Question

Evaluate each expression. \(3+3 \cdot 2+2\)

Short answer

11

Step-by-step solution

Identify the Order of Operations

First, identify the order of operations needed to solve the expression. According to PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), we need to perform multiplication before addition.

Perform Multiplication

Next, perform the multiplication: \(3 + 3 \times 2 + 2\). Multiply 3 and 2 to get 6, so the expression becomes: \(3 + 6 + 2\).

Perform Addition

Finally, perform the addition from left to right. First, add 3 and 6 to get 9. Then, add 9 and 2 to get 11. Therefore, \(3 + 6 + 2 = 11\).

Key concepts

PEMDAS

To solve any mathematical expression, it's essential to follow a specific order of operations known as PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This order ensures that everyone solves the expression the same way and gets the correct result.

• Parentheses: Perform operations inside parentheses first.
• Exponents: Next, handle exponents (powers and roots).
• Multiplication and Division: These operations come next and are done from left to right.
• Addition and Subtraction: Finally, perform addition and subtraction from left to right.

In the expression given in the exercise, you don't have parentheses or exponents. Therefore, we start directly with multiplication, followed by addition, in the correct order.

Multiplication

Multiplication is a fundamental arithmetic operation that combines groups of equal sizes. In the context of the exercise, following PEMDAS, we first need to spot the multiplication operation in the expression. In the expression \(3 + 3 \times 2 + 2\), the multiplication part is \(3 \times 2\).

Performing this operation, we get: \[3 \times 2 = 6.\]. So, the expression now transforms to \[3 + 6 + 2\]. Multiplication must always be tackled before any addition or subtraction.

Addition

Addition is the process of finding the total or sum by combining two or more numbers. After handling multiplication in our given expression, the updated expression is now \[3 + 6 + 2\].

According to the PEMDAS rule, addition comes after multiplication and division and must be performed from left to right.

• First step: Add 3 and 6 to get 9.
• Second step: Then, add 9 and 2 to get 11.

The final result of the expression is therefore 11. Always ensure to follow the left-to-right order when performing addition and subtraction.