Solve: 6 × 2 ÷ 3 Using Order of Operations

Q: Why don't I do division first since it comes after multiplication in PEMDAS?

Great question! In PEMDAS, multiplication and division have equal priority. The MD part means you do them together, working left to right. Same rule applies to addition and subtraction (AS).

Q: What if I accidentally did 2 ÷ 3 first and got a different answer?

If you calculated $ 2 \div 3 = 0.67... $ then $ 6 \times 0.67 = 4 $, you'd still get 4! But this longer method increases chances for errors. Always work left to right for cleaner calculations.

Q: How can I remember to go left to right with equal operations?

Think of it like reading a sentence - you read from left to right! When multiplication and division are together, treat them like words in a sentence and solve in the order you encounter them.

Q: What would happen if there were parentheses in this problem?

Parentheses always come first! If you had $ 6 \times (2 \div 3) $, you'd calculate inside the parentheses first: $ 2 \div 3 = 0.67... $, then multiply by 6.

Q: Is there a way to check my work without a calculator?

Yes! Work backwards: if your answer is 4, then $ 4 \times 3 = 12 $ and $ 12 \div 2 = 6 $. Since you get back to the original 6, your answer is correct!

Order of Operations with Mixed Operations

$6 \times 2 \div 3 =$

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Understand the problem

$6 \times 2 \div 3 =$

Step-by-step solution

To solve $6 \times 2 \div 3$ , you need to follow the order of operations: first perform the multiplication and then the division.

Step 1: Multiply 6 by 2: $6 \times 2 = 12$

Step 2: Divide the result by 3: $12 \div 3 = 4$

So, the answer is $4$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Multiplication and division have equal priority, work left to right
Technique: First calculate $6 \times 2 = 12$ , then $12 \div 3 = 4$
Check: Verify by following PEMDAS order: no parentheses or exponents, multiply then divide ✓

Common Mistakes

Avoid these frequent errors

Doing division before multiplication
Don't calculate 2 ÷ 3 first then multiply by 6 = 4 instead of the correct answer! Multiplication and division have equal priority, so you must work from left to right. Always follow the left-to-right rule when operations have the same priority level.

Practice Quiz

Test your knowledge with interactive questions

$8 + 3 \times 2 =$

FAQ

Everything you need to know about this question

Why don't I do division first since it comes after multiplication in PEMDAS?

Great question! In PEMDAS, multiplication and division have equal priority. The MD part means you do them together, working left to right. Same rule applies to addition and subtraction (AS).

What if I accidentally did 2 ÷ 3 first and got a different answer?

If you calculated $2 \div 3 = 0.67...$ then $6 \times 0.67 = 4$ , you'd still get 4! But this longer method increases chances for errors. Always work left to right for cleaner calculations.

How can I remember to go left to right with equal operations?

Think of it like reading a sentence - you read from left to right! When multiplication and division are together, treat them like words in a sentence and solve in the order you encounter them.

What would happen if there were parentheses in this problem?

Parentheses always come first! If you had $6 \times (2 \div 3)$ , you'd calculate inside the parentheses first: $2 \div 3 = 0.67...$ , then multiply by 6.

Is there a way to check my work without a calculator?

Yes! Work backwards: if your answer is 4, then $4 \times 3 = 12$ and $12 \div 2 = 6$ . Since you get back to the original 6, your answer is correct!

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