Problem 9 - Prealgebra

Question

Find each sum or product. Explain your reasoning. $$8+11+22+4$$

Step-by-Step Solution

Answer

The sum is 45.

Step 1: Identify the Operation

The problem is asking for a sum of the given numbers. Recognize that you need to add the numbers: 8, 11, 22, and 4.

Step 2: Add the Numbers Sequentially

Start by adding the first two numbers together: 8 + 11 = 19.

Step 3: Add the Next Number to the Current Sum

Take the sum from Step 2, which is 19, and add the next number in the list: 19 + 22 = 41.

Step 4: Add the Final Number

Use the current sum from Step 3, which is 41, and add the last number: 41 + 4 = 45.

Step 5: Verify the Calculation

Review each step to ensure all numbers were added correctly. Verifying: 8 + 11 = 19, then 19 + 22 = 41, and finally 41 + 4 = 45.

Key Concepts

Understanding the Sum

In mathematics, the term "sum" refers to the result of adding two or more numbers. It's a fundamental concept in arithmetic operations. Adding numbers together is one of the simplest, yet most essential, mathematical skills. For example, in the problem we are considering, the numbers 8, 11, 22, and 4 need to be added to find their total. The process of addition is straightforward, where you increase the total by including each subsequent number. Recognizing when to find a sum is important. Any time you see a plus sign "+" between numbers, you're looking at an addition operation. Becoming familiar with this operation lays the foundation for more complex math problems later on.

Exploring Arithmetic Operations

Arithmetic operations are the basic calculations you perform with numbers, and they include addition, subtraction, multiplication, and division. Each of these operations has its own rules and purposes. Addition is usually the first arithmetic operation students learn because it involves simple counting. The operation is binary, meaning it operates on two numbers or variables at a time, which then combine to form a sum. Here's a quick outline of arithmetic operations:

• Addition: Combining values to find their total sum.
• Subtraction: Determining the difference between two values.
• Multiplication: Repeated addition of the same number.
• Division: Splitting a number into equal parts.

By understanding the basic arithmetic operations, you're equipped to tackle a wide range of mathematical problems, making these skills critical for progression in mathematics.

Following a Step-by-Step Solution

When solving math problems, particularly those involving several steps, a step-by-step solution can help clarify each part of the process. Breaking down problems into manageable steps allows you to focus on each part separately, reducing mistakes and confusion. In our specific problem of finding the sum of 8, 11, 22, and 4, a step-by-step approach ensures accuracy:

• Step 1: Identify the operation needed. Here, it's addition.
• Step 2: Start with the first two numbers: 8 + 11 = 19.
• Step 3: Take the result, 19, and add the next number: 19 + 22 = 41.
• Step 4: Add the final number: 41 + 4 = 45.
• Step 5: Review each step to verify the accuracy of your results.

By following a methodical approach, even complex problems become easier to solve, and your answers remain reliable. Such practice also sharpens your problem-solving skills over time.