Problem 60 - Elementary Algebra

Question

Perform the operations. $$ 0-(-8)-12 $$

Step-by-Step Solution

Answer

-4

Step 1: Understanding the Problem

We need to evaluate the expression \( 0 - (-8) - 12 \). This expression involves the subtraction of integers, where one of them is negative.

Step 2: Simplifying the Double Negative

The first operation is to simplify \( 0 - (-8) \). A double negative turns into a positive, so \( 0 - (-8) \) becomes \( 0 + 8 \).

Step 3: Evaluate First Operation

Now, evaluate \( 0 + 8 \). This simplifies to \( 8 \).

Step 4: Subtract 12 from the Result

The next step is to perform the subtraction \( 8 - 12 \). Calculate the result by understanding that subtracting a larger number from a smaller one results in a negative number.

Step 5: Find the Final Answer

The result of \( 8 - 12 \) is \( -4 \). This is the final result of the operations.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are represented by a minus sign in front of the number, such as

• -1
• -5
• -12

Understanding negative numbers is crucial because they appear frequently in various mathematical contexts, especially when dealing with subtraction and addition operations. In the context of an integer number line, negative numbers lie to the left of zero.
When performing operations with negative numbers, it's important to remember how they interact with positive numbers. For instance, adding a negative number is the same as subtracting its absolute value from a positive number.

Double Negatives

One of the interesting aspects of mathematics is the concept of 'double negatives'. This concept is used in solving problems where you encounter two negatives consecutively. In most cases, these double negatives will transform into a positive number. In the given problem, you encounter an expression like this:

• 0 - (-8)

This setup involves a double negative. The subtraction of

• -8 is indeed the same as adding 8, resulting in 0 + 8.

Simplifying with double negatives can often make seemingly complex calculations much simpler. Always remember, two negatives make a positive.
This rule is applicable in a variety of mathematical operations and can simplify equations or expressions that might otherwise look intimidating.

Order of Operations

When solving mathematical problems, the order of operations is crucial to ensure that you perform calculations correctly. The order in which operations are performed can drastically change the outcome.
An easy way to remember the sequence of operations is the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication and Division
• Addition and Subtraction

For the exercise in question, the operations inside parentheses would be handled first if they existed. However, here we deal directly with addition and subtraction from left to right.
This means you would first resolve the subtraction involving the double negative (making it an addition) before moving on to any other subtraction or addition in the expression. This orderly approach helps in simplifying problems systematically and arriving at the correct answer.