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Order of OperationsFREEWorksheet Generator(Grades 5-8)

Order of Operations worksheets with step-by-step answer keys. Generate unlimited unique practice sheets with fresh problems for Grades 5–8.

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Set A • 10 Qs

PanMaths.comOrder of Operations Worksheets (PEMDAS / BODMAS) • Set A (Medium)

Name: __________________________

Date: _____________ Period: ____

Score: _____ / 10

(2+7)×6= ______

Workspace:

(7+5)÷3+1= ______

Workspace:

2×(4+3)−2= ______

Workspace:

(3+7)×2= ______

Workspace:

(2+8)×4= ______

Workspace:

(5+1)×3= ______

Workspace:

5×(3+5)−23= ______

Workspace:

2×(1+4)−7= ______

Workspace:

(6+1)×5= ______

Workspace:

10.

(5+10)÷5+10= ______

Workspace:

PanMaths.com • Free Math Worksheet Generator • Set A (Medium)Page 1 of 2

PanMaths.comAnswer Key & Worked Solutions • Set A (Medium)

Answer Key

Total Problems: 10

(2+7)×6= 54

1. Parentheses: (2 + 7) = 9

2. Multiply: 9 × 6 = 54

(7+5)÷3+1= 5

1. Parentheses: (7 + 5) = 12

2. Divide: 12 ÷ 3 = 4

3. Add: 4 + 1 = 5

2×(4+3)−2= 12

1. Parentheses: (4 + 3) = 7

2. Multiply: 2 × 7 = 14

3. Subtract: 14 − 2 = 12

(3+7)×2= 20

1. Parentheses: (3 + 7) = 10

2. Multiply: 10 × 2 = 20

(2+8)×4= 40

1. Parentheses: (2 + 8) = 10

2. Multiply: 10 × 4 = 40

(5+1)×3= 18

1. Parentheses: (5 + 1) = 6

2. Multiply: 6 × 3 = 18

5×(3+5)−23= 17

1. Parentheses: (3 + 5) = 8

2. Multiply: 5 × 8 = 40

3. Subtract: 40 − 23 = 17

2×(1+4)−7= 3

1. Parentheses: (1 + 4) = 5

2. Multiply: 2 × 5 = 10

3. Subtract: 10 − 7 = 3

(6+1)×5= 35

1. Parentheses: (6 + 1) = 7

2. Multiply: 7 × 5 = 35

10.

(5+10)÷5+10= 13

1. Parentheses: (5 + 10) = 15

2. Divide: 15 ÷ 5 = 3

3. Add: 3 + 10 = 13

PanMaths.com • Answer Key & Worked SolutionsPage 2 of 2

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Worksheet Info

Categoryarithmetic

Grade LevelGrades 5-8

DifficultyEasy to Hard

Time15-25 min

Skills Practiced

✓ PEMDAS / BODMAS rule mastery
✓ Parentheses and grouping symbols
✓ Exponents and powers
✓ Multi-step arithmetic evaluation

Key Strategies

Underline & Rewrite: Underline the single highest-priority operation, solve it, and rewrite the whole line.
Left-to-Right Sweep: Scan left to right for multiplication/division pairs before touching addition/subtraction.
Innermost to Outermost: When nested parentheses ( ) inside [ ] appear, always solve the inside bubble first.

🎮 Interactive Warm-Up

Order of Operations (PEMDAS) Number Snake Arcade

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Strategies

Underline & Rewrite: Underline the single highest-priority operation, solve it, and rewrite the whole line.
Left-to-Right Sweep: Scan left to right for multiplication/division pairs before touching addition/subtraction.
Innermost to Outermost: When nested parentheses ( ) inside [ ] appear, always solve the inside bubble first.

Mastering Order of Operations: Core Concepts & Mental Models

Order of Operations worksheets with step-by-step answer keys. Generate unlimited unique practice sheets with fresh problems for Grades 5–8.

💡 Essential Strategies for Order of Operations

Underline & Rewrite

Underline the single highest-priority operation, solve it, and rewrite the whole line.

Left-to-Right Sweep

Scan left to right for multiplication/division pairs before touching addition/subtraction.

Innermost to Outermost

When nested parentheses ( ) inside [ ] appear, always solve the inside bubble first.

❓ Frequently Asked Questions

Why do we need order of operations in math?

Without a standardized order of operations, mathematical expressions would be ambiguous. For example, 10 + 2 × 3 could equal 36 if added first, or 16 if multiplied first. Standardizing PEMDAS ensures that scientific formulas, financial calculations, and computer programs produce identical, verifiable results.

Does multiplication always come before division in PEMDAS?

No! Multiplication and division have equal priority. You solve them in whichever order they appear from left to right. In 12 ÷ 3 × 2, you divide first to get 4 × 2 = 8.

Are these worksheets free to print and photocopy for classrooms?

Yes! All PanMaths worksheets, answer keys, and generator tools are 100% free for teachers, homeschoolers, tutors, and students with no sign-up or registration required.

How does the Step-by-Step Answer Key help teachers and students?

