Problem 65 - Elementary and Intermediate Algebra

Question

Subtract. $$ 0-(-10) $$

Step-by-Step Solution

Answer

10

Step 1: Identify the Operation

Recognize that the operation involves subtracting a negative number. Here, we have to subtract \( -10 \) from \( 0 \).

Step 2: Apply the Rule for Subtracting Negatives

Use the rule that subtracting a negative number is the same as adding its positive counterpart. This means \( 0 - (-10) \) is equivalent to \( 0 + 10 \).

Step 3: Perform the Addition

Add the numbers. \( 0 + 10 = 10 \).

Key Concepts

operation identification

When solving mathematical problems, it's essential to first identify the operation required. This is especially true with operations involving negative numbers. In this exercise, the expression is
0 - (-10)
. Here, we need to subtract a negative number. This step may seem simple, but recognizing the specific operation can make solving the problem much easier. Misidentifying the operation can lead to mistakes. Therefore, always ensure you know whether you are adding, subtracting, multiplying, or dividing numbers.

rules for subtracting negatives

Subtracting negative numbers can be tricky, but there's a straightforward rule to remember: Subtracting a negative number is the same as adding the positive counterpart of that number. This rule can be summarized as follows:

• When you see a subtraction sign followed by a negative number, convert it to addition.
• This means changing the subtraction to addition and the negative number to its positive equivalent.

Let's apply this rule to our exercise:
The problem is
0 - (-10)
When using the rule, it becomes:
0 + 10. This step helps transform what seems complicated into a simpler addition problem.

integer addition

Now that we've converted our original problem using the rule for subtracting negatives, we just need to perform an addition involving integers. Adding integers involves combining their values. For our exercise, this means:
0 + 10
When you add zero to any number, the number remains unchanged. Thus, the result of our addition is simply:
10
This method of converting and then adding simplifies the process of dealing with operations involving negative numbers. Always follow the steps of identifying the operation, applying the rules for subtracting negatives, and then performing the integer addition.