Problem 61 - Fundamentals of Mathematics

Question

Add and subtract as in dicated. Add the sum of \(2,273,3,304,847,\) and 16 to the difference of 4,365 and 864 .

Step-by-Step Solution

Answer

The final result is 9,941.

Step 1: Identify the Expression

We need to find the sum of \(2,273 + 3,304 + 847 + 16\) and the difference \(4,365 - 864\). This means our expression is: \[(2,273 + 3,304 + 847 + 16) + (4,365 - 864)\]

Step 2: Calculate the Sum

First, we'll calculate the sum of the numbers in the first part of the expression: \(2,273 + 3,304 + 847 + 16\). Add them step by step:- \(2,273 + 3,304 = 5,577\)- \(5,577 + 847 = 6,424\)- \(6,424 + 16 = 6,440\)

Step 3: Calculate the Difference

Next, find the difference \(4,365 - 864\). Subtract:- \(4,365 - 864 = 3,501\)

Step 4: Add the Sum and the Difference

Finally, we add the results from Step 2 and Step 3:\(6,440 + 3,501 = 9,941\)

Key Concepts

Understanding the Step by Step Solution

It's important to approach arithmetic problems systematically to ensure accuracy. In this exercise, the aim was to break down a complex expression into manageable parts. Here’s a quick overview of the step-by-step thought process:

• **Identifying the Expression:** Recognize the entire arithmetic expression you’re dealing with. In this exercise, we had a combined operation involving addition and subtraction.
• **Processing Each Part Separately:** First, handle the sum part of the expression separately from the difference. This segmentation helps maintain clarity and focus.
• **Combining Results:** After calculating each part, we sum the outcomes to arrive at the final result.

By following these steps, you minimize errors and maintain a clear understanding of each component of the problem.

Exploring Arithmetic Operations

Arithmetic operations are the basic building blocks of mathematics. They include addition, subtraction, multiplication, and division. In this exercise, we utilized two of these operations: addition and subtraction. Here’s a bit more about how these operations work:

• **Addition:** This is the process of calculating the total or sum by combining numbers. In the exercise, adding several numbers was required to find a collective sum.
• **Subtraction:** This operation is about finding the difference by removing one quantity from another. We subtracted to find the difference between two numbers.

Both operations follow a sequential process, meaning you work through each number step by step. Using methods like column addition or borrowing in subtraction can help ensure accuracy. Understanding these can enhance your ability to tackle various arithmetic challenges effectively!

Calculating the Sum and Difference

A crucial part of this exercise involved calculating the sum and difference separately before combining them. Here’s a closer look at these terms: - **Sum:** Refers to the result of addition. When you add numbers together, the total amount is the sum. In this example, we found the sum of 2,273, 3,304, 847, and 16, which resulted in 6,440. - **Difference:** This term indicates the result of subtraction. It represents how much one number differs from another. For 4,365 and 864, the difference came to 3,501. Combining these techniques allows you to solve more complex equations efficiently, as seen in the final result of 9,941. Grasping these concepts provides a strong foundation for handling diverse mathematical problems, whether they involve simple or intricate equations.