Quick guide
How to use this calculator
- Choose the equation form that matches the unknown position.
- Enter the two known values.
- Read the exact solution or the correct no-solution, infinite, or undefined state.
- For a unique result, the calculator substitutes it back into the original equation.
Calculation method
Inverse operations with domain checks
Addition is undone with subtraction; multiplication is undone with division; subtraction and division depend on which operand is unknown.
Zero cases are handled explicitly. For example, ? × 0 = 0 has infinitely many solutions, while ? × 0 = 2 has none. A divisor can never be zero.
Worked example
Solve 12 ÷ ? = 3
The unknown divisor is found by dividing the dividend by the result. Substitution confirms 12 ÷ 4 = 3.
12 ÷ ? = 3 → ? = 12/3 = 4
Supported inputs
Precision and limits
Eight equation forms
The unknown may occupy either operand position across the four operations.
Exact rational result
Non-integer solutions remain reduced fractions with a decimal representation.
Zero-domain truth table
No-solution, infinite-solution, and undefined cases are distinguished.
Verified solution
Every unique answer is checked by exact substitution before display.