Problem 16 - Beginning and Intermediate Algebra

Question

Find each sum. $$ 11+(-8) $$

Step-by-Step Solution

Answer

3

Step 1: Identify the integers

First, identify the two numbers involved in the sum. In this case, they are 11 and -8.

Step 2: Understand the operation with negative numbers

Recognize that adding a negative number is the same as subtracting its absolute value. Therefore, adding -8 is the same as subtracting 8.

Step 3: Perform the subtraction

Subtract 8 from 11: \[ 11 - 8 = 3 \]

Step 4: Write down the result

The result of the sum is 3.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers that are less than zero. They are written with a minus sign (-) in front of them. For example, -8 is less than 0. Understanding negative numbers is essential for solving problems that involve addition and subtraction with these numbers.When dealing with negative numbers, it's helpful to visualize the number line:

• Numbers to the right are positive.
• Numbers to the left are negative.

By understanding where negative numbers are positioned on the number line, you can more easily perform arithmetic operations that involve them.

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. Absolute value is always a non-negative number. You can represent this with vertical bars, like so: \(|−8| = 8\).Absolute value helps simplify calculations, especially when dealing with negative numbers:

• The absolute value of \(11\) is \(11\).
• The absolute value of \(−8\) is \(8\).

In the context of adding and subtracting, understanding absolute values allows you to convert complicated negative numbers into simple positive ones for easy calculations. When you add \(11−8\), you simply recognize that you are finding the difference between the absolute values and considering the direction based on their signs.

Subtraction by Adding Negative Numbers

Subtraction can be thought of as the addition of a negative number. For instance, subtracting \(8\) from \(11\) is the same thing as adding \(−8\) to \(11\).Using the exercise example:

• The problem starts with \(11+(-8)\).
• Recognize that \(−8\) is a negative number; essentially, you need to subtract \(8\) from \(11\).
• Perform the subtraction: \(11−8\) to get \(3\).

Breaking it down into these steps makes it clear that negative numbers and subtraction are closely related concepts. This understanding helps simplify and solve similar problems.