Problem 26 - Prealgebra

Question

Find each sum or product. Explain your reasoning. $$11+8+19$$

Step-by-Step Solution

Answer

The sum is 38.

Step 1: Identify the Numbers

We need to find the sum of the numbers given in the problem: 11, 8, and 19. These are the numbers we will be adding together.

Step 2: Add the First Two Numbers

Start by adding the first two numbers together: 11 and 8. Perform the addition: \[ 11 + 8 = 19 \]So, the sum of the first two numbers is 19.

Step 3: Add the Result to the Third Number

Now take the result from Step 2, which is 19, and add it to the third number, which is also 19:\[ 19 + 19 = 38 \]This gives us the total sum of all three numbers.

Key Concepts

Understanding Step-by-Step Solutions

Approaching problems with a step-by-step solution is a methodical way to break down what might seem complicated at first glance. By dividing the process into smaller, more manageable actions, it becomes easier to avoid mistakes and to see the direct path to the answer. This approach helps students by:

• Clarifying what needs to be done at each stage.
• Providing a sense of accomplishment as each step is completed.
• Building confidence in handling more complex problems.

In our exercise, identifying the numbers, then systematically adding them in stages, showcases how step-by-step reasoning simplifies arithmetic operations.

The Concept of Sum in Addition

The term "sum" refers to the result of adding two or more numbers together. It's a fundamental concept in mathematics, especially in basic arithmetic operations. When finding a sum:

• You start with an initial number and continue adding subsequent numbers.
• Each addition results in an intermediate sum, which evolves as more numbers are added.
• Finally, the total sum of all numbers is determined.

In our example, we calculate the sum by first finding the intermediate sum of 11 and 8, which gives 19. Adding the next number, 19, results in the final sum of 38. Understanding how to determine a sum is crucial for developing further skills in mathematics.

The Role of Arithmetic Reasoning

Arithmetic reasoning is the process of using logical thinking to solve problems involving numbers. It requires more than just performing calculations; it involves:

• Recognizing patterns or methods that simplify the task.
• Ensuring accuracy through verification of each step.
• Understanding the underlying concept behind the operations.

In our exercise, arithmetic reasoning is demonstrated by the logical breakdown of the sum problem. By addressing each number one by one and verifying each result before proceeding, the problem is tackled efficiently. This type of reasoning helps foster a solid understanding that is beneficial in mathematics and everyday life.

Foundational Number Operations

Number operations form the basics of arithmetic and include addition, subtraction, multiplication, and division. Each operation helps in performing calculations necessary for problem-solving. Focusing on addition, the steps are:

• Identifying numbers that need to be combined.
• Performing calculations through basic addition.
• Repeating the process across more numbers if necessary.

In this example, each number is sequentially added: first two numbers, followed by an addition of the intermediate sum with the next number. This process exemplifies how number operations are foundational tools that, once mastered, assist in tackling more complicated mathematical problems.