Problem 32 - Algebra 1: Concepts and Skills

Question

RULES OF ADDITION Find the sum. $$-6+(-3)$$

Step-by-Step Solution

Answer

The sum of -6 and -3 is -9.

Step 1: Understand the operation

The operation is addition, but since we are adding two negative numbers, we need to understand how this affects the calculation. In general, when you add two negative numbers together, you get a more negative number. This is because you are moving further away from zero in the negative direction.

Step 2: Add the values

In this step, ignore the negative signs and add the numbers together as if they were positive. So, 6 + 3 = 9.

Step 3: Assign the negative sign

Since we are adding together two negative numbers, the result will also be negative. Therefore, the answer to -6 + (-3) is -9.

Key Concepts

Integer Operations

Integer operations include addition, subtraction, multiplication, and division using whole numbers. Integers encompass both positive numbers, negative numbers, and zero. Understanding how these operations work is crucial, as they provide the foundation for more complex mathematical concepts.
Combining integers follows specific rules that are important to memorize:

• Adding positive integers moves you to the right on the number line.
• Adding negative integers moves you to the left, further from zero.

Addition is performed by combining the values of the integers, but the direction on the number line changes based on whether the integers are positive or negative. Let's detail how to add negative numbers.

Negative Numbers

Negative numbers are integers less than zero. They are represented with a negative sign in front, such as \(-1, -2, -3\), and are the opposite of positive numbers. In practical terms, negative numbers often illustrate concepts like debt or loss in contexts where a deficit is involved.
When dealing with the addition of negative numbers:

• If both numbers are negative, the sum is also negative.
• The result is found by adding the absolute values of the numbers (ignoring the negative signs) and then assigning a negative sign to the result.

Adding \(-6\) + \(-3\) uses these rules. You add the values \6\ and \3\ just as if they were positive, resulting in \9\, but since both numbers are negative, the result is \-9\.

Basic Algebraic Operations

Basic algebraic operations involve manipulation and calculation using numbers and variables. In algebra, operations include addition, subtraction, multiplication, and division. These basic operations form the core of algebraic problem-solving.
When performing any algebraic operation, including adding negative numbers:

• Ensure you understand the sign of each number involved.
• Apply the correct rules such as those involving opposite signs.

For addition particularly, like \(-6\) + \(-3\), follow these steps: first add the absolute values, then assess the operation's result based on initial signs of the numbers involved. Remember, managing signs and values correctly is integral to mastering algebraic problems.