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Chapter 1: Problem 12

Find each sum. $$ -9+(-2) $$

Short Answer

Expert verified
The sum is \( -11 \).

Step by step solution

01

Understand the Problem

The task is to find the sum of two negative integers, \( -9 \) and \( -2 \).
02

Add the Integers

When adding two negative numbers, keep the negative sign and add their absolute values. Calculate \( 9 + 2 = 11 \).
03

Apply the Negative Sign

Since both integers are negative, the result will also be negative. Therefore, the sum is \( -11 \).

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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 values less than zero. Think of them as being to the left of zero on a number line.
For example, numbers like -1, -5, and -9 are all negative numbers.
When dealing with negative numbers, it's important to understand the following:
  • When you add negative numbers, you are essentially moving further to the left on the number line.
  • Negative numbers are written with a minus sign (-) before them.
  • The more negative a number, the smaller its value. For instance, -9 is smaller than -3.

Knowing how to handle negative numbers will help when you perform operations like addition, subtraction, multiplication, and division.
Next, let鈥檚 understand the concept of absolute value, which is essential for adding negative numbers.
absolute value
The absolute value of a number is its distance from zero on the number line, regardless of direction.
In mathematical terms, the absolute value of a number is always a positive number, or zero.
It's denoted by two vertical bars around the number, like this: \(|x|\rightarrow Positive \ or \ Zero\).
For example:
  • The absolute value of -9 is \(|-9| = 9\).
  • The absolute value of 5 is \(|5| = 5\).

Why is absolute value important?
  • It helps us understand the

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Most popular questions from this chapter

The two tables show the heights of some selected mountains and the depths of some selected trenches. Use the information given to answer. \( \)\begin{array}{|l|c|}\hline \text { Mountain } & {\text { Height (in feet) }} \\\ {\text { Foraker }} & {17,400} \\ {\text { Wilson }} & {14,246} \\\ {\text { Pikes Peak }} & {14,110} \\ \hline\end{array} $$ \begin{array}{|l|c|}\hline\text {} & {\text { Depth }( \text { in feet } } \\ {\text { Trench }} & {\text { as a negative number }} \\ {\text { Philippine }} & {-32,995} \\ {\text { Cayman }} & {-24,721} \\ {\text { Java }} & {-23,376} \\ \hline \end{array} $$ How much higher is Mt. Wilson than Pikes Peak?

Find each difference. $$ -3-(4-11) $$

Perform each indicated operation. $$ -7.6247-[(-3.9928+1.42773)-(-2.80981)] $$

Perform each indicated operation. $$ -9+[(3-2)-(-4+2)] $$

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. See Example \(9 .\) 7 less than a number is 2
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