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Chapter 1: Problem 22

In Exercises \(1-72\), compute the value of each expression. $$-4+(-9)$$

Short Answer

Expert verified
The value of the expression is \(-13\).

Step by step solution

01

Identify the terms in the expression

The given expression is \(-4 + (-9)\). Identify the two terms: \(-4\) and \(-9\).
02

Understand the addition of negative numbers

When adding two negative numbers, the result is also a negative number. The absolute values of the numbers are added, and the sign is kept negative.
03

Add the absolute values

Add the absolute values of the two terms: \(4 + 9\) which gives \(13\).
04

Apply the negative sign

Since both terms were negative, the result is also negative. Therefore, the value of the expression is \(-13\).

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Key Concepts

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

negative numbers
Negative numbers are numbers less than zero and are typically represented with a minus sign (-) in front of them. Understanding negative numbers is crucial because they play a vital role in various mathematical concepts and real-life situations like temperature measurements, debts, and more.

Here are some key points to understand about negative numbers:
  • Negative numbers are to the left of 0 on a number line.
  • When adding a negative number, you move to the left on the number line.
  • When subtracting a negative number, you move to the right on the number line because subtracting a negative amount is like adding a positive amount.
With these ideas, you'll be better equipped to handle operations involving negative numbers, including addition, subtraction, multiplication, and division.
absolute value
Absolute value refers to the distance of a number from zero on the number line, regardless of direction. Therefore, the absolute value is always a non-negative number. It is denoted by two vertical bars, for example, \(|-4|\).\br>
Some important points about absolute value include:
  • \(| -4 |= 4\) because -4 is four units away from 0.
  • \(| 9 |= 9\) because 9 is nine units away from 0.
  • Absolute value is used to determine the magnitude of a number without considering its sign, which is useful in various mathematical calculations.
In the exercise, the absolute values of -4 and -9 are 4 and 9 respectively. Adding these gives us 13, which is the magnitude we need for the final answer.
arithmetic operations
Arithmetic operations are basic math operations that include addition, subtraction, multiplication, and division. They are fundamental operations used in almost every aspect of mathematics.

Let's discuss the addition of negative numbers explicitly:
  • When you add two negative numbers, you add their absolute values and then place a negative sign in front of the result. For instance, \(-4 + (-9)\) becomes \(|-4| + |-9| = 4 + 9 = 13\), and we place a negative sign to get \-13\.
  • Essentially, adding negative numbers involves counting 'backwards' or increasing the 'debt.'
This rule helps simplify the task by allowing you to focus on just the magnitude first. Then, apply the negative sign to the result to complete the operation correctly. Understanding these rules makes problems involving negative numbers easier to manage.

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