PEMDAS for Grade 5: Teaching Guide, Practice and Free Worksheets
PEMDAS is the order of operations students use to decide which part of a mathematical expression to calculate first. By Grade 5, students should be able to use parentheses, exponents, multiplication, division, addition and subtraction in the correct order — without simply working from left to right.
This guide explains PEMDAS in a student-friendly way, shows worked examples, addresses the mistakes students commonly make, and provides 10 free Grade 5 PEMDAS worksheets for targeted practice. Every worksheet includes an answer key.
TL;DR — Grade 5 PEMDAS at a Glance
By the end of Grade 5, a student should be able to:
- Recognize the order of operations in a numerical expression.
- Solve expressions containing parentheses before operations outside them.
- Evaluate exponents before multiplication and division.
- Perform multiplication and division from left to right when they appear at the same level.
- Perform addition and subtraction from left to right when they appear at the same level.
- Check an answer by reviewing each step rather than guessing from the final number.
The most important idea: PEMDAS does not mean multiplication always comes before division. Multiplication and division have equal priority and are evaluated from left to right. Addition and subtraction work the same way.
1. What Does PEMDAS Mean?
PEMDAS is a memory aid for the standard order of operations:
P — Parentheses
E — Exponents
M — Multiplication
D — Division
A — Addition
S — Subtraction
However, the letters should not be interpreted as six completely separate levels. Multiplication and division are at the same level. Addition and subtraction are also at the same level.
2. How to Solve a PEMDAS Problem
A reliable strategy is to work through an expression one level at a time.
Step 1 — Parentheses
Complete calculations inside parentheses first.
8 × (5 + 2)
First calculate 5 + 2 = 7.
Then calculate 8 × 7 = 56.
Step 2 — Exponents
Evaluate powers before multiplication, division, addition or subtraction.
3² + 4
3² = 9, so 9 + 4 = 13.
Step 3 — Multiplication and Division
Complete multiplication and division from left to right.
24 ÷ 6 × 5
24 ÷ 6 = 4, then 4 × 5 = 20.
Step 4 — Addition and Subtraction
Complete addition and subtraction from left to right.
18 − 7 + 4
18 − 7 = 11, then 11 + 4 = 15.
3. Worked PEMDAS Examples
| Expression | Steps | Answer |
|---|---|---|
| 7 + 3 × 4 | 3 × 4 = 12; 7 + 12 | 19 |
| (12 − 5) × 3 | 12 − 5 = 7; 7 × 3 | 21 |
| 2³ + 5 × 2 | 2³ = 8; 5 × 2 = 10; 8 + 10 | 18 |
| 36 ÷ 6 + 4 × 3 | 36 ÷ 6 = 6; 4 × 3 = 12; 6 + 12 | 18 |
| 20 − (6 + 2) ÷ 4 | 6 + 2 = 8; 8 ÷ 4 = 2; 20 − 2 | 18 |
4. Five Common PEMDAS Mistakes
Mistake 1 — Multiplying before dividing every time
What the student does: Treats M as more important than D because M appears first in PEMDAS.
Why it happens: The acronym looks like a strict sequence.
The fix: Teach students to group multiplication and division together. Start at the left and work toward the right.
Example: 24 ÷ 6 × 5 = 4 × 5 = 20, not 24 ÷ 30.
Mistake 2 — Adding before multiplying
What the student does: Solves 7 + 3 × 4 as 10 × 4 = 40.
Why it happens: The student reads from left to right without applying the order of operations.
The fix: Circle multiplication and division first. Then return to addition and subtraction.
Mistake 3 — Forgetting parentheses
What the student does: Treats the expression 5 × (8 − 3) as 5 × 8 − 3.
Why it happens: Parentheses are seen as decoration rather than instructions.
The fix: Have students say, “Inside the parentheses first,” before solving.
Mistake 4 — Treating exponents as multiplication
What the student does: Reads 4² as 4 × 2.
Why it happens: Students understand the small raised number as an ordinary multiplication number.
The fix: Connect the exponent to repeated multiplication: 4² means 4 × 4.
Mistake 5 — Doing addition before subtraction every time
What the student does: Assumes A always comes before S because of the acronym.
Why it happens: The letters appear in a fixed order in PEMDAS.
