Problem 111 - Algebra A Combined Function

Question

Subtract. $$ -11-(-4) $$

Step-by-Step Solution

Answer

-7

Step 1: Identify the Operation

The problem is \(-11 - (-4)\). This expression is a subtraction operation involving negative numbers. When you see a negative number being subtracted, it can be converted into an addition operation.

Step 2: Convert the Subtraction to Addition

According to the rule of subtracting negative numbers, \(-a - (-b) = -a + b\). Therefore, the given problem becomes:\[-11 - (-4) = -11 + 4\].

Step 3: Perform the Addition

The new expression is \(-11 + 4\). To solve this, think of starting at -11 on a number line and moving 4 units to the right (since you're adding a positive number).This results in:\[-11 + 4 = -7\].

Key Concepts

Integer Operations

Integer operations are the arithmetic procedures that involve whole numbers. Whole numbers can be positive, negative, or zero. When performing operations such as addition, subtraction, multiplication, and division involving integers, it is crucial to pay attention to their signs.
- **Addition**: The sum of two positive integers is positive, while two negative signs will also yield a negative result. - **Subtraction**: Often involves converting to addition by changing the sign of the second number. - **Multiplication and Division**: Two like signs (both positive or both negative) result in a positive, while two unlike signs result in a negative.
Subtracting integers can be tricky because the operation is not simply the opposite of addition. By understanding the basic rules associated with the signs, students can master integer operations more easily.

Number Line

The number line is a fundamental visual tool that helps us understand integer operations, including subtraction and addition. It is a straight horizontal line with numbers placed at even intervals along its length. Each number to the right of zero is a positive integer, and each number to the left is a negative integer.
When working on subtraction, particularly with negative numbers, the number line offers a clear way to visualize the process:

• To subtract a positive number, move left.
• To subtract a negative number, move right, as this converts the subtraction to addition.

By using the number line, students can effectively see the movement and better understand how the rules of integer operations work.

Converting Subtraction to Addition

Converting subtraction to addition is a crucial skill when working with integers, especially negatives. This conversion simplifies the process by following a simple rule: subtracting a number is equivalent to adding its opposite.
For example, in the exercise \[-11 - (-4)\]we can change the operation from subtraction to addition by changing the negative sign in front of \[-4\] to a positive. This alters the expression to:\[-11 + 4\]Effectively, this step turns a potentially confusing operation into a more straightforward one. The complexity of handling negative signs is reduced, aiding in the calculation. Students should remember this rule as it applies universally in integer arithmetic, making it a valuable tool in solving similar problems.