Problem 49 - Beginning and Intermediate Algebra

Question

Add See Examples \(\ell\) through 7 . $$ 6+(-4)+9 $$

Step-by-Step Solution

Answer

The result of adding 6, -4, and 9 is 11.

Step 1: Understanding the Problem

The problem involves adding a series of numbers: 6, -4, and 9. This requires understanding the order and the effect of adding a negative number.

Step 1: Add the First Two Numbers

First, we add 6 and -4 together. Adding a negative number is the same as subtraction: 6 + (-4) = 6 - 4 = 2.

Step 2: Add the Result to the Next Number

Now, take the result from Step 1, which is 2, and add it to 9: 2 + 9 = 11.

Step 3: Verify the Calculation

Check that each step was done correctly: 1. 6 + (-4) = 2 2. 2 + 9 = 11 Every step matches the given arithmetic operations, confirming our final result.

Key Concepts

Negative Numbers

Understanding negative numbers is crucial for solving arithmetic problems that involve these values. A negative number is any number less than zero, represented with a minus sign (-) in front of it. They often denote a decrease, such as a drop in temperature or a reduction in balance.
Negative numbers can sometimes be confusing, especially when dealing with addition and subtraction. When you add a negative number, it's similar to subtracting its positive counterpart. For example, adding -4 to 6 is the same as subtracting 4 from 6.

• Negative numbers are numbers below zero.
• They are represented with a '-' sign.
• Adding a negative number is equivalent to subtraction.

Understanding the role of negative numbers is key to mastering integer addition and solving problems effectively.

Arithmetic Operations

Arithmetic operations are basic math processes that include addition, subtraction, multiplication, and division. In our current problem, we're focusing on the operation of addition, which combines numbers to find their total.
The operation might seem simple, but it becomes slightly more complex with the involvement of negative numbers. To correctly perform arithmetic operations with negative and positive integers, remember:

• Adding positive numbers results in a larger number.
• Adding negative numbers decreases the total.
• The order of operations in a sequence doesn't affect the final total, but always process them carefully to avoid mistakes.

Understanding how these operations work together allows for accurate and efficient problem solving.

Problem Solving Steps

Successfully solving math problems often involves following clear, logical steps to ensure accuracy. When approaching an addition problem like this, break it down into manageable parts:
1. **Understand the Problem:** Identify all the numbers involved and their roles in the operation. 2. **Add Numbers Sequentially:** Combine numbers step-by-step, especially when dealing with negatives. For instance, begin with the first two numbers, then proceed with the sum and the remaining number. 3. **Verify Your Work:** Double-check each step to ensure calculations were performed correctly and agree with the operation's rules.
Following these steps not only eases the problem-solving process but also boosts confidence in your math skills. Practice often to become proficient at handling similar problems.