Signed Integer Calculator
Master operations with positive and negative numbers. This tool visualizes sign rules and step-by-step logic for adding, subtracting, multiplying, and dividing integers.
About
Understanding signed integers is a primary hurdle in pre-algebra. Errors often stem from counter-intuitive rules like "subtracting a negative equals addition." This calculator does not just produce an answer. It acts as a logic engine that explicitly states the sign rule being applied. Accountants and students use this verification to audit lengthy ledgers or homework problems where a single sign flip invalidates the entire result. The focus is on the mechanism of the sign interaction rather than the arithmetic itself.
Formulas
The calculator adheres to the algebraic field properties of integers Z.
The absolute value |x| determines the sign when adding integers with different signs. If |negative| > |positive|, the result is negative.
Reference Data
| Operation | Input Signs | Sign Change Rule | Example |
|---|---|---|---|
| Addition | + + + | Add values, keep sign | 2 + 3 = 5 |
| Addition | - + - | Add values, keep sign | -2 + -3 = -5 |
| Subtraction | + − - | Double negative becomes positive | 2 − (-3) → 2 + 3 |
| Subtraction | - − + | Same as adding two negatives | -2 − 3 → -5 |
| Multiply/Div | + × + | Positive Result | 2 × 3 = 6 |
| Multiply/Div | - × - | Positive Result | -2 × -3 = 6 |
| Multiply/Div | - × + | Negative Result | -2 × 3 = -6 |
| Multiply/Div | + × - | Negative Result | 2 × -3 = -6 |