Notebook Sales Calculation How Many Notebooks Did The Shopkeeper Sell
Introduction: The Shopkeeper's Notebook Venture
In the bustling world of commerce, every transaction tells a story. Today, we delve into a fascinating scenario involving a shopkeeper, their notebooks, and a tidy sum earned. The core of our investigation lies in understanding how many notebooks this diligent shopkeeper managed to sell to amass a total of ₹ 1225, given that each notebook was priced at ₹ 12 rac{1}{4}. This article isn't just about crunching numbers; it's about unraveling the relationship between price, quantity, and earnings in a real-world context. We'll embark on a step-by-step journey, meticulously breaking down the problem, employing fundamental mathematical principles, and arriving at a solution that sheds light on the shopkeeper's successful venture. So, buckle up as we navigate the realms of fractions, division, and practical problem-solving, all while keeping an eye on the fascinating interplay of economics and everyday mathematics. Our goal isn't just to find an answer, but to understand the process, the logic, and the underlying concepts that make this mathematical puzzle a captivating exploration of commerce and calculation.
Understanding the Problem: Price Per Notebook and Total Earnings
At the heart of our mathematical quest lies a simple yet profound question: How many notebooks did the shopkeeper sell? To answer this, we must first dissect the information provided. The shopkeeper sells each notebook at a rate of ₹ 12 rac{1}{4}. This seemingly straightforward figure is a mixed fraction, a combination of a whole number and a fraction. To make calculations easier, we'll convert this mixed fraction into an improper fraction. Multiplying the whole number (12) by the denominator (4) gives us 48, and adding the numerator (1) results in 49. Thus, ₹ 12 rac{1}{4} is equivalent to ₹ rac{49}{4}. This means each notebook fetches the shopkeeper ₹ rac{49}{4}. The shopkeeper's total earnings from these notebook sales amount to ₹ 1225. This is the total revenue generated from selling an unknown number of notebooks. Our mission is to bridge the gap between the price per notebook and the total earnings to reveal the quantity of notebooks sold. This involves a fundamental concept in mathematics: division. We'll divide the total earnings by the price per notebook to find the number of notebooks sold. This is where the beauty of mathematical operations comes into play, allowing us to transform raw data into meaningful insights about the shopkeeper's sales performance. The process will not only give us the answer, but also reinforce the practical applications of mathematical concepts in our daily lives.
Converting Mixed Fraction to Improper Fraction: A Crucial Step
Before we dive into the calculation, let's solidify our understanding of converting mixed fractions to improper fractions. This conversion is not merely a mathematical trick; it's a foundational skill that simplifies calculations involving fractions. Our notebook price, ₹ 12 rac{1}{4}, is a classic example of a mixed fraction. It comprises a whole number (12) and a proper fraction ( rac{1}{4}). To convert this to an improper fraction, we follow a simple yet powerful procedure. We multiply the whole number by the denominator of the fraction and then add the numerator. The result becomes the new numerator, while the denominator remains the same. In our case, we multiply 12 by 4, which equals 48. Then, we add the numerator, 1, resulting in 49. Thus, the improper fraction equivalent of 12 rac{1}{4} is rac{49}{4}. This conversion is crucial because it allows us to perform division with greater ease and accuracy. Dividing by a mixed fraction can be cumbersome, but dividing by an improper fraction is a more streamlined process. It's akin to choosing the right tool for the job; the improper fraction is the right tool for our division task. This step underscores the importance of mastering fundamental mathematical conversions, as they pave the way for more complex calculations and problem-solving.
Calculation: Dividing Total Earnings by Price Per Notebook
Now comes the pivotal moment where we put our mathematical skills to the test. We know the shopkeeper earned a total of ₹ 1225, and each notebook was sold for ₹ rac49}{4}. To find the number of notebooks sold, we need to divide the total earnings by the price per notebook. This can be expressed as4}) Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of rac{49}{4} is rac{4}{49}. So, our equation transforms into{49}) Now, we can simplify this multiplication. We notice that 1225 and 49 share a common factor: 49. Dividing 1225 by 49 gives us 25. Thus, our equation simplifies further: Number of notebooks = 25 * 4 Multiplying 25 by 4, we arrive at our final answer: Number of notebooks = 100 This calculation demonstrates the power of mathematical operations in solving real-world problems. By dividing the total earnings by the price per notebook, we've successfully determined the number of notebooks the shopkeeper sold. This isn't just a numerical answer; it's a testament to the practical application of mathematical principles in commerce and everyday life.
