Order of operations
GEMDAS grouping rules chart
Use an order-of-operations handout that treats parentheses, brackets and braces as grouping symbols. Follow a nested example from the innermost group outward.
Preview and downloadOrder of operations practice
Advanced order of operations worksheets
Work through twelve expressions with positive, negative or mixed inputs. Combine easy or hard practice with grouping, nested groups and exponents, and check a separate answer key.
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Evaluate each expression, keeping each sign with its operand. A positive-input setting does not require a positive result.
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Choose the expression, then explain the order
Choose easy or hard practice, then select the grouping and exponent form. Advanced and algebraic worksheets also let you choose positive, negative or mixed inputs. These settings describe the operands; a positive-input expression can still have a negative answer.
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Learning objective
What this activity builds
Combine arithmetic precedence with accurate sign handling and unambiguous exponent scope.
Worked example
Compare (−3)² + 4 with −(3²) + 4.
The first is 9 + 4 = 13. The second is −9 + 4 = −5.
In the first expression the negative sign is inside the squared base. In the second it is outside the power. Grouping determines which quantity is raised to the exponent.
Teaching notes
Make the practice count
- Check sign reasoning separately from the order of calculation.
- Have learners identify the complete base of every power.
- Move from one pair of parentheses to nested grouping gradually.
- Use mixed inputs only after the learner can explain products and quotients involving negatives.
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Order of operations
Basic order of operations worksheets
Evaluate ten expressions with all four arithmetic operations. Select easy or hard practice and five grouping/exponent formats, then print the questions and a separate worked key.
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Algebraic order of operations worksheets
Simplify twelve expressions containing x, with configurable signs, grouping and powers. Practice combining like terms and simplifying products and quotients without substituting a number for x.
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