Problem 87 - Prealgebra and Introductory Algebra

Question

Subtract. $$-4-(-4)$$

Step-by-Step Solution

Answer

0

Step 1: Understand the problem

The problem is asking to subtract negative 4 from negative 4, which can be simplified as adding 4 to negative 4. While dealing with negative numbers, subtracting a negative number means adding that number. Hence, the problem can be rewritten as -4 + 4.

Step 2: Solve the problem

The problem simplifies as follows: \[ -4+4 = 0 \]

Key Concepts

Integer Operations

When we work with integer operations, we are dealing with whole numbers which can be positive, negative, or zero. These operations include addition, subtraction, multiplication, and division. It's important to remember a few key points:

• Addition: When you add two positive integers, the result is positive. Adding two negative integers results in a negative sum.
• Subtraction: Subtracting an integer is like adding its opposite. For example, subtracting -3 is the same as adding 3.
• Multiplication and Division: When multiplying or dividing two integers, if both have the same sign, the result is positive. If they have different signs, the result is negative.

Understanding these basics helps when solving more complex problems involving integers, like subtracting negative numbers. This operation can initially appear tricky but really is just about rewriting the expression in terms of addition.

Simplifying Expressions

Simplifying expressions is about altering the expression to make it easier to understand or work with, without changing its value. This often involves combining like terms and using mathematical operations effectively.

• For expressions involving subtraction and negative numbers, converting all subtraction to addition of negatives can simplify the process. For instance, converting \[ -4 - (-4) \] to \[ -4 + 4 \]
• This step helps avoid errors and provides a clearer path toward finding the solution.
• Look for patterns or components that can be simplified, such as \( 2a - 3a \) becoming \(-a \), as you combine like terms.

Simplifying expressions makes mathematics more accessible and allows us to see equivalent simpler forms, facilitating easier computation.

Negative Numbers

Negative numbers can sometimes be confusing, especially when combined with different mathematical operations. They represent values less than zero and follow specific rules when used in calculations.

• Representation: Negative numbers are usually denoted with a minus sign ("-").
• Behavior in Subtraction: In subtraction, the expression \( -a - (-b) \) should be viewed as \( -a + b \).
• Example: Considering our original problem, \( -4 - (-4) \), the subtraction of negative (-4) translates to addition, resulting in \( -4 + 4 = 0 \).

Mastering the use of negative numbers helps in achieving accurate results, especially in more complex operations where keeping track of signs matters immensely. Recognizing that subtracting a negative is akin to adding its positive form is crucial in simplifying any mathematical expression.