Solve the Operation Sequence: 6 × 3 ÷ 2 × 1 Using PEMDAS

Q: Why don't I do all the multiplications first?

Multiplication and division have equal priority in PEMDAS! When operations have the same level, you must work from left to right, not group them by type.

Q: What if I get a different answer working right to left?

That's exactly why order matters! Working $ 6 \times 3 ÷ 2 \times 1 $ right-to-left would give you a wrong answer. Always follow the left-to-right rule for equal operations.

Q: Is multiplying by 1 really necessary?

Yes! Even though $ 9 \times 1 = 9 $, you should still perform this step to follow the complete sequence and avoid mistakes in more complex problems.

Q: How can I remember to work left to right?

Think of reading: you read from left to rightUse your finger to point to each operation as you workWrite out each step: 6 × 3 = 18, then 18 ÷ 2 = 9, then 9 × 1 = 9

Q: What would happen if I did division first?

If you calculated $ 3 ÷ 2 = 1.5 $ first, then $ 6 \times 1.5 \times 1 = 9 $, you'd get the right answer by luck! But this wrong method fails in other problems, so always work left to right.

Order of Operations with Multiple Mixed Operations

$6 \times 3 \div 2 \times 1 =$

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Understand the problem

$6 \times 3 \div 2 \times 1 =$

Step-by-step solution

Start by performing the multiplication and division from left to right according to the order of operations.

First, calculate the multiplication: $6 \times 3 = 18$

Next, divide the result by 2: $18 \div 2 = 9$

Finally, multiply by 1: $9 \times 1 = 9$

Thus, the correct answer is $9$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Perform multiplication and division from left to right
Technique: Calculate step by step: 6 × 3 = 18, then 18 ÷ 2 = 9
Check: Work through each operation in sequence: 6 × 3 ÷ 2 × 1 = 9 ✓

Common Mistakes

Avoid these frequent errors

Doing all multiplications first, then all divisions
Don't calculate 6 × 3 × 1 = 18, then 18 ÷ 2 = 9! This ignores the left-to-right rule and can give wrong answers in other problems. Always work multiplication and division from left to right in the order they appear.

Practice Quiz

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$3 + 4 \times 2 =$

FAQ

Everything you need to know about this question

Why don't I do all the multiplications first?

Multiplication and division have equal priority in PEMDAS! When operations have the same level, you must work from left to right, not group them by type.

What if I get a different answer working right to left?

That's exactly why order matters! Working $6 \times 3 ÷ 2 \times 1$ right-to-left would give you a wrong answer. Always follow the left-to-right rule for equal operations.

Is multiplying by 1 really necessary?

Yes! Even though $9 \times 1 = 9$ , you should still perform this step to follow the complete sequence and avoid mistakes in more complex problems.

How can I remember to work left to right?

Think of reading: you read from left to right
Use your finger to point to each operation as you work
Write out each step: 6 × 3 = 18, then 18 ÷ 2 = 9, then 9 × 1 = 9

What would happen if I did division first?

If you calculated $3 ÷ 2 = 1.5$ first, then $6 \times 1.5 \times 1 = 9$ , you'd get the right answer by luck! But this wrong method fails in other problems, so always work left to right.

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