Order of Operations: Mastering PEMDAS in 3rd Grade Math

Learn and practice the order of operations with 5 detailed exercises. Understand PEMDAS, solve expressions step-by-step with visual examples.

Order of Operations Infographic
📋 PEMDAS
Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
PEMDAS Workflow
1
Parentheses
2
Exponents
3
Multiply/Divide
4
Add/Subtract
Key Rules:

• Parentheses First: Solve expressions inside parentheses first

• Left to Right: When operations have the same priority, work left to right

• Multiplication/Division: These have equal priority

• Addition/Subtraction: These have equal priority

Key Definitions:

Order of Operations: Rules that determine the sequence in which operations are performed in an expression

PEMDAS: Acronym for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Expression: A mathematical phrase with numbers and operations

Tip 1: Always look for parentheses first - they are the most important!
Tip 2: When multiplying/dividing, go left to right as they appear.
Tip 3: Rewrite the expression after each step to stay organized.
Solution: Exercises 1 to 3
1 Basic Addition/Subtraction
Exercise 1
Evaluate: 8 + 3 - 2
Definition:

Addition/Subtraction: Operations with equal priority, solved left to right

Solution method:
  1. Identify operations: addition and subtraction have equal priority
  2. Solve left to right: perform operations in order from left to right
  3. Calculate final result
Original
8 + 3 - 2
Step 1
11 - 2
Result
9
Step 1: Perform addition first (left to right)

8 + 3 = 11

Step 2: Perform subtraction

11 - 2 = 9

8 + 3 - 2 = 9
Final answer:

8 + 3 - 2 = 9

Applied rules:

• Left to Right: Addition and subtraction have equal priority

• Sequential Processing: Process operations in order from left to right

2 Multiplication/Division
Exercise 2
Evaluate: 12 ÷ 4 × 3
Definition:

Multiplication/Division: Operations with equal priority, solved left to right

Original
12 ÷ 4 × 3
Step 1
3 × 3
Result
9
Step 1: Perform division first (left to right)

12 ÷ 4 = 3

Step 2: Perform multiplication

3 × 3 = 9

12 ÷ 4 × 3 = 9
Final answer:

12 ÷ 4 × 3 = 9

Applied rules:

• Left to Right: Multiplication and division have equal priority

• Sequential Processing: Process operations in order from left to right

3 With Parentheses
Exercise 3
Evaluate: (6 + 2) × 3
Definition:

Parentheses: Operations inside parentheses are performed first

Original
(6 + 2) × 3
Step 1
8 × 3
Result
24
Step 1: Solve parentheses first

(6 + 2) = 8

Step 2: Perform multiplication

8 × 3 = 24

(6 + 2) × 3 = 24
Final answer:

(6 + 2) × 3 = 24

Applied rules:

• Parentheses First: Always solve expressions inside parentheses first

• Sequential Processing: Continue with remaining operations

Solution: Exercises 4 to 5
4 Mixed Operations
Exercise 4
Evaluate: 15 - 3 × 2 + 4
Definition:

Mixed Operations: Multiple operation types requiring proper order

Original
15 - 3 × 2 + 4
Step 1
15 - 6 + 4
Step 2
9 + 4
Result
13
Step 1: Perform multiplication first

3 × 2 = 6

Step 2: Now solve left to right (addition/subtraction)

15 - 6 = 9

Step 3: Complete the addition

9 + 4 = 13

15 - 3 × 2 + 4 = 13
Final answer:

15 - 3 × 2 + 4 = 13

Applied rules:

• Multiplication Before Addition/Subtraction: Higher priority operation

• Left to Right: Addition and subtraction have equal priority

5 Complex Expression
Exercise 5
Evaluate: (10 - 4) ÷ 2 + 3 × 2
Definition:

Complex Expression: Multiple operation types with parentheses

Original
(10 - 4) ÷ 2 + 3 × 2
Step 1
6 ÷ 2 + 3 × 2
Step 2
3 + 6
Result
9
Step 1: Solve parentheses first

(10 - 4) = 6

Step 2: Perform division and multiplication (left to right)

6 ÷ 2 = 3

3 × 2 = 6

Step 3: Perform addition

3 + 6 = 9

(10 - 4) ÷ 2 + 3 × 2 = 9
Final answer:

(10 - 4) ÷ 2 + 3 × 2 = 9

Applied rules:

• Parentheses First: Highest priority operation

• Multiplication/Division Next: Equal priority, left to right

• Addition/Subtraction Last: Equal priority, left to right

Order of Operations: Complete Guide
📋 PEMDAS
Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
Key definitions:

Order of Operations: The sequence in which mathematical operations are performed in an expression

PEMDAS: Acronym to remember the order: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

Expression: A combination of numbers, variables, and operators

Complete methodology:
  1. Parentheses: Solve all operations inside parentheses first
  2. Exponents: Solve any exponents (not covered in 3rd grade)
  3. Multiplication/Division: Solve from left to right
  4. Addition/Subtraction: Solve from left to right
Tip 1: Always do parentheses first - they are like a priority zone!
Tip 2: Remember: Multiplication and division are equals - go left to right.
Tip 3: Same for addition and subtraction - they are equals too!
Tip 4: Write down each step to avoid mistakes.
Common errors: Forgetting parentheses, doing operations in wrong order, mixing up left-to-right rule.
Key to success: Practice with parentheses first, then mixed operations, always going step by step.
Order to remember:

• Parentheses first (operations inside brackets)

• Multiplication/Division next (left to right)

• Addition/Subtraction last (left to right)

Questions & Answers

Question: Why do we need to follow the order of operations? Can't we just solve from left to right?

Answer: Great question! We need the order of operations because without it, the same expression could have multiple answers. Look at this example:

Expression: 3 + 4 × 2

  • If solved left to right: (3 + 4) × 2 = 7 × 2 = 14
  • If using order of operations: 3 + (4 × 2) = 3 + 8 = 11

Both methods are logical, but they give different results! The order of operations ensures everyone gets the same answer. It's like a universal agreement in mathematics.

Think of it like traffic rules - if everyone didn't follow the same rules, there would be chaos!

Question: I see different letters like BODMAS and PEMDAS. Are they the same thing?

Answer: Yes, they are the same concept but with different names used in different countries:

  • PEMDAS (USA): Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
  • BODMAS (UK/Australia): Brackets, Orders, Division, Multiplication, Addition, Subtraction

They both mean the same thing - parentheses/brackets come first, then exponents/orders, then multiplication/division (left to right), then addition/subtraction (left to right).

In 3rd grade, we focus on Parentheses, then Multiplication/Division, then Addition/Subtraction since exponents aren't typically introduced yet.

The important thing is understanding the sequence, not the acronym!

Question: My child keeps forgetting to do parentheses first. Any tips to help them remember?

Answer: Here are some effective strategies to help children remember parentheses:

  • Visual cues: Circle or highlight parentheses in a different color before starting
  • Story method: Tell them parentheses are like "secret codes" that must be opened first
  • Physical action: Have them point to parentheses and say "DO ME FIRST!"
  • Memory trick: "Parentheses are like hugging - everything inside gets special attention first"

Practice with simple expressions like (5 + 3) × 2 vs 5 + 3 × 2 to show why it matters.

Also, encourage them to write the expression with the parentheses result substituted before continuing: (5 + 3) × 2 → 8 × 2 → 16