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Order of operations reference

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.

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Reference · LetterReference · A4
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Start with the innermost group. Continue through powers, multiplication/division and addition/subtraction, using left-to-right order within tied levels.

Download the complete reference with its explanations and worked examples. This handout does not need a separate answer key.

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Reference handout

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Reference handout
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Print the English reference in Letter or A4, or choose another printed language below. The handout includes the explanation and examples together on one page.

Pair the reference with a focused worksheet. The important habit is identifying the next operation and explaining why it comes first.

Learning objective

What this activity builds

Recognize equivalent grouping symbols and evaluate nested groups before surrounding operations.

Worked example

Evaluate 2 × [3 + (8 − 5)].

2 × [3 + 3] = 2 × 6 = 12.

The parentheses are inside the brackets, so 8 − 5 is calculated first. Then finish the bracket before multiplying by 2. The shape of the grouping symbol does not create a new arithmetic priority.

Teaching notes

Make the practice count

  • Trace the matching opening and closing symbols before beginning.
  • Work from the deepest group outward, keeping the rest of the expression unchanged.
  • Rewrite the full expression after each step to avoid losing terms.
  • Show that replacing a matched pair of brackets with parentheses does not change its meaning.

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Configured PDF · GEMDAS Rules · US Letter

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Math SheetNameScoreTeacherDateGEMDAS RulesEvaluate grouping and powers first. Operations on the same level are completed from left to right.1GGroupingWork inside parentheses, brackets, and braces from the innermost group outward.2EExponentsEvaluate powers before multiplication, division, addition, or subtraction.3MDMultiplication and divisionWork from left to right; multiplication does not automatically come before division.4ASAddition and subtractionWork from left to right; addition does not automatically come before subtraction.Example[18 ÷ (5 - 2)] × 2 + 4 = 6 × 2 + 4 = 16math-sheet.comPage 1 / 1

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