Problem 56 - Elementary and Intermediate Algebra

Question

Subtract. $$ 6-(-6) $$

Step-by-Step Solution

Answer

12

Step 1: Understanding the Problem

Determine what needs to be solved. In this case, we are asked to subtract from 6.

Step 2: Apply the Rule for Subtraction of Negative Numbers

When subtracting a negative number, it is equivalent to adding the positive version of that number. Therefore, subtracting is equivalent to adding 6.

Step 3: Perform the Addition

Add the numbers: 6 + 6 = 12

Key Concepts

Subtraction

Subtraction is one of the four basic arithmetic operations. It involves taking one number away from another. For example, in our exercise, we have the expression \(6 - (-6)\). At first, this looks like a typical subtraction problem, but the presence of the negative sign changes things slightly. Here, the operation is not straightforward subtraction because we are asked to subtract a negative number. It is crucial to understand that subtracting a negative number transforms the operation.

Negative Numbers

Negative numbers are numbers less than zero and are represented with a minus sign (-). They can sometimes be confusing, especially when involving operations like subtraction. When you subtract a negative number, you are essentially performing a different operation: adding the absolute value of that number. For example, in our exercise \(6 - (-6)\), the subtraction of \(-6\) turns into an addition of \(6\). This is because the two negatives (the one in subtraction and the one indicating a negative number) cancel each other out. This concept can be summarized by the rule: subtracting a negative number is the same as adding its positive counterpart.

Addition

Addition is another fundamental arithmetic operation, often considered the opposite of subtraction. In our specific exercise, after understanding the rule that subtracting a negative number is akin to adding, the expression \(6 - (-6)\) converts to \(6 + 6\). When you perform the addition: \(6 + 6\), you get \(12\). So, our final answer is \(12\). To see why this works, consider that subtracting negatives swaps back to positive, making the arithmetic simpler to grasp.