Chocolate Distribution Problem Solving Math Step By Step

In this mathematical problem, we will explore how Ray distributes his chocolates among his friends. Ray has a specific arrangement of chocolates within boxes, layers, rows, and individual pieces. To solve this, we need to determine the total number of chocolates Ray possesses and then divide that quantity equally among his 16 friends. This exercise involves understanding basic arithmetic operations such as multiplication and division and applying them in a real-world scenario. We will break down the problem step by step, first calculating the total number of chocolates and then determining how many each friend receives.

Understanding the Problem

To begin, let's clarify the specifics of the problem. Ray has 3 boxes of chocolates. Within each box, there are 4 layers of chocolates. Each layer is further divided into 4 rows, with each row containing 4 chocolates. The core of the problem lies in calculating the total number of chocolates and then distributing them equally among 16 friends. To solve this, we must first determine the total number of chocolates Ray has. This requires multiplying the number of boxes by the number of layers per box, then by the number of rows per layer, and finally by the number of chocolates per row. Once we have the total, we will divide it by the number of friends to find out how many chocolates each friend receives. This problem is a practical application of multiplication and division, demonstrating how these operations are used to solve real-world distribution problems. Understanding the problem's structure is crucial for setting up the correct mathematical expression.

Step-by-Step Calculation

The first step in solving this problem is to calculate the number of chocolates in a single layer. Each layer has 4 rows, and each row contains 4 chocolates. To find the total number of chocolates in a layer, we multiply the number of rows by the number of chocolates per row: 4 rows * 4 chocolates/row = 16 chocolates per layer. Now that we know there are 16 chocolates in one layer, we can calculate the number of chocolates in one box. Each box has 4 layers, so we multiply the number of chocolates per layer by the number of layers: 16 chocolates/layer * 4 layers = 64 chocolates per box. Next, we need to find the total number of chocolates Ray has. He has 3 boxes, so we multiply the number of chocolates per box by the number of boxes: 64 chocolates/box * 3 boxes = 192 chocolates. Finally, we distribute these chocolates among 16 friends. To find out how many chocolates each friend receives, we divide the total number of chocolates by the number of friends: 192 chocolates / 16 friends = 12 chocolates per friend. This step-by-step approach ensures that we accurately calculate the final result, breaking down the problem into smaller, manageable parts.

Forming the Expression

Now, let's formulate the mathematical expression that represents the problem. This expression should encapsulate all the steps we took to solve the problem. We started by calculating the chocolates in a layer (4 * 4), then the chocolates in a box (4 * 4 * 4), then the total chocolates (3 * 4 * 4 * 4), and finally, the chocolates per friend (3 * 4 * 4 * 4) / 16. Therefore, the expression can be written as (3 * 4 * 4 * 4) / 16. This expression clearly shows the sequence of operations needed to arrive at the solution. It highlights the multiplication steps required to find the total number of chocolates and the division step to distribute them among the friends. The expression is a concise representation of the entire problem, making it easy to understand the mathematical process involved. Using a single expression helps to simplify the problem and provides a clear roadmap for the calculation. This mathematical expression accurately mirrors our step-by-step calculation process, ensuring a correct and efficient solution.

Calculating the Value

To calculate the value of the expression (3 * 4 * 4 * 4) / 16, we follow the order of operations, which dictates that we perform multiplication before division. First, we multiply 4 * 4 to get 16. Then, we multiply that result by 4, giving us 64. Next, we multiply 64 by 3, which equals 192. So, the numerator of our expression is 192. Now, we divide 192 by 16. When we divide 192 by 16, we get 12. Therefore, the value of the expression (3 * 4 * 4 * 4) / 16 is 12. This means that each of Ray's 16 friends will receive 12 chocolates. This calculation confirms our step-by-step method and provides a clear answer to the problem. Calculating the value involves carefully performing each operation in the correct order to ensure accuracy. The result, 12 chocolates per friend, is a practical and understandable solution to the distribution problem. This final calculation completes our problem-solving process, providing a definitive answer.

Final Answer

In summary, the expression that represents the distribution of chocolates among Ray's friends is (3 * 4 * 4 * 4) / 16. This expression encapsulates the entire process of calculating the total number of chocolates and dividing them equally among the 16 friends. The value of this expression, which we calculated step-by-step, is 12. Therefore, each of Ray's 16 friends will receive 12 chocolates. This result provides a clear and concise answer to the problem. We arrived at this solution by first determining the number of chocolates in each layer, then in each box, and finally, the total number of chocolates. We then divided the total number of chocolates by the number of friends to find the number of chocolates each friend would receive. The expression (3 * 4 * 4 * 4) / 16 accurately represents this process, and the value of 12 is the final, definitive answer. This complete solution demonstrates the application of basic arithmetic operations in a practical context.