Order of Operations Practice Problems | ChiliMath - Free Printable

The expression given is:

6 ÷ 2(1 + 2) = ?

We are to determine whether the answer is 9 or 1.

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Step-by-step Solution:

Let's evaluate this using the order of operations, commonly remembered by the acronym PEMDAS:

- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)

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Step 1: Evaluate inside the parentheses

$$
1 + 2 = 3
$$

So the expression becomes:

$$
6 ÷ 2(3) = ?
$$

Now we have:

$$
6 ÷ 2 \times 3
$$

Note: The expression $2(3)$ is equivalent to $2 \times 3$, so it's multiplication.

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Step 2: Perform division and multiplication from left to right

We now evaluate:

$$
6 ÷ 2 \times 3
$$

First, do 6 ÷ 2:

$$
6 ÷ 2 = 3
$$

Then multiply by 3:

$$
3 \times 3 = 9
$$

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Final Answer:

$$
\boxed{9}
$$

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Why not 1?

Some people might interpret $2(1+2)$ as a single unit (implied multiplication) that should be evaluated *before* division, thinking it's like:

$$
6 ÷ [2(3)] = 6 ÷ 6 = 1
$$

But according to standard mathematical convention, multiplication and division have equal precedence and are evaluated left to right. So:

$$
6 ÷ 2 \times 3 = (6 ÷ 2) \times 3 = 3 \times 3 = 9
$$

Unless there are explicit grouping symbols (like parentheses around the entire denominator), implied multiplication does not take precedence over division.

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Conclusion:

✔ Correct answer: 9

This is consistent with how most modern calculators and programming languages evaluate such expressions.

> Answer: 9 ✔