Solve Mixed Operations: 9 - 3 + 6 ÷ 2 Using Order of Operations

Q: Why can't I just work from left to right like reading?

Mathematics has a special order called PEMDAS (or BODMAS). Division and multiplication are stronger operations that must be done first, even if they appear later in the expression.

Q: What if there were parentheses in this problem?

Parentheses would come first in PEMDAS! For example, if we had $ (9 - 3) + 6 \div 2 $, we'd calculate 9 - 3 = 6 first, then the division.

Q: How can I remember to do division first?

Think of division and multiplication as grouping operations - they're stronger than addition and subtraction. Always scan the expression for ×, ÷, *, / symbols and do those first!

Q: What if I get a different answer?

Double-check your work step by step! Write out: $ 9 - 3 + 6 \div 2 = 9 - 3 + 3 = 6 + 3 = 9 $. If you got 6 or 12, you likely worked left to right incorrectly.

Order of Operations with Mixed Arithmetic

$9 - 3 + 6 \div 2 =$

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Understand the problem

$9 - 3 + 6 \div 2 =$

Step-by-step solution

1. Follow the order of operations (PEMDAS/BODMAS).

2. First do the division: $6 \div 2 = 3$ .

3. Then, perform the addition/subtraction from left to right: $9 - 3 = 6$ , then $6 + 3 = 9$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Division comes before addition and subtraction operations
Technique: First calculate $6 \div 2 = 3$ , then work left to right
Check: Verify each step: 9 - 3 + 3 = 6 + 3 = 9 ✓

Common Mistakes

Avoid these frequent errors

Working strictly from left to right without considering operation priority
Don't calculate 9 - 3 = 6 first, then 6 + 6 ÷ 2 = wrong answer! This ignores division priority and gives 9 instead of the correct answer. Always do division before addition and subtraction, regardless of position.

Practice Quiz

Test your knowledge with interactive questions

$8 + 3 \times 2 =$

FAQ

Everything you need to know about this question

Why can't I just work from left to right like reading?

Mathematics has a special order called PEMDAS (or BODMAS). Division and multiplication are stronger operations that must be done first, even if they appear later in the expression.

What does PEMDAS stand for again?

Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Remember: multiplication and division have equal priority!

What if there were parentheses in this problem?

Parentheses would come first in PEMDAS! For example, if we had $(9 - 3) + 6 \div 2$ , we'd calculate 9 - 3 = 6 first, then the division.

How can I remember to do division first?

Think of division and multiplication as grouping operations - they're stronger than addition and subtraction. Always scan the expression for ×, ÷, *, / symbols and do those first!

What if I get a different answer?

Double-check your work step by step! Write out: $9 - 3 + 6 \div 2 = 9 - 3 + 3 = 6 + 3 = 9$ . If you got 6 or 12, you likely worked left to right incorrectly.

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