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Chapter 1: Problem 45

Subtract. $$ -8-(-8) $$

Short Answer

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Step by step solution

01

Identify the Terms

Identify the terms involved in the subtraction. Here, the terms are -8 and -(-8).
02

Understand the Subtraction of Negatives

Remember that subtracting a negative number is equivalent to adding the positive of that number, due to the rule: -(-a) = a.
03

Apply the Rule

Apply the rule to the expression: -8 - (-8) becomes -8 + 8.
04

Perform the Addition

Now, calculate the result of -8 + 8. Adding these two numbers gives 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Integer Subtraction
When subtracting integers, it is helpful to focus on a few key rules. Integers are whole numbers which include both positive and negative numbers as well as zero. Subtracting one integer from another can either increase or decrease the overall value. Any subtraction can be thought of as 'adding the opposite'. For example, subtracting 3 is the same as adding -3. This makes calculations easier to handle. Always convert subtraction into addition, as this clarifies the operation needed.
Negative Numbers
Negative numbers are numbers less than zero. They are usually shown with a minus sign in front. Negative numbers follow special rules when it comes to arithmetic operations. When dealing with negative numbers, subtraction is often seen as tricky. Remember two essential rules:
  • Subtracting a negative number turns into addition. For example, -(-4) becomes +4.
  • Adding a negative number is like subtraction. For instance, +(-4) becomes -4.
Recognizing these key points makes negative numbers easier to manage in arithmetic problems.
Algebraic Rules
Understanding algebraic rules is crucial for solving problems involving negative numbers and integer subtraction. The main rule to keep in mind is: -(-a) = a. This means that subtracting a negative number is the same as adding the positive version of that number. When you see double negatives, they cancel out. Here is a step-by-step example using this rule: Imagine the problem is -8 - (-8). First, rewrite the expression by removing the double negative: -8 + 8. Finally, perform the addition: -8 plus 8 equals 0. This simple application of algebraic rules helps in avoiding confusion and errors.

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