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Chapter 1: Problem 14

In Exercises \(1-66,\) compute the value of each expression. $$-9+(+8)$$

Short Answer

Expert verified
-1

Step by step solution

01

Identify the terms

The given expression is -9+(+8). Here, the terms to be combined are -9 and +8.
02

Understand the operation

The expression involves adding two numbers: -9 and +8. Here, adding a positive number to a negative number should be handled like combining positive and negative counters.
03

Perform the addition

Combine -9 and +8 by treating +8 as positive counters and -9 as negative counters. When 8 positive counters are added to 9 negative counters, the negative counters dominate and the result is -1.

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Key Concepts

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

Integer Operations
Integer operations are the basic arithmetic processes involving whole numbers, including addition, subtraction, multiplication, and division. When dealing with addition, it's crucial to understand the nature of the numbers involved, whether they are positive or negative.

To add integers:
  • If both integers are positive, simply add their absolute values.
  • If both integers are negative, add their absolute values and then apply the negative sign to the result.
  • If one integer is positive and the other is negative, subtract the smaller absolute value from the larger absolute value. The result takes the sign of the number with the larger absolute value.
In our exercise, we added -9 and +8. Since one integer is negative and the other positive, we subtracted 8 from 9, resulting in -1, as -9 has the larger absolute value.
Positive and Negative Numbers
In arithmetic, numbers can be either positive or negative.
Positive numbers are greater than zero and typically represent gains or increases, while negative numbers are less than zero and often indicate losses or decreases.

When adding positive and negative numbers, think of it as combining gains and losses:
  • Adding a positive number to a negative number is like offsetting a loss with a gain. The result depends on which is greater, the gain or the loss.
  • Adding two negative numbers increases the overall loss, making the number more negative.
  • Adding two positive numbers increases the overall gain.
For instance, in the exercise -9 + (+8), the positive 8 attempts to offset some of the negative 9, leaving us with a final loss of -1.
Basic Arithmetic
Basic arithmetic refers to the fundamental operations of mathematics: addition, subtraction, multiplication, and division.
Addition is the process of combining two numbers to get their total sum.

Here are some key points about basic arithmetic:
  • Addition: Combining numbers by adding their values to find the total.
  • Subtraction: Finding the difference between two numbers by taking the second number away from the first.
  • Multiplication: Repeated addition of the same number. For example, 3 multiplied by 4 (3 脳 4) is the same as adding 3 four times (3 + 3 + 3 + 3).
  • Division: Splitting a number into equal parts or groups.
In our example, using addition: -9 + (+8) required understanding how to handle adding a positive number to a negative one. This step-by-step approach helps in mastering the basics of arithmetic concepts efficiently.

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Most popular questions from this chapter

At the beginning of the month Carla's checking account had a balance of \(\$ 643.47,\) while at the end of the month the balance was \(-\$ 82.94 .\) If she made no deposits during this month, what was the total of the checks that Carla wrote during this month?

Evaluate the given expression. Remember to follow the order of operations. $$30-5(4-2)$$

Graph the given set on a number line. \(\\{a | a \text { is a natural number less than } 12 \text { and not divisible by } 3\\}\)

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