Calculating The Cost Of Rice Purchase A Mathematical Problem
This article delves into a practical mathematical problem involving the calculation of the total cost of a rice purchase. We will explore the steps required to solve the problem, focusing on the conversion of mixed fractions to improper fractions, multiplication of fractions, and the final calculation of the total amount paid. Understanding these concepts is crucial for everyday financial transactions and problem-solving.
Understanding the Problem
The problem states that Rohit purchased 7 1/2 kg of rice at a rate of ₹25 1/2 per kg. The task is to determine the total amount of money Rohit paid to the shopkeeper. This involves multiplying the quantity of rice purchased by the price per kilogram. Before we can perform the multiplication, we need to convert the mixed fractions (7 1/2 and 25 1/2) into improper fractions. This conversion is essential because it simplifies the multiplication process. Mixed fractions consist of a whole number and a proper fraction, while improper fractions have a numerator that is greater than or equal to the denominator. Converting to improper fractions allows us to treat the entire quantity as a single fractional value, making the calculation straightforward. The core concept here is to translate the real-world scenario into a mathematical equation, which then needs to be solved using appropriate arithmetic operations. By breaking down the problem into smaller, manageable steps, we can ensure accuracy and clarity in our solution. Furthermore, this type of problem reinforces the practical application of mathematical concepts in everyday life, demonstrating how fractions and multiplication are used in financial transactions. The ability to confidently handle such calculations is a valuable skill for anyone, regardless of their mathematical background.
Step 1: Converting Mixed Fractions to Improper Fractions
To solve this problem, the first step is to convert the mixed fractions into improper fractions. A mixed fraction is a whole number and a fraction combined, such as 7 1/2. An improper fraction, on the other hand, has a numerator greater than or equal to its denominator. Converting mixed fractions to improper fractions makes multiplication easier. To convert 7 1/2 into an improper fraction, we multiply the whole number (7) by the denominator (2) and add the numerator (1). This gives us (7 * 2) + 1 = 15. We then place this result over the original denominator, resulting in 15/2. Similarly, for 25 1/2, we multiply 25 by 2 and add 1, which gives us (25 * 2) + 1 = 51. Placing this over the original denominator, we get 51/2. This conversion is a fundamental step in working with fractions and is essential for accurate calculations. Understanding the process behind this conversion is crucial. It involves recognizing that a mixed fraction represents a whole number plus a fraction, and the improper fraction form represents the same quantity as a single fraction. By converting to improper fractions, we eliminate the need to deal with whole numbers separately during multiplication, which simplifies the process significantly. This step highlights the importance of understanding the different forms of fractions and how to convert between them. The ability to perform this conversion quickly and accurately is a valuable skill in various mathematical contexts, not just in this specific problem.
Step 2: Multiplying the Fractions
Now that we have converted the mixed fractions into improper fractions, we can proceed with the multiplication. We have 15/2 kg of rice and the price is ₹51/2 per kg. To find the total amount Rohit paid, we need to multiply these two fractions: (15/2) * (51/2). To multiply fractions, we multiply the numerators together and the denominators together. So, (15 * 51) / (2 * 2) gives us 765/4. This step demonstrates the fundamental principle of fraction multiplication, which is a crucial concept in arithmetic. The process is straightforward: multiply the top numbers (numerators) and then multiply the bottom numbers (denominators). This results in a new fraction that represents the product of the original two fractions. In this context, multiplying the fractions represents multiplying the quantity of rice by the price per kilogram, which will give us the total cost. Understanding this step is essential for solving similar problems involving fractional quantities and prices. The ability to confidently multiply fractions is a valuable skill in various real-world applications, from calculating recipe ingredients to determining the cost of items sold by weight or volume. This step reinforces the importance of understanding the mechanics of fraction multiplication and its practical implications.
Step 3: Converting the Improper Fraction to a Mixed Number or Decimal
We have the result as 765/4, which is an improper fraction. To make this result more understandable, we can convert it to a mixed number or a decimal. Converting to a mixed number involves dividing the numerator (765) by the denominator (4). 765 divided by 4 is 191 with a remainder of 1. This means that 765/4 is equal to 191 1/4. Alternatively, we can convert the improper fraction to a decimal by dividing 765 by 4, which gives us 191.25. This conversion is important because it transforms the answer into a more easily interpretable format. While the improper fraction 765/4 is mathematically correct, it may not be immediately clear what this value represents in terms of money. Converting to a mixed number (191 1/4) provides a better sense of the magnitude of the amount, as it shows the whole number part (191) and the fractional part (1/4) separately. Converting to a decimal (191.25) provides the most straightforward representation of the amount in monetary terms. The choice between a mixed number and a decimal often depends on the context and the preference of the individual. In financial calculations, decimals are commonly used because they allow for precise representation of amounts. This step highlights the importance of being able to convert between different forms of fractions and decimals, as well as understanding the practical implications of each form.
Final Answer
Therefore, Rohit paid ₹191.25 to the shopkeeper. This answer is derived from multiplying the amount of rice purchased (7 1/2 kg) by the price per kilogram (₹25 1/2). We converted the mixed fractions to improper fractions, multiplied them, and then converted the resulting improper fraction to a decimal for clarity. This final answer represents the total cost of the rice and provides a clear and concise solution to the problem. The process of arriving at this answer demonstrates the importance of understanding and applying various mathematical concepts, including fraction conversion, multiplication, and decimal representation. The ability to solve such problems is not only valuable in academic settings but also in everyday financial transactions. This example underscores the practical relevance of mathematics in real-life situations. Furthermore, it reinforces the importance of breaking down complex problems into smaller, manageable steps, which can lead to a more accurate and understandable solution. By following this step-by-step approach, we can confidently tackle similar problems and make informed financial decisions.
