Problem 19 - Elementary Algebra

Question

For exercises 15-100, evaluate. $$ -2+(-3) $$

Step-by-Step Solution

Answer

-5

Step 1: Understand the Problem

This exercise requires evaluating the sum of two negative numbers: \(-2\) and \(-3\).

Step 2: Combining Negative Numbers

When adding two negative numbers, combine their absolute values and keep the negative sign. Here, the absolute values are 2 and 3.

Step 3: Perform the Addition

Add the absolute values: \[ 2 + 3 = 5 \]Then attach the negative sign to the result.

Step 4: Write the Final Answer

The final answer is \[ -2 + (-3) = -5 \]

Key Concepts

Negative Numbers Addition

Adding negative numbers can be tricky but becomes easier with some practice. When you add two negative numbers, you essentially combine their magnitudes (absolute values) and keep the negative sign. This is because negative numbers represent values below zero.
For example, consider \(-2 + (-3)\). Here’s how you do it:

• Identify the absolute values, which are 2 and 3
• Add those values together: 2 + 3 = 5
• Since both original numbers are negative, the result will also be negative

Thus, \(-2 + (-3) = -5\).
This method makes addition of negative numbers straightforward and intuitive. Remember, the absolute value helps simplify the process.

Absolute Value

Understanding absolute value is crucial when working with negative numbers. The absolute value of a number is its distance from zero on the number line, regardless of direction.
For example:

• The absolute value of \(-2\) is 2.
• The absolute value of \(-3\) is 3.

Absolute value essentially removes the negative sign, showing us the 'size' of the number. It is always a positive number or zero. Mathematically, the absolute value of a number \( a \) is denoted as \(|a|\). For \(-2 + (-3)\), the process involves using these absolute values before applying the negative sign to the result.

Arithmetic Operations

Arithmetic operations like addition and subtraction form the foundation of math. When working with negative numbers, it’s essential to follow specific rules to get accurate results.
For our example \(-2 + (-3)\):

• First, recognize both numbers are negative
• Add their absolute values: 2 + 3 = 5
• Since original numbers were negative, the result stays negative.

This approach is not only useful for addition but also applies to subtraction involving negative numbers. For instance, subtracting a negative number is like adding its positive counterpart. Understanding these basic principles makes handling negative numbers straightforward and helps avoid errors.