 60 and 7) by 125 and then adding the results. First, we multiply 125 by 7, which gives us 875. Next, we multiply 125 by 60. To do this, we can multiply 125 by 6 and then multiply the result by 10. Multiplying 125 by 6 gives us 750. Now, multiplying 750 by 10 simply means adding a zero at the end, resulting in 7500. Finally, we add the two results: 875 and 7500. Adding these numbers gives us the total amount collected. This method provides a straightforward and accurate way to determine the total funds raised for the picnic. By understanding the concept of multiplication, students can apply this approach to various similar problems involving repeated addition. This skill is essential for handling more complex calculations in mathematics and real-world scenarios. Therefore, mastering multiplication is a crucial step in developing mathematical proficiency.
Step-by-Step Calculation: Breaking Down the Multiplication
Let's break down the multiplication process step-by-step to ensure clarity and understanding. Our goal is to multiply 125 (the amount each student contributed) by 67 (the number of students). This step-by-step approach will make the calculation more manageable and less intimidating. First, we will multiply 125 by the ones digit of 67, which is 7. 1. Multiply 125 by 7: * 7 multiplied by 5 (the ones digit of 125) equals 35. Write down 5 and carry over 3. * 7 multiplied by 2 (the tens digit of 125) equals 14. Add the carried-over 3, which gives us 17. Write down 7 and carry over 1. * 7 multiplied by 1 (the hundreds digit of 125) equals 7. Add the carried-over 1, which gives us 8. Write down 8. So, 125 multiplied by 7 equals 875. Next, we will multiply 125 by the tens digit of 67, which is 6 (representing 60). To do this, we can multiply 125 by 6 and then multiply the result by 10. 2. Multiply 125 by 6: * 6 multiplied by 5 (the ones digit of 125) equals 30. Write down 0 and carry over 3. * 6 multiplied by 2 (the tens digit of 125) equals 12. Add the carried-over 3, which gives us 15. Write down 5 and carry over 1. * 6 multiplied by 1 (the hundreds digit of 125) equals 6. Add the carried-over 1, which gives us 7. Write down 7. So, 125 multiplied by 6 equals 750. Now, multiply 750 by 10 by adding a zero at the end, which gives us 7500. Finally, we will add the two results: 875 (from 125 multiplied by 7) and 7500 (from 125 multiplied by 60). 3. Add 875 and 7500: * Write the numbers vertically, aligning the digits by place value. * Add the digits in each column: * Ones column: 5 + 0 = 5 * Tens column: 7 + 0 = 7 * Hundreds column: 8 + 5 = 13. Write down 3 and carry over 1. * Thousands column: 0 + 7 + 1 (carried over) = 8. * The sum is 8375. Therefore, the total amount collected is ₹8375. This step-by-step breakdown of the multiplication process helps in understanding each part of the calculation, making it easier to grasp and remember. By following this method, students can confidently solve similar problems involving multiplication.
Method 2: Repeated Addition - Understanding the Concept
While multiplication provides an efficient method for solving this problem, understanding the concept of repeated addition helps reinforce the fundamental principle behind multiplication. In essence, multiplication is a shortcut for adding the same number multiple times. In our scenario, we have 67 students, each contributing ₹125. Therefore, to find the total amount collected, we could theoretically add ₹125 to itself 67 times. Although this method is time-consuming and impractical for larger numbers, it offers a clear visualization of what multiplication represents. To illustrate this, let’s consider adding ₹125 a few times: * ₹125 + ₹125 = ₹250 (2 students) * ₹250 + ₹125 = ₹375 (3 students) * ₹375 + ₹125 = ₹500 (4 students) We can see that with each addition, the total amount increases by ₹125. If we were to continue this process 67 times, we would eventually arrive at the same answer as we did with multiplication. However, it's evident that this method is significantly more tedious and prone to errors, especially with larger numbers. Understanding repeated addition is crucial for grasping the concept of multiplication, but for practical calculations, multiplication is the preferred method. By recognizing the relationship between repeated addition and multiplication, students can develop a deeper understanding of mathematical operations. This understanding is valuable for problem-solving and for applying math concepts to real-world situations. While we wouldn't recommend using repeated addition for this specific problem due to its inefficiency, it serves as a valuable educational tool for solidifying the concept of multiplication.
