Problem 62 - Beginning and Intermediate Algebra

Question

Find each difference. $$ 9-(-2) $$

Step-by-Step Solution

Answer

The difference is 11.

Step 1: Understand the Problem

The exercise requires finding the difference between the numbers 9 and -2. This involves the operation of subtracting a negative number.

Step 2: Rewrite the Expression

Subtracting a negative number is the same as adding its positive counterpart. Therefore, we rewrite the expression as: \( 9 - (-2) = 9 + 2 \)

Step 3: Perform the Addition

Now, simply add the two numbers: \( 9 + 2 = 11 \)

Step 4: State the Result

The result of the expression \( 9 - (-2) \) is 11.

Key Concepts

algebra subtraction

In algebra, subtraction operates under specific rules, especially when involving negative numbers. We often see problems like 9 - (-2), which may look tricky at first. To solve these, the key is to understand that subtracting a negative number is equivalent to adding its positive counterpart. When we change the subtraction of a negative number to addition, it simplifies the process.

For example, consider the expression 9 - (-2). Subtracting -2 is the same as adding 2. This changes it to 9 + 2. The fundamentals of algebra subtraction hold this transformation as a core principle, making it easier to work with equations involving negative numbers.

basic arithmetic

Basic arithmetic, the foundation of mathematics, includes operations like addition, subtraction, multiplication, and division. A common confusion arises when these operations involve negative numbers. Subtracting a negative number is an important concept.

In the expression given, 9 - (-2), we use basic arithmetic rules: changing the subtraction of a negative to addition. This is crucial for correctly solving arithmetic problems.

Let's look at it step-by-step:

• Rewrite the subtraction: 9 - (-2) becomes 9 + 2.
• Then, perform the simple addition: 9 + 2 = 11.

Understanding these steps is essential for mastering arithmetic operations.

negative numbers

Negative numbers are numbers less than zero, commonly represented with a minus sign (-). Adding and subtracting them follow particular rules which can initially feel non-intuitive.

For instance, when subtracting a negative number, you are essentially adding its positive counterpart. With 9 - (-2), the two negative signs (one from subtraction and one from the negative number) combine to form a positive, making it 9 + 2. This rule arises because the operation 'subtracting a negative' negates the minus, similar to how removing a debt increases your total.

For clarity:

• Start with identifying the operation: subtraction of a negative.
• Convert it: subtracting -2 is adding 2.
• Finally, add: 9 + 2 = 11.

Grasping these rules helps handle negative numbers confidently in complex equations.