Problem 12 - Beginning and Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

-11

Step 1: Identify the Numbers

Identify the numbers involved in the sum: -9 and -2.

Step 2: Understanding the Operation

Both numbers are negative. When adding two negative numbers, you add their absolute values and keep the negative sign.

Step 3: Adding the Absolute Values

Add the absolute values of -9 and -2. The absolute value of -9 is 9 and the absolute value of -2 is 2. So, calculate 9 + 2.

Step 4: Apply the Negative Sign

Since both numbers are negative, the result will also be negative. So, the sum is -(9 + 2) which equals -11.

Key Concepts

absolute value

In mathematics, the absolute value of a number is its distance from zero on the number line, disregarding any negative sign. You can think of it as the 'magnitude' of the number.
For example:

• The absolute value of -9 is 9, because -9 is 9 units away from zero.
• The absolute value of 2 is 2, because 2 is 2 units away from zero.

When working with absolute values, it’s important to remember that: \[ |x| = \begin{cases} x & \text{if } x \geq 0 \ -x & \text{if } x < 0 \ \] This means you take the number itself if it’s positive or zero, and take the opposite if it’s negative.

negative numbers

Negative numbers are those that are less than zero and are typically denoted with a minus sign (-). They represent values less than nothing and are found to the left of zero on the number line.
Here's a quick overview:

• -9 is a negative number.
• -2 is also a negative number.
• Both are to the left of zero on the number line.

When you add two negative numbers, you are essentially combining their distances from zero and keeping the negative direction. For instance, knowing that -9 and -2 are both negative, you combine their absolute values (9 + 2) which equals 11, and then add the negative sign back to get -11. So, -9 + (-2) = -11.

basic arithmetic

Basic arithmetic refers to the most fundamental mathematical operations: addition, subtraction, multiplication, and division. When adding negative numbers, like in this exercise, it’s crucial to understand how these basic operations apply to them.
Here are the steps:

• Identify the numbers: We have -9 and -2.
• Understand the operation: Both numbers are negative.
• Add the absolute values: The absolute value of -9 is 9, and the absolute value of -2 is 2. Add these together: 9 + 2 = 11.
• Apply the negative sign: Because we are adding negative numbers, the result will be negative. Thus, -9 + (-2) equals -11.

Following these steps can simplify the process and make it easier to understand how to add negative numbers correctly.