The fix: Teach addition and subtraction as one level, evaluated from left to right.
5. PEMDAS, PEDMAS and BEDMAS
Students may encounter different names for the order of operations. PEMDAS is common in the United States and many North American resources. PEDMAS and BEDMAS are also used, particularly in Canadian classrooms.
| Term | Meaning |
|---|---|
| PEMDAS | Parentheses, Exponents, Multiplication, Division, Addition, Subtraction |
| PEDMAS | Parentheses, Exponents, Division, Multiplication, Addition, Subtraction |
| BEDMAS | Brackets, Exponents, Division, Multiplication, Addition, Subtraction |
The important mathematics is the same: multiplication and division have equal priority and are solved from left to right, while addition and subtraction also have equal priority and are solved from left to right.
6. How to Teach PEMDAS in Grade 5
Start with simple expressions
Begin with expressions such as 6 + 4 × 3. Once students consistently recognize that multiplication comes before addition, introduce parentheses and exponents.
Use one step at a time
Ask students to underline the operation they are solving before they calculate it. This makes their thinking visible and makes errors easier to diagnose.
Make students show intermediate steps
For example:
18 − 2 × (4 + 3)
18 − 2 × 7
18 − 14
4
This is much easier to check than a single unexplained answer.
Use error analysis
Give students an incorrect solution and ask them to identify the first step where the calculation went wrong. This is especially useful once students understand the basic procedure.
7. Free Grade 5 PEMDAS Worksheets
WorksheetGalaxy's Grade 5 PEMDAS collection includes ten printable worksheets covering rules, basic practice, parentheses, exponents, mixed expressions, multi-step problems and reasoning challenges. Each worksheet includes an answer key.
Use this introductory sheet to review the order of operations and see worked examples before beginning independent practice.
Basic order-of-operations expressions for building confidence and procedural fluency.
Focuses on completing calculations inside parentheses before continuing with the rest of the expression.
Provides practice evaluating exponents as part of the order of operations.
Combines two important PEMDAS skills for students ready for more complex expressions.
Mixed expressions requiring students to apply the complete order of operations.
Longer expressions that require students to work carefully through several operations.
Students evaluate completed calculations and decide whether each statement is correct.
Students analyze incorrect solutions and identify where the order of operations was applied incorrectly.
A more challenging set of expressions for students who are ready to apply multiple PEMDAS skills independently.
Tip: The worksheets can be used progressively. Start with Rules & Examples, move through Basic, Parentheses and Exponents practice, and finish with Mixed, Multi-Step and Challenge work.
8. A Simple PEMDAS Practice Routine
A short daily routine can be more effective than giving students a large worksheet all at once.
- Review: Solve one simple order-of-operations example together.
- Model: Demonstrate one problem while explaining each step aloud.
- Practice: Have students complete 3–5 expressions independently.
- Discuss: Compare different solution steps and identify mistakes.
- Extend: Give one challenge expression requiring several operations.
9. PEMDAS Practice Quiz
After students have completed several practice worksheets, a short quiz can be used to check whether they can independently apply the order of operations.
A useful Grade 5 PEMDAS quiz should include a mixture of straightforward expressions, parentheses, exponents, multiplication and division, and multi-step problems. Include at least one question designed to reveal the common misconception that multiplication must always be completed before division.
Frequently Asked Questions
What does PEMDAS stand for?
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition and Subtraction. It is a mnemonic for remembering the order of operations.
Does multiplication always come before division?
No. Multiplication and division have equal priority. When both appear in an expression, solve them from left to right.
Does addition always come before subtraction?
No. Addition and subtraction have equal priority. Solve them from left to right.
What grade do students learn PEMDAS?
Students encounter the ideas behind order of operations across elementary mathematics, with increasingly complex expressions as they progress. Grade 5 is an appropriate level for systematic practice with parentheses, exponents and multiple operations.
Is PEMDAS the same as BEDMAS?
They are different mnemonics for the same underlying order-of-operations rules. PEMDAS uses Parentheses while BEDMAS uses Brackets, and the acronym places multiplication/division in a different written order. In both cases, multiplication and division are performed from left to right, as are addition and subtraction.
Are these PEMDAS worksheets free?
Yes. The Grade 5 PEMDAS worksheets listed above are available as printable PDF resources from WorksheetGalaxy.