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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.

negative numbers integers math rules sign changes algebra

Formulas

The calculator adheres to the algebraic field properties of integers Z.

For Subtraction: a (b) a + b
For Multiplication: a × b = ab

The absolute value |x| determines the sign when adding integers with different signs. If |negative| > |positive|, the result is negative.

Reference Data

OperationInput SignsSign Change RuleExample
Addition+ + +Add values, keep sign2 + 3 = 5
Addition- + -Add values, keep sign-2 + -3 = -5
Subtraction+ -Double negative becomes positive2 (-3)2 + 3
Subtraction- +Same as adding two negatives-2 3-5
Multiply/Div+ × +Positive Result2 × 3 = 6
Multiply/Div- × -Positive Result-2 × -3 = 6
Multiply/Div- × +Negative Result-2 × 3 = -6
Multiply/Div+ × -Negative Result2 × -3 = -6

Frequently Asked Questions

Subtraction is defined as adding the additive inverse. The inverse of a negative number is positive. Therefore, removing a debt (negative) is mathematically equivalent to receiving a gain (positive).
The negatives cancel each other out. The rule is that like signs result in a positive quotient, while unlike signs result in a negative quotient.
Zero is neither positive nor negative. Operations involving zero follow standard identity properties (e.g., adding zero changes nothing; multiplying by zero results