A signed integer is a whole number with a direction: positive values lie above or to the right of zero, while negative values lie below or to the left.
They are useful for gains and losses, temperature changes, elevations, balances, and movement in opposite directions. The sign is part of the number, not decoration.
Addition combines movement on the number line; subtraction adds an opposite. For multiplication and division, matching signs give a positive result and different signs give a negative result.
Key idea
See the relationship
−3←0→+3
Quick guide
How to use this calculator
Enter two signed integers.
Choose addition, subtraction, multiplication, or division.
Read the exact integer or reduced fraction.
Review the sign rule displayed with the result.
Calculation method
Signed-number rules made explicit
Addition and subtraction compare signs and magnitudes; subtraction can be understood as adding the opposite.
For multiplication and division, matching signs produce a positive result and different signs produce a negative result. Non-integral division remains an exact reduced fraction.
Worked example
Divide −21 by 6
Different signs give a negative result. Reducing the fraction by the common factor three gives the exact quotient.
−21 ÷ 6 = −21/6 = −7/2
Supported inputs
Precision and limits
Signed integers
Each input may have an optional leading + or − sign and up to 1,000 digits.
Four operations
Addition, subtraction, multiplication, and division are supported.
Exact division
Non-integral quotients remain reduced fractions with a decimal representation.
Undefined state
Division by zero is rejected rather than displayed as Infinity.
