Problem 74 - Elementary and Intermediate Algebra

Question

Add. $$ -3+6+(-9)+(-6) $$

Step-by-Step Solution

Answer

The sum is -12.

Step 1: Identify the Numbers

List the numbers given in the problem: -3, 6, -9, and -6. Recognize which are negative and which are positive.

Step 2: Combine Positive and Negative Numbers Separately

First, add the positive numbers together: 6. Then, add the negative numbers together: -3 + (-9) + (-6). This becomes -18.

Step 3: Add the Results Together

Now, combine the results from Step 2. The positive sum is 6 and the negative sum is -18. Add these: 6 + (-18).

Step 4: Calculate the Final Sum

Perform the addition: 6 + (-18) = 6 - 18 = -12.

Key Concepts

Positive and Negative Numbers

When learning about integer addition, it's crucial to understand the difference between positive and negative numbers.

• Positive Numbers: These are numbers greater than zero. They are usually written without a plus sign. For instance, numbers like 6, 25, and 132 are positive.
• Negative Numbers: These are numbers less than zero, denoted by a minus sign before them. Examples include -3, -9, and -20.

Positive numbers represent a gain, while negative numbers often signify a loss or decrease.
To get comfortable with these numbers, visualize a number line. Positive numbers extend to the right of zero, and negative numbers extend to the left.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and operators (like addition or subtraction).
In the exercise, the expression consists of four terms: -3, 6, -9, and -6. Each of these terms is treated as a separate component of the expression.
Recognizing each part of an algebraic expression helps in understanding how to rearrange and simplify the terms.

• Identify terms: An expression may have constants (fixed numbers like -6 or 6) and can include negative values.
• Combine terms: Group similar items, such as all positive numbers or all negative numbers when simplifying or solving an expression.

Understanding these basics will make working with expressions more straightforward, especially when they get more complex.

Adding Integers Step by Step

Adding integers becomes clear when approached methodically. Let's break down the process:

• Identify the Integers: First, list all the numbers you need to work with, noting which are positive and which are negative. For example: -3, 6, -9, and -6.
• Separate Them: Add all the positive numbers together and all the negative numbers together separately. From our example:
  • Positive: only 6.
  • Negative: -3 + (-9) + (-6) which sums up to -18.
• Combine the Results: Finally, take the sum of the positive integers and add it to the sum of the negative integers. Use the formula:\[6 + (-18) = 6 - 18 = -12.\]This is your answer!

Understanding each step simplifies the process. It ensures you can handle a mix of positive and negative numbers with confidence, leading to correct results each time.