Problem 77 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. $$ (4-6)+12 $$

Step-by-Step Solution

Answer

10

Step 1: Perform the subtraction inside the parentheses

First, solve the expression inside the parentheses. Calculate the result of (4 - 6).So we have:4 - 6 = -2

Step 2: Add the result to 12

Now take the result from Step 1, which is -2, and add it to 12:-2 + 12 = 10

Key Concepts

Understanding Addition

Addition is one of the fundamental operations in arithmetic. It involves combining two or more numbers to get a total sum. The numbers you add together are called addends, and the result is known as the sum.

For example, in the original exercise: \(-2 + 12 = 10\). Here, -2 and 12 are the addends, and 10 is the sum. Addition is a straightforward operation when you carefully align the numbers and operate on them. When adding positive numbers to negative numbers, you are essentially subtracting the absolute value of the negative number from the positive number.

Mastering Subtraction

Subtraction is another core arithmetic operation. It involves taking one number away from another. The first number is called the minuend, and the second number is the subtrahend. The result is the difference.

In our example, we had to perform the subtraction \(4 - 6\). Here, 4 is the minuend and 6 is the subtrahend, giving us a result of -2, which is the difference. Notice that when you subtract a larger number from a smaller one, you get a negative result.

Following the Order of Operations

The order of operations is a set of rules used to ensure that arithmetic calculations are performed correctly and consistently. The acronym PEMDAS can help you remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

In the given exercise, we first addressed the operation inside the parentheses: \(4 - 6\). After simplifying this to -2, we then moved to the next step, which involved an addition: \(-2 + 12\). By following these steps, we ensure accuracy in our calculations.

Always remember to solve expressions inside parentheses first before moving on to other operations.