https://file.aiquickdraw.com/mathbot/file/1727074518007cmwrqnxe.jpg

The expression in the image is:

\[
6 \div 2(1+2)
\]

Let's break this down using the correct order of operations, often referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step 1: Solve inside the parentheses
First, calculate \(1 + 2\):

\[
6 \div 2(3)
\]

### Step 2: Deal with division and multiplication from left to right
Now, perform the division and multiplication. The expression becomes:

\[
6 \div 2 \times 3
\]

Since division and multiplication are performed from left to right:

\[
\frac{6}{2} = 3
\]

Then,

\[
3 \times 3 = 9
\]

So, the final result of the expression is:

\[
\boxed{9}
\]

Let me know if you'd like further clarification! Here are five related questions:

1. What would change if the parentheses were placed differently, such as \( 6 \div (2(1+2)) \)?
2. How does PEMDAS help in evaluating more complex expressions?
3. What happens if you change the division to multiplication in a similar expression?
4. How does left-to-right execution of multiplication and division impact the result?
5. What are other common mistakes people make when interpreting such expressions?

**Tip:** Always follow the order of operations carefully, especially when both division and multiplication are present in an expression!

Learn how to correctly solve the expression 6 ÷ 2(1 + 2) by applying the order of operations (PEMDAS). This detailed guide walks through solving step-by-step, starting with parentheses and moving through multiplication and division.

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