GEMDAS — Definition, Formula & Examples
GEMDAS is a memory aid that tells you the order in which to solve parts of a math expression: Grouping symbols first, then Exponents, then Multiplication and Division (left to right), and finally Addition and Subtraction (left to right).
GEMDAS is an acronym representing the conventional hierarchy of arithmetic operations: Grouping symbols (parentheses, brackets, braces) → Exponents → Multiplication and Division (evaluated left to right with equal precedence) → Addition and Subtraction (evaluated left to right with equal precedence).
How It Works
Each letter in GEMDAS names one step. **G** means handle anything inside grouping symbols like parentheses first. **E** means evaluate exponents next. **M** and **D** share the same priority — work them left to right. **A** and **S** also share the same priority and are worked left to right last. The word "Grouping" instead of "Parentheses" (as in PEMDAS) reminds you that brackets and braces count too, not just parentheses.
Worked Example
Problem: Evaluate:
G – Grouping: Solve inside the parentheses first.
E – Exponents: Apply the exponent to the result.
M/D – Multiply and Divide left to right: Multiply 3 × 36, then divide 6 ÷ 3.
A/S – Add and Subtract left to right: Subtract to get the final result.
Answer:
Why It Matters
GEMDAS is used in the same situations as PEMDAS or BODMAS — any time you need to simplify or evaluate a math expression with more than one operation. Using "Grouping" instead of "Parentheses" can help you remember that brackets [ ] and braces { } follow the same rule, which becomes important in algebra and beyond.
Common Mistakes
Mistake: Treating multiplication as higher priority than division because M comes before D in the acronym.
Correction: Multiplication and division have equal priority. Always work them left to right in the expression, not in the order of the letters.