Problem 67 - Elementary and Intermediate Algebra

Question

Subtract. $$ -5-(-2) $$

Step-by-Step Solution

Answer

-3

Step 1 - Identify the operation

Identify that you need to subtract one negative number from another. The problem is \[ -5 - (-2) \].

Step 2 - Convert double negative to positive

When subtracting a negative number, it is the same as adding the positive of that number: \[ -5 - (-2) \] becomes \[ -5 + 2 \].

Step 3 - Perform the addition

Add the numbers obtained in Step 2: \[ -5 + 2 = -3 \].

Key Concepts

Integer Operations

Integer operations involve basic math skills like addition, subtraction, multiplication, and division applied to whole numbers that can be positive, negative, or zero. When dealing with integer operations, it is crucial to understand the properties of these numbers and how they interact.

For example, consider the exercise, \( -5 - (-2) \). Here, we are dealing with integer subtraction amongst negative numbers. To perform these operations accurately:

• First, identify the integers involved (in this case, \( -5 \) and \( -2 \)).
• Next, recognize the operation to be performed (here, it is subtraction).
• Lastly, carefully follow rules for dealing with negative signs.

Double Negative

In mathematics, encountering 'double negatives' can initially seem confusing. However, they follow a straightforward rule: two negative signs transform into a positive sign. In the given exercise, we see this rule in action:

Initially, we have \( -5 - (-2) \). Here, \( -(-2) \) represents a double negative. According to the double negative rule, \( -(-2) \) simplifies to \( +2 \). Effectively, subtraction of a negative number is the same as adding its positive counterpart.

This principle helps simplify complicated expressions and ensures clarity while performing algebraic manipulations.

Algebraic Subtraction

Algebraic subtraction extends the concept of basic subtraction to include variables and more complex expressions. Even without variables, understanding this concept is crucial for problems involving integers, as seen in the exercise \( -5 - (-2) \).

To perform algebraic subtraction:

• First, convert any double negatives to positives, which makes the operation simpler.
• Next, follow the basic rules of subtraction.
• Finally, ensure all similar terms are combined correctly to reach the solution.

For our exercise, this means converting \( -5 - (-2) \) to \( -5 + 2 \) and then performing the operation to get \( -3 \). Properly applying these steps ensures accurate results in algebraic problems.