Problem 66 - Algebra 1

Question

Find the sum. $$-9+11$$

Step-by-Step Solution

Answer

The sum of \( -9 \) and \( 11 \) is \( 2 \).

Step 1: Understand Integer Addition

To add integers, if they are both positive, we just add them as usual. However, if one integer is negative (like in this case), it means the number is being subtracted from the other one. So, \( -9 + 11 \) will actually mean that \( 9 \) is being subtracted from \( 11 \).

Step 2: Perform the Operation

Now, we perform the operation. \( 11 - 9 \) gives us a result of \( 2 \).

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are often used to represent deficits, debts, or temperatures below freezing.
Unlike positive numbers, negative numbers have a minus sign (-) in front of them. When visualizing numbers on a number line, negative numbers are to the left of zero. It's important to understand that the value of a negative number decreases as it moves away from zero. For instance,

• -1 is greater than -2,
• -2 is greater than -3,
• and so on.

When dealing with negative numbers in everyday situations, such as temperature or bank balances, they indicate a 'below zero' state. Being comfortable with negative numbers is crucial, not just in mathematics, but also in real-world applications.

Addition Rules

When adding numbers, there are a few simple rules to follow which make the process easier.

• When both numbers are positive, add them as usual.
• When both numbers are negative, add the absolute values and keep the negative sign.
• When one number is positive and one is negative, subtract the smaller absolute value from the larger one, and keep the sign of the number with the larger absolute value.

Let's look at the given exercise. For \(-9 + 11\):

• Identify the larger absolute value: 11.
• Subtract the absolute values: 11 - 9 = 2.
• Since 11 has a larger absolute value and is positive, the result is positive 2.

Understanding these rules can simplify handling everyday arithmetic tasks.

Basic Arithmetic Operations

Basic arithmetic operations lay the foundation for mathematics. These operations include addition, subtraction, multiplication, and division. Let's focus on addition and subtraction, as they are most relevant to the exercise. When adding numbers, you're essentially increasing the value. When subtracting, you are reducing the value of one number by the value of another. In a situation like \(-9 + 11\), we can reframe it as a subtraction question: \(11 - 9\). This is because adding a negative number is equivalent to subtracting the positive version of that number.

• Addition leads to a positive movement on the number line.
• Subtraction leads to a negative movement.

Grasping these basic operations helps in understanding the broader field of mathematics and in solving more complex problems.