To solve the expression \(4 + 9 - 6 \div 2 \times 3\), we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). First, perform the division and multiplication from left to right, then proceed with addition and subtraction.
Step 1: Evaluate Division and Multiplication
First, we perform the division and multiplication in the expression \(4 + 9 - 6 \div 2 \times 3\).
Calculating \(6 \div 2\) gives \(3\), and then multiplying by \(3\) results in \(3 \times 3 = 9\).
Step 2: Substitute and Simplify
Now, substitute back into the expression:
\[
4 + 9 - 9
\]
Step 3: Perform Addition and Subtraction
Next, we perform the addition and subtraction from left to right:
\[
4 + 9 = 13
\]
Then,
\[
13 - 9 = 4
\]