Problem 1 - Discrete Mathematics with Applications

Question

Using Example \(12.2,\) evaluate each. $$6+10$$

Step-by-Step Solution

Answer

The result of the arithmetic expression \(6 + 10\) is \(16\).

Step 1: Identify the operation

In this arithmetic expression, we need to add the two numbers 6 and 10.

Step 2: Perform the addition

Add the two numbers together: \[6 + 10 = 16\]

Step 3: Write the final result

The result of the arithmetic expression is 16.

Key Concepts

Addition

Addition is one of the most basic arithmetic operations. It involves combining two or more numbers to find their total value. When you add numbers, you are essentially putting together their values to get a sum. This operation is represented by the plus sign "+". Understanding addition is crucial, as it forms the foundation for more complex mathematical operations.
Addition is commutative, which means that you can change the order of the numbers and still get the same result. For instance, adding 6 to 10 gives the same sum as adding 10 to 6:

• 6 + 10 = 16
• 10 + 6 = 16

Additionally, addition is associative, suggesting that when you have three or more numbers, you can group them in any manner and achieve the same total. For example, with numbers 3, 6, and 10:
- (3 + 6) + 10 = 19
- 3 + (6 + 10) = 19
These properties make addition an essential tool for solving mathematical problems in everyday life.

Example Problems

Working through example problems is one of the best ways to understand addition. Let's consider the example given:
**Example:** Evaluate the expression, adding 6 and 10.

• The operation involves two numbers: 6 and 10.
• By performing the addition, these two values are combined to get a final result.

This example illustrates how numbers are combined in a straightforward, clear manner. Solving problems step-by-step helps solidify understanding, allowing you to apply these skills confidently to new problems.
Examples often vary in complexity, from the simple addition of integers like this to problems involving decimals, fractions, or even larger numbers. Through practice, one gains speed and efficiency, developing the ability to approach more intricate mathematical questions with ease.

Step-by-Step Solutions

Breaking down solutions into simple, manageable steps is very helpful for understanding mathematical operations like addition. The example solution illustrates how solving an addition problem can be streamlined into three easy steps:
**Step 1:** Identify the operation. Recognize that you are performing addition on two numbers, in this case, 6 and 10. Understanding the type of operation you are working with helps you approach the problem correctly.
**Step 2:** Perform the addition. Add the two numbers together. This is the core of the solution where you execute the operation:

• 6 + 10 = 16

**Step 3:** Write the final result. Express the outcome of the addition operation clearly and confidently, which in this situation is 16.
By following these steps, you can ensure clarity and accuracy in solving arithmetic problems. This systematic approach reduces the chances of errors and boosts comprehension, making it easier to tackle a wide range of mathematical challenges in the future.