3 + 3 × 3 + 3: Understanding the Order of Operations
Have you ever come across an expression like 3 + 3 × 3 + 3 and wondered what the correct answer is? The key to solving this problem lies in understanding the order of operations.
The Order of Operations
In mathematics, the order of operations is a set of rules that dictates the order in which we perform mathematical operations when more than one operation is present in an expression. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponents or powers next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Solving the Expression
Now, let's apply the order of operations to our expression: 3 + 3 × 3 + 3.
Step 1: Evaluate the Multiplication
First, we need to evaluate the multiplication operation: 3 × 3 = 9.
So, our expression becomes: 3 + 9 + 3.
Step 2: Evaluate the Addition and Subtraction
Next, we evaluate the addition and subtraction operations from left to right: 3 + 9 = 12, and then 12 + 3 = 15.
The Final Answer
Therefore, the correct answer is: 3 + 3 × 3 + 3 = 15.
By following the order of operations, we can ensure that we are evaluating expressions correctly and avoiding any potential pitfalls. Remember, when in doubt, always follow PEMDAS!
