Problem 24 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ (18-12) \div 2+1 $$

Step-by-Step Solution

Answer

4

Step 1 - Calculate Inside the Parentheses

First, evaluate the expression inside the parentheses: \( (18 - 12) \) This simplifies to: \( 6 \)

Step 2 - Division

Next, divide the result from step 1 by 2: \( 6 \div 2 \) This simplifies to: \( 3 \)

Step 3 - Addition

Finally, add 1 to the result from step 2: \( 3 + 1 \) This simplifies to: \( 4 \)

Key Concepts

Parentheses

When working with algebraic expressions, understanding parentheses is crucial. Parentheses help group parts of the expression that should be calculated first. In our given problem, we start with: \((18 - 12) \div 2 + 1\).
According to the order of operations, remember the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Parentheses always come first. So, we calculate the expression inside the parentheses: \(18-12\), which simplifies to \(6\). Now our expression looks like this: \(6 \div 2 + 1\).

Division

Division is among the next steps in the order of operations. After parentheses, we move on to any multiplication or division from left to right. In our simplified expression from the previous section, we have: \(6 \div 2 + 1\).
Now we need to perform the division operation. Dividing 6 by 2 gives us \(3\).
So, the expression becomes: \(3 + 1\). Remember, always handle multiplication and division before moving on to addition and subtraction.

Addition

The final step involves addition. Now that we have simplified the expression to \(3 + 1\), we proceed with the addition operation.
Adding 3 and 1 gives us the final value of \(4\).
To summarize, we carefully followed the order of operations: first handling the parentheses, then performing the division, and finally completing the task with addition. This approach ensures that we arrive at the correct answer: \(4\).