Result: The Shopkeeper Sold 100 Notebooks
After our meticulous calculations, the mystery is solved. The shopkeeper, with their astute pricing strategy and diligent salesmanship, managed to sell a grand total of 100 notebooks. This number isn't just a statistic; it's a narrative of commerce, a testament to the shopkeeper's efforts, and a concrete answer to our initial question. Each of those 100 notebooks represents a transaction, a customer served, and a contribution to the shopkeeper's earnings. This result underscores the power of mathematical problem-solving in real-world scenarios. We started with a question, a set of figures, and a desire to understand the dynamics of the shopkeeper's sales. Through careful analysis, conversion of fractions, and strategic division, we've arrived at a definitive answer. This journey exemplifies how mathematics isn't just an abstract discipline confined to textbooks; it's a practical tool that empowers us to unravel complexities, make informed decisions, and gain insights into the world around us. The shopkeeper's sale of 100 notebooks is a tangible illustration of the interplay between commerce and calculation, a story told through the language of mathematics.
Alternative approach
To ensure a comprehensive understanding, let's explore an alternative approach to solving this problem. This method reinforces the core concepts and provides a different perspective on the calculation. We know the shopkeeper earned ₹ 1225 by selling notebooks priced at ₹ 12 rac1}{4} each. Our initial approach involved converting the mixed fraction to an improper fraction and then dividing the total earnings by the price per notebook. For this alternative approach, we'll stick with the mixed fraction and see how we can manipulate the numbers to arrive at the same answer. Let's assume the shopkeeper sold 'x' notebooks. The total earnings can be expressed as4} * x Now, we can convert 12 rac{1}{4} to its improper fraction form, which we already know is rac{49}{4}. So, the equation becomes4} * x To isolate 'x', we need to multiply both sides of the equation by the reciprocal of rac{49}{4}, which is rac{4}{49}{49} = x This is the same equation we arrived at in our initial approach. As we demonstrated earlier, 1225 divided by 49 is 25. Therefore, x = 25 * 4 x = 100 This alternative approach, while seemingly different, ultimately converges on the same mathematical principles and the same solution. It reinforces the idea that there are often multiple paths to the same destination in mathematics, and choosing the most efficient path depends on one's understanding of the underlying concepts. Both approaches highlight the power of algebraic manipulation and the versatility of mathematical tools in problem-solving.
Conclusion: The Power of Mathematical Problem-Solving
In conclusion, our journey through the shopkeeper's notebook sales has been more than just a mathematical exercise; it's been a testament to the power and practicality of mathematical problem-solving. We started with a seemingly simple question: How many notebooks did the shopkeeper sell to earn ₹ 1225 at a rate of ₹ 12 rac{1}{4} per notebook? Through meticulous analysis, strategic conversion of fractions, and the application of fundamental mathematical operations, we've arrived at a definitive answer: The shopkeeper sold 100 notebooks. This exploration has underscored several key concepts. First, we've reinforced the importance of converting mixed fractions to improper fractions for ease of calculation. Second, we've demonstrated the power of division in solving real-world problems involving price, quantity, and earnings. Third, we've highlighted the versatility of mathematical approaches, showcasing how different methods can lead to the same solution. Beyond the numerical answer, this exercise has provided a valuable lesson in critical thinking and problem-solving. It's a reminder that mathematics isn't just a subject confined to textbooks; it's a tool that empowers us to understand, analyze, and navigate the complexities of the world around us. The shopkeeper's successful sale of 100 notebooks is a tangible example of how mathematical principles underpin everyday commerce and contribute to our understanding of the world. This journey from question to answer exemplifies the beauty and practicality of mathematics in action.