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§ Arithmetic·Grades 5–6

Order of Operations Worksheets

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Easy

10 problems

Medium

20 problems

Hard

20 problems

Mixed

30 problems

Free printable order of operations worksheets with step-by-step answer keys. Every worksheet is uniquely generated so students never see the same problems twice. Topics covered range from multiplication before addition (pemdas) at the easy level through to exponents, full pemdas at the advanced level.

CCSS.5.OACCSS.6.EE

What is order of operations?

Order of operations is a set of rules that determines which mathematical operations to perform first in an expression containing multiple operations. The standard convention follows PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Without these rules, the expression 3 + 4 × 2 could equal either 11 or 14, creating mathematical ambiguity.

Why it matters

Order of operations ensures mathematical expressions have a single, unambiguous answer across all contexts. In programming, calculators follow PEMDAS to execute formulas correctly — a payroll system calculating 40 hours × $15 per hour + $50 bonus must compute 40 × 15 + 50 = $650, not 40 × (15 + 50) = $2,600. Scientific formulas rely on precise operation order: calculating kinetic energy as ½mv² requires squaring velocity before multiplying by mass. Financial calculations like compound interest use exponents that must be evaluated before multiplication. Architecture and engineering depend on correct formula evaluation when calculating loads, angles, and measurements. Students encounter order of operations in CCSS 5.OA when evaluating expressions with parentheses, building foundation skills for algebra, where expressions like 3x + 2(x - 4) require systematic evaluation order.

Common mistakes to watch for

  • ✗Working left to right without regard for operation priority produces 3 + 4 × 2 = 14 instead of the correct answer 11
  • ✗Ignoring parentheses leads to calculating 7 × 8 + 3 = 59 when the expression 7 × (8 + 3) actually equals 77
  • ✗Treating exponents as regular multiplication gives 2 × 3² = 36 instead of the correct result 2 × 9 = 18

Questions teachers ask

What does PEMDAS stand for?+
PEMDAS stands for Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Some remember it with the phrase 'Please Excuse My Dear Aunt Sally.' Multiplication and division have equal priority, as do addition and subtraction, so these pairs are evaluated from left to right.
Why do multiplication and division have equal priority?+
Multiplication and division are inverse operations with the same priority level. When both appear in an expression like 12 ÷ 3 × 2, they're evaluated left to right: 12 ÷ 3 = 4, then 4 × 2 = 8. This gives 8, not 12 ÷ 6 = 2, which would result from doing multiplication first.
How do you remember the order of operations?+
PEMDAS provides the standard memory aid: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. The phrase 'Please Excuse My Dear Aunt Sally' helps recall the sequence. Remember that operations at the same level (like multiplication/division) work left to right, not in strict MD then AS order.
What happens if there are no parentheses in an expression?+
Without parentheses, follow the remaining PEMDAS rules: exponents first, then multiplication and division (left to right), finally addition and subtraction (left to right). For example, 5 + 3² × 2 becomes 5 + 9 × 2 = 5 + 18 = 23. The exponent 3² = 9 is calculated first, then multiplication, then addition.
Do calculators automatically follow order of operations?+
Most scientific and graphing calculators follow PEMDAS automatically, but basic four-function calculators often calculate left to right regardless of operation priority. Entering 3 + 4 × 2 on a basic calculator might display 14 instead of the mathematically correct answer 11. Always verify calculator behavior with known expressions.
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Beginner

Generate →
Concepts
Multiplication before addition (PEMDAS)
Range
1–5
Steps
2 steps
Example
2 + 3 × 4

Easy

Generate →
Concepts
Two operations, PEMDAS order
Range
2–10
Steps
2–3 steps
Example
5 × 6 + 3

Medium

Generate →
Concepts
Parentheses, three operations
Range
2–10
Steps
3–4 steps
Example
5 × (3 + 2) − 4

Hard

Generate →
Concepts
Exponents, full PEMDAS
Range
2–8
Steps
3–4 steps
Example
3² + 2 × 4 − 1

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