Our answer keys provide intermediate evaluation lines (e.g. 1. Parentheses -> 2. Multiply -> 3. Final Answer). This allows teachers to grade student work in seconds and helps students immediately diagnose where an order-of-operations mistake occurred.

Common Mistakes to Avoid

The #1 misconception students make is thinking Multiplication ALWAYS comes before Division, or Addition ALWAYS comes before Subtraction. In reality, Multiplication and Division hold equal priority and must be solved from left to right. The same rule applies to Addition and Subtraction.

Worksheet Customization by Grade

Select Easy for Grade 5 introduction (2-step problems without exponents), Medium for Grade 6 (includes single parentheses and multiple operations), or Hard for Grades 7-8 (includes exponents, squared quantities, and nested operations). Every sheet includes an instant printable answer key.

💡 Work Left to Right for Multiplication & Division

Multiplication does not outrank division. When both appear, evaluate them in order from left to right: 12 ÷ 3 × 2 = 4 × 2 = 8 (not 12 ÷ 6).

12 ÷ 3 × 2 = 4 × 2 = 8

💡 Parentheses Grouping First

Always simplify everything inside parentheses or brackets before applying outer exponents or operations.

3 × (4 + 5) = 3 × 9 = 27

💡 Addition & Subtraction Tie-Breaker

Just like multiplication and division, addition and subtraction share equal priority and are solved strictly left to right.

10 - 3 + 2 = 7 + 2 = 9 (not 10 - 5)

Worksheet Facts by Grade Level

Grade Level	Common Core Standard	Target Operations & Complexity	Recommended Drills
Grade 3	CCSS.MATH.CONTENT.3.OA.D.8	Two-step word problems with +, −, ×	Set A (Standard) - Basic addition/multiplication
Grade 4	CCSS.MATH.CONTENT.4.OA.A.3	Multi-step whole numbers with parentheses	Set A & Set B - 2-step parentheses equations
Grade 5	CCSS.MATH.CONTENT.5.OA.A.1	Parentheses, brackets & nested braces	Set B & Set C - Multi-nested grouping symbols
Grade 6	CCSS.MATH.CONTENT.6.EE.A.2	Whole number exponents & algebraic variables	Set C (Challenging & Exponents)
Grades 7–8	CCSS.MATH.CONTENT.7.NS.A.2	Negative signed integers, fractions & powers	Set C & Unlimited Studio custom counts

Mastering the Order of Operations: PEMDAS vs BODMAS

The Order of Operations is the foundational mathematical rulebook that ensures everyone evaluates algebraic expressions to the exact same correct value. Without a standardized order, an expression like 8 + 2 × 5 could yield either 18 or 50.

PEMDAS vs BODMAS: What Is the Difference?

Different English-speaking countries use different mnemonics for the exact same four-step hierarchy:

PEMDAS (US & Canada): Parentheses ➔ Exponents ➔ Multiplication & Division (Left-to-Right) ➔ Addition & Subtraction (Left-to-Right). Mnemonic: "Please Excuse My Dear Aunt Sally"
BODMAS (UK, India, Australia): Brackets ➔ Orders (Powers/Roots) ➔ Division & Multiplication (Left-to-Right) ➔ Addition & Subtraction (Left-to-Right).
BIDMAS / GEMDAS: Indices or Grouping symbols (brackets, braces, absolute value bars).

The 4 Core Steps of Order of Operations

Step 1: Grouping Symbols First (P / B) — Simplify innermost parentheses ( ), brackets [ ], braces { }, and radical radicands first.
Step 2: Exponents & Roots (E / O / I) — Evaluate all powers, square roots, and indices from left to right (e.g., 3² = 9, √16 = 4).
Step 3: Multiplication & Division (M & D / D & M) — Perform all multiplications and divisions as they appear sequentially from left to right. Neither operation has priority over the other!
Step 4: Addition & Subtraction (A & S) — Perform all additions and subtractions as they appear sequentially from left to right.

Common Student Pitfalls & How to Avoid Them

Over 80% of student calculation mistakes on standardized math tests come from these two common misconceptions:

Mistake 1: Forcing Multiplication before Division
Incorrect: 20 ÷ 4 × 5 = 20 ÷ 20 = 1
Correct: 20 ÷ 4 × 5 = 5 × 5 = 25 (Divide first because it appears first on the left).
Mistake 2: Forcing Addition before Subtraction
Incorrect: 15 - 5 + 3 = 15 - 8 = 7
Correct: 15 - 5 + 3 = 10 + 3 = 13 (Subtract first because it appears first on the left).

Benefits of Mastery

📐 Pre-Algebra Mastery

Order of operations is the critical prerequisite for solving one-step, two-step, and multi-variable linear equations.

🎯 Error Prevention

Step-by-step unravelling trains students to write intermediate mathematical proofs without skipped logical steps.

⚡ Standardized Test Confidence

Directly aligns with Common Core State Standards (CCSS) 5.OA.A.1 and 6.EE.A.2 for state exam success.

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