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Chapter 1: Problem 17

In Exercises \(1-72\), compute the value of each expression. $$-5-(-8)$$

Short Answer

Expert verified
The value of the expression is 3.

Step by step solution

01

Identify the operation

Recognize that the expression involves both subtraction and dealing with parentheses that indicate a negative number: $$-5-(-8)$$.
02

Simplify inside the parentheses

Understanding that subtracting a negative number is equivalent to adding its positive counterpart: $$-5 - (-8) = -5 + 8.$$
03

Perform the addition

Add $$-5 + 8.$$ Answer: $$3.$$

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Key Concepts

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

Integer Operations
In elementary algebra, integers are whole numbers that can be either positive or negative, including zero. Working with integers involves understanding how to perform basic mathematical operations like addition, subtraction, multiplication, and division.

Integer operations are fundamental in algebra and are often presented in problems involving both negative and positive numbers.
  • Adding two positive integers always results in a positive integer.
  • Adding two negative integers always results in a negative integer.
  • When adding a positive integer and a negative integer, subtract the smaller absolute value from the larger absolute value, and the sign will be of the number with the larger absolute value.
Being comfortable with these rules helps solve more complex problems later. Practice is key!

Subtracting Negative Numbers
Subtracting negative numbers can sometimes seem confusing. However, once you understand the rule, it becomes straightforward. The rule is: Subtracting a negative number is the same as adding the positive equivalent of that number.

For example, in the expression \(-5-(-8)\), note the double negative. Simplify this by converting subtraction of a negative into addition of a positive. This turns the expression from \(-5-(-8)\) to \(-5 + 8\).

Here are some steps to remember when subtracting negative numbers:
  • Look for the minus sign in front of the parentheses.
  • Replace the subtraction of the negative number with the addition of the positive number.
  • Proceed with the regular addition or subtraction as needed.
Practicing this simple switch helps avoid confusion and prevents common arithmetic mistakes.

Simplification Steps
After understanding how integer operations and subtracting negative numbers work, it's crucial to know how to simplify mathematical expressions.

Simplification involves breaking down expressions into simpler forms. Here are the steps used in the exercise to simplify \(-5-(-8)\):
  • First, identify the operations involved. In our example, it's subtraction of a negative number.
  • Simplify the expression inside the parentheses. Replace the subtraction of the negative with addition: \(-5 - (-8) = -5 + 8\).
  • Perform the addition. Here, \(-5 + 8 = 3\).
Simplification makes complex problems easier to manage. Always tackle expressions step-by-step, and use fundamental rules of arithmetic to ensure accuracy. With practice, these steps will become more intuitive.

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Most popular questions from this chapter

Sketch the given set on a number line. $$\\{x | 3

Sketch the given set on a number line. $$\\{x |-3 \leq x \leq 2\\}$$

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