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PEMDAS / BODMAS Order of Operations Drill Maker

Creates order of operations worksheets with progressive difficulty: basic operations without parentheses, simple parentheses, nested brackets, exponents, and mixed integer operations with stepped evaluation trees.

PEMDAS / BODMAS Order of Operations Drill Maker

Create order of operations drill sheets with stepped evaluation trees and answer keys

Order of Operations (PEMDAS) Practice

Evaluate each expression step-by-step. Show intermediate work.
Score: _______ / 10
1) (4 + 2) × 2 − 6
Show Evaluation Steps:
Final Result:
2) (3 + 4) × 5 − 3
Show Evaluation Steps:
Final Result:
3) (4 + 7) × 4 − 4
Show Evaluation Steps:
Final Result:
4) (2 + 3) × 2 − 2
Show Evaluation Steps:
Final Result:
5) (5 + 4) × 5 − 1
Show Evaluation Steps:
Final Result:
6) (7 + 4) × 2 − 1
Show Evaluation Steps:
Final Result:
7) (2 + 3) × 2 − 6
Show Evaluation Steps:
Final Result:
8) (2 + 6) × 4 − 6
Show Evaluation Steps:
Final Result:
9) (2 + 3) × 4 − 7
Show Evaluation Steps:
Final Result:
10) (7 + 3) × 4 − 4
Show Evaluation Steps:
Final Result:

What is Order of Operations (PEMDAS/BODMAS)?

The order of operations is the universal convention establishing the sequence in which mathematical operations must be evaluated to ensure a unique, correct result.

PEMDAS stands for Parentheses, Exponents, Multiplication & Division (left-to-right), and Addition & Subtraction (left-to-right); also known internationally as BODMAS (Brackets, Orders, Division & Multiplication, Addition & Subtraction).

Formula & Step-by-Step Calculation

\text{PEMDAS: } () \longrightarrow x^n \longrightarrow \{ \times, \div \}_{L\to R} \longrightarrow \{ +, - \}_{L\to R}

Universal hierarchical evaluation precedence.

Worked Step-by-Step Examples

Example 1

Evaluate: 5 + (8 - 3)^2 × 2

Solution: 55
• Parentheses: (8 - 3) = 5 ⟹ 5 + 5^2 × 2
• Exponent: 5^2 = 25 ⟹ 5 + 25 × 2
• Multiplication: 25 × 2 = 50 ⟹ 5 + 50
• Addition: 5 + 50 = 55

Common Real-World & Academic Use Cases

  • ✓ 5th and 6th grade introduction to algebraic hierarchy
  • ✓ Eliminating common left-to-right calculation fallacies
  • ✓ Preparing students for nested expressions in high school algebra
  • ✓ Classroom error-analysis activities

How to Use the PEMDAS / BODMAS Order of Operations Drill Maker

1

Select Difficulty Level

Choose Level 1 (No Parentheses), Level 2 (Parentheses Only), Level 3 (Exponents & Parentheses), or Level 4 (Nested Brackets).

2

Choose Problem Count

Select 10, 15, or 20 problems.

3

Print & Review Steps

Print student test sheet and teacher step-by-step evaluation key.

Frequently Asked Questions

Q: Does multiplication always come before division?

No, multiplication and division have equal precedence and must be evaluated strictly from left to right as they appear in the expression (similarly for addition and subtraction).

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