Verification: Ensuring Accuracy of the Result
After performing the calculation, it is crucial to verify the result to ensure accuracy. Verification is an essential step in problem-solving as it helps identify and correct any errors that might have occurred during the calculation process. There are several methods to verify the result of our multiplication problem. One simple method is to estimate the answer and compare it with the calculated result. We can round ₹125 to ₹100 and 67 students to 70 students. The estimated total would then be ₹100 multiplied by 70, which equals ₹7000. This provides a rough estimate of the total amount collected. Our calculated result of ₹8375 is reasonably close to this estimate, suggesting that our answer is likely correct. Another method is to divide the total amount collected by the number of students. If we divide ₹8375 by 67, we should get approximately ₹125, which is the amount each student contributed. Performing this division: 8375 ÷ 67 = 125 This confirms that our calculation is correct. Additionally, we can use a calculator to verify the multiplication. Multiplying 125 by 67 using a calculator should yield 8375, further validating our result. By employing these verification methods, we can be confident in the accuracy of our answer. Ensuring accuracy is a critical skill in mathematics and in practical situations. It prevents errors and helps in making informed decisions based on reliable data. Therefore, always take the time to verify your results, especially in situations where precision is important.
Answer: The Total Amount Collected
After performing the multiplication and verifying the result, we can confidently state the answer to our problem. The question was: If all 67 students in Class 4 of a school planned a picnic, and each student contributed ₹125, how much total amount was collected? Through our calculations, we found that the total amount collected is ₹8375. This total amount is the sum of all the individual contributions made by the students. To recap, we multiplied the amount each student contributed (₹125) by the number of students (67) to find the total collection. The calculation was as follows: 125 × 67 = 8375 Therefore, the class collected ₹8375 for their picnic. This amount should be sufficient to cover the expenses of the picnic, depending on the planned activities and resources needed. Understanding how to calculate such totals is a valuable skill for students, as it has practical applications in various real-life scenarios, such as planning events, managing finances, or organizing group activities. By solving this problem, students not only enhance their mathematical skills but also learn to apply these skills in practical contexts. The ability to calculate total contributions accurately is essential for effective planning and financial management. So, the final answer is ₹8375, which is the total amount collected by the 67 students of Class 4 for their picnic.
Conclusion: Applying Math to Real-World Scenarios
In conclusion, the problem of calculating the total amount collected for a class picnic demonstrates the practical application of mathematics in real-world scenarios. By multiplying the contribution per student (₹125) by the number of students (67), we determined that the total amount collected was ₹8375. This exercise not only reinforces the concept of multiplication but also highlights the importance of mathematical skills in everyday situations. Understanding how to calculate total amounts, whether for a picnic, a fundraiser, or any other event, is a valuable life skill. It enables individuals to plan and manage resources effectively. Moreover, the process of solving this problem involves several critical steps, including problem analysis, calculation, and verification, which are all essential components of mathematical problem-solving. By breaking down the problem into manageable steps, we made the calculation process clear and accessible. We also emphasized the importance of verifying the result to ensure accuracy. Mathematics is not just an abstract subject taught in classrooms; it is a practical tool that helps us navigate and make sense of the world around us. Problems like this one bridge the gap between theory and practice, showing students how mathematical concepts can be applied to solve real-life challenges. By engaging with such problems, students develop a deeper appreciation for the relevance of mathematics and its role in their lives. Therefore, it is crucial to encourage students to apply their mathematical skills in various contexts and to see mathematics as a valuable and practical tool. The picnic contribution problem serves as a simple yet powerful example of how math can be used to address real-world needs and challenges.