Order of Operations Practice Questions with Answers - Complete Guide for Grade 3 Students

Learn the order of operations with detailed practice questions and comprehensive answers.

Practice Questions 1 to 3
1 Addition and subtraction
Question 1
Solve: 12 + 5 - 3. What is the answer? Show your work.
Definition:

Order of operations: The rules that determine the sequence in which operations should be performed in a mathematical expression.

Order of operations method:
  1. Perform operations from left to right when they are the same level
  2. For addition and subtraction, work left to right
  3. Calculate each operation step by step
  4. Write down intermediate results
Original expression
12 + 5 - 3
Step 1
12 + 5 = 17
Step 2
17 - 3 = 14
Step 1: Perform addition first (left to right)

12 + 5 = 17

Step 2: Perform subtraction next

17 - 3 = 14

Step 3: Write the final answer

12 + 5 - 3 = 14

12 + 5 - 3 = 14
Answer:

The answer is 14. Work from left to right: 12 + 5 = 17, then 17 - 3 = 14.

Applied rules:

• Left to right: For addition and subtraction at the same level

• Same precedence: Addition and subtraction have equal priority

• Sequential calculation: Perform operations one at a time

2 Multiplication and division
Question 2
Solve: 24 ÷ 4 × 2. What is the answer? Show your work.
Definition:

Multiplication and division: Operations with equal precedence that are performed from left to right.

Original expression
24 ÷ 4 × 2
Step 1
24 ÷ 4 = 6
Step 2
6 × 2 = 12
Step 1: Perform division first (left to right)

24 ÷ 4 = 6

Step 2: Perform multiplication next

6 × 2 = 12

Step 3: Write the final answer

24 ÷ 4 × 2 = 12

24 ÷ 4 × 2 = 12
Answer:

The answer is 12. Work from left to right: 24 ÷ 4 = 6, then 6 × 2 = 12.

Applied rules:

• Left to right: For multiplication and division at the same level

• Same precedence: Multiplication and division have equal priority

• Sequential calculation: Perform operations one at a time

3 Mixed operations
Question 3
Solve: 15 + 6 ÷ 2 - 4. What is the answer? Show your work.
Definition:

Mixed operations: Expressions containing different types of operations with different precedence levels.

Original expression
15 + 6 ÷ 2 - 4
Step 1
6 ÷ 2 = 3
Step 2
15 + 3 - 4
Step 3
18 - 4 = 14
Step 1: Perform division first (higher precedence)

6 ÷ 2 = 3

Step 2: Rewrite the expression with the result

15 + 3 - 4

Step 3: Perform addition and subtraction from left to right

15 + 3 = 18, then 18 - 4 = 14

Step 4: Write the final answer

15 + 6 ÷ 2 - 4 = 14

15 + 6 ÷ 2 - 4 = 14
Answer:

The answer is 14. Division comes first: 6 ÷ 2 = 3, then left to right: 15 + 3 = 18, then 18 - 4 = 14.

Applied rules:

• Division precedence: Division is performed before addition and subtraction

• Left to right: For operations at the same level

• Sequential calculation: Work through the problem step by step

Practice Questions 4 to 5
2 × (3 + 4) = 2 × 7 = 14
Parentheses Example
Level 1
Parentheses
Do first
Level 2
Multiplication/Division
Left to right
Level 3
Addition/Subtraction
Left to right
Key definitions:

Order of operations: The sequence in which mathematical operations should be performed: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

PEMDAS: A memory device: Please Excuse My Dear Aunt Sally (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

Precedence: The priority level of different operations in mathematical expressions.

Left to right: The direction in which operations of equal precedence are performed.

Intermediate results: Temporary answers calculated during multi-step problems.

Sequential calculation: Performing operations one at a time in the correct order.

Complete order of operations methodology:
  1. Identify all operations: Look for parentheses, exponents, multiplication, division, addition, subtraction
  2. Follow precedence rules: Perform operations in order of priority
  3. Handle equal precedence: For operations at the same level, work from left to right
  4. Calculate step by step: Perform one operation at a time
  5. Write intermediate results: Keep track of partial answers
  6. Complete the calculation: Continue until you have a final answer
Tip 1: Always look for parentheses first - they come before everything else.
Tip 2: Multiplication and division have equal precedence - work left to right.
Tip 3: Addition and subtraction have equal precedence - work left to right.
Tip 4: Write down each step to avoid mistakes.
Common errors: Performing operations in the wrong order, forgetting left-to-right rule for equal precedence, not following precedence rules.
Benefits: Consistent results, standardized approach, prevents calculation errors.
Order of operations rules to know:

• Parentheses first: Calculate expressions inside parentheses before anything else

• Multiplication/Division: Perform these operations before addition/subtraction

• Left to right: For operations of equal precedence, work from left to right

• Sequential calculation: Perform one operation at a time

Additional Practice Questions
4 Parentheses included
Question 4
Solve: (8 + 4) ÷ 2 × 3. What is the answer? Show your work.
Definition:

Parentheses: Indicate that operations inside should be performed first, before any other operations.

Original expression
(8 + 4) ÷ 2 × 3
Step 1
8 + 4 = 12
Step 2
12 ÷ 2 = 6
Step 3
6 × 3 = 18
Step 1: Perform operations inside parentheses first

8 + 4 = 12

Step 2: Rewrite the expression

12 ÷ 2 × 3

Step 3: Perform division and multiplication from left to right

12 ÷ 2 = 6, then 6 × 3 = 18

Step 4: Write the final answer

(8 + 4) ÷ 2 × 3 = 18

(8 + 4) ÷ 2 × 3 = 18
Answer:

The answer is 18. Parentheses first: 8 + 4 = 12, then left to right: 12 ÷ 2 = 6, then 6 × 3 = 18.

Applied rules:

• Parentheses first: Always calculate inside parentheses before other operations

• Left to right: For multiplication and division at the same level

• Sequential calculation: Perform operations one at a time

5 Complex mixed operations
Question 5
Solve: 20 - 2 × 3 + 8 ÷ 4. What is the answer? Show your work.
Definition:

Complex mixed operations: Expressions containing multiple operations of different precedence levels that must be evaluated in the correct order.

Original expression
20 - 2 × 3 + 8 ÷ 4
Step 1
2 × 3 = 6
Step 2
8 ÷ 4 = 2
Step 3
20 - 6 + 2
Step 4
14 + 2 = 16
Step 1: Perform multiplication and division first (highest precedence)

2 × 3 = 6 and 8 ÷ 4 = 2

Step 2: Rewrite the expression with results

20 - 6 + 2

Step 3: Perform addition and subtraction from left to right

20 - 6 = 14, then 14 + 2 = 16

Step 4: Write the final answer

20 - 2 × 3 + 8 ÷ 4 = 16

20 - 2 × 3 + 8 ÷ 4 = 16
Answer:

The answer is 16. First, 2 × 3 = 6 and 8 ÷ 4 = 2, then 20 - 6 + 2 = 14 + 2 = 16.

Applied rules:

• Higher precedence first: Multiplication and division before addition and subtraction

• Left to right: For operations at the same level

• Sequential calculation: Work through the problem step by step

Complete Summary: Order of Operations Practice
PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
Order of Operations Rule
Comprehensive definitions:

Order of operations: A set of rules that determines the sequence in which mathematical operations should be performed in an expression to ensure consistent results.

PEMDAS: A memory device for remembering the order: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Precedence: The priority level of different operations in mathematical expressions.

Left to right rule: When operations have equal precedence, they are performed in the order they appear from left to right.

Intermediate results: Temporary answers calculated during multi-step problems that lead to the final answer.

Sequential calculation: Performing operations one at a time in the correct order.

Expression evaluation: The process of calculating the value of a mathematical expression following order of operations rules.

Complete order of operations methodology:
  1. Scan the expression: Identify all operations and their types
  2. Check for parentheses: Calculate expressions inside parentheses first
  3. Look for exponents: Calculate any exponents (not covered in grade 3)
  4. Perform multiplication/division: Work from left to right
  5. Perform addition/subtraction: Work from left to right
  6. Verify your answer: Check that you followed the correct order
Tip 1: Always circle or highlight operations in the order you plan to perform them.
Tip 2: Write down intermediate results to keep track of your progress.
Tip 3: For operations with equal precedence, always work from left to right.
Tip 4: Practice with simple problems first, then work up to more complex expressions.
Tip 5: Always check your final answer by working through the problem again.
Tip 6: Remember that multiplication and division have equal precedence.
Common errors: Performing operations in the order they appear rather than by precedence, forgetting the left-to-right rule, not following the correct sequence.
Real-world applications: Calculating costs, measuring distances, solving problems with multiple steps.
Learning benefits: Develops logical thinking, builds foundation for advanced math, improves calculation accuracy.
Essential order of operations rules:

• Parentheses first: Always calculate expressions inside parentheses before anything else

• Multiplication/Division: Perform these operations before addition/subtraction

• Equal precedence: For operations of the same level, work from left to right

• Sequential calculation: Perform one operation at a time in the correct order

• Verification: Always check that you followed the correct sequence

Order of Operations Infographic
🔢
Parentheses

• Calculate inside parentheses first

• ( ) symbols indicate priority

• Solve from innermost to outermost

• Highest precedence level

Multiplication/Division

• Perform before addition/subtraction

• Equal precedence level

• Work left to right

• Higher than addition/subtraction

Addition/Subtraction

• Perform after multiplication/division

• Equal precedence level

• Work left to right

• Lowest precedence level

Order of Operations Process
1
Parentheses
2
Multiply/Divide
3
Add/Subtract
4
Left to Right
PEMDAS Memory Device

Please Excuse My Dear Aunt Sally

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

🔢 Master Order of Operations!

Questions & Answers

Question: Why can't I just calculate from left to right all the time? Why do I need special rules?

Answer: Great question! Without order of operations rules, the same expression could have different answers:

  • Without rules: 2 + 3 × 4 could be (2 + 3) × 4 = 20 OR 2 + (3 × 4) = 14
  • With rules: We always do multiplication before addition, so 2 + 3 × 4 = 2 + 12 = 14
  • Consistency: Everyone gets the same answer using the same rules
  • Mathematical agreement: The rules provide a universal standard for calculations

The order of operations ensures everyone calculates the same way and gets the same answer!

Question: Why do multiplication and division have the same precedence? Shouldn't one come before the other?

Answer: Multiplication and division have equal precedence because they are closely related operations:

  • Related operations: Division is the inverse of multiplication
  • Equal priority: They have the same level of importance in calculations
  • Left to right: When both appear, work from left to right
  • Example: 12 ÷ 4 × 2 = 3 × 2 = 6 (not 12 ÷ 8 = 1.5)

This relationship ensures consistent and logical mathematical results!

Question: Do I always do what's in parentheses first, even if there's multiplication outside?

Answer: Yes, parentheses always come first! Here's why:

  • Top priority: Parentheses override all other operations
  • Grouping: They indicate what should be calculated together
  • Example: 3 × (4 + 2) = 3 × 6 = 18 (not 12 + 2 = 14)
  • Inner to outer: For nested parentheses, solve the innermost first

Parentheses are like a "calculate me first" sign that always gets priority!