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Chapter 1: Problem 9

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

Short Answer

Expert verified
3

Step by step solution

01

Understand the signs

Identify the signs of the numbers in the expression. Here, '-5' is a negative number and '+8' is a positive number.
02

Simplify the expression

The expression is [-5 + (+8)]. Since adding a positive number is just the same as addition, we simplify to: -5 + 8.
03

Perform the addition

To add a negative and a positive number, subtract the smaller absolute value from the larger absolute value. Here, |8| - |5| = 3. Since 8 is the larger number and it's positive, the answer is +3.

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Key Concepts

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

Integer Operations
Integer operations involve basic arithmetic operations like addition, subtraction, multiplication, and division with whole numbers. In our example, the integers are -5 and +8. Integers can be positive, negative, or zero. When working with integers, it is essential to understand their signs:
  • Positive numbers do not have a sign or explicitly carry a '+' symbol.
  • Negative numbers explicitly carry a '-' symbol.
  • Zero (0) is considered neutral and does not carry any sign.
Understanding the signs is crucial for correct computation, as it guides how we combine these numbers. Other fundamental operations include taking the opposite (negation) and understanding order when presented in expressions.
Addition and Subtraction
Addition and subtraction with integers follow straightforward rules but can confuse some students. For the expression -5 + (+8), we first simplify to -5 + 8. Here's how we handle it:
  • Addition of integers: Combine the values directly if they have the same sign.
  • Subtraction appears when combining numbers with different signs.
When adding numbers with opposite signs, subtract the smaller absolute value from the larger absolute value. In our example:
\(|8| - |5| = 3.\)
Since the larger number (8) is positive, the final result is positive 3. Such operations simplify into performing absolute value calculations and deciding the final sign based on the larger absolute value.
Absolute Value
Absolute value measures the distance a number is from zero on the number line, disregarding its sign. We use the notation |x| to denote the absolute value of x. In our example, we deal with |8| and |5|:
  • |8| = 8
  • |5| = 5
The concept of absolute value helps in operations involving both positive and negative integers by focusing on magnitude. For subtraction involving absolute values, as in \(|8| - |5| = 3\), understanding absolute value allows correct computational steps irrespective of the original signs of the numbers. Remember:
  • Absolute value is always non-negative.
  • This concept is critical for correctly performing addition and subtraction involving negative numbers.

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Most popular questions from this chapter

In Exercises \(1-72\), compute the value of each expression. $$100-83-45-24$$

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