Basic Math Calculator
Solve math expressions using standard arithmetic operators and parentheses. Get a detailed step-by-step simplification breakdown showing the order of operations (BODMAS/PEMDAS).
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Final Computed Result
16.5
Rounded to 4 decimal places
BODMAS Step-by-Step Resolution
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Understanding the Order of Operations
In mathematics, the order of operations is a collection of rules that reflect conventions about which procedures to perform first in a given mathematical expression. This ensures that everyone calculates the same expression in the same way, leading to the same correct result.
BODMAS vs. PEMDAS
Depending on where you study, you might refer to this rule as either **BODMAS** or **PEMDAS**:
- BODMAS: Brackets, Orders (exponents/roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
- PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
It is a common misconception that Multiplication always precedes Division in PEMDAS, or that Division always precedes Multiplication in BODMAS. In reality, they hold equal precedence and are solved strictly in the order they appear from left to right.
Why showing steps matters
When learning or auditing basic math expressions (like household budgeting, invoice deductions, or homework), it is easy to make precedence mistakes. Our calculator parses the expression into a safe token stream, validates its syntax (preventing invalid entries like mismatched parentheses or empty brackets), and provides a step-by-step resolution showing exactly how brackets are collapsed and expressions are reduced.