Problem 63 - Beginning and Intermediate Algebra

Question

Find each difference. $$ -6-(-2) $$

Step-by-Step Solution

Answer

-6 - (-2) = -4

Step 1: Understand the Problem

The exercise asks to find the difference between -6 and -2. In mathematical terms, it is written as \(-6 - (-2)\).

Step 2: Rewrite the Expression

Subtracting a negative number is the same as adding its positive equivalent. Thus, \(-6 - (-2)\) can be rewritten as \(-6 + 2\).

Step 3: Perform the Addition

Now, perform the simple addition: \(-6 + 2 = -4\).

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They are represented with a minus sign (-) before the number. For example, -6 means 6 units less than zero.
When working with negative numbers, it's crucial to understand their properties:

• Negatives are to the left of zero on the number line.
• Subtracting a negative number is like adding a positive number.
• Adding two negative numbers gives a larger negative number.

In our exercise, we start with -6, which is 6 units to the left of zero on the number line.

Addition

Addition involves combining two or more numbers to get a total sum. When dealing with negative numbers, some specific rules apply:

• Adding a negative number is similar to subtracting its positive counterpart.
• Subtracting a negative number is the same as adding its positive counterpart.

For example, in the expression \(-6 - (-2)\), subtracting -2 is the same as adding 2. Thus, it becomes \(-6 + 2 = -4\). Remember: Two negative signs make a positive when directly next to each other!

Mathematical Expressions

Mathematical expressions represent numbers and operations in a structured form. They help us understand and solve problems involving arithmetic operations. For example, the expression \(-6 - (-2)\) includes a subtraction operation between negative numbers.
Breaking down expressions helps clarify their meaning. First, we recognize \(- (-2)\) as adding 2. This turns our initial expression into a simpler form, \(-6 + 2\), which is straightforward to solve. Always review the order of operations (PEMDAS):

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

This ensures correct handling of complex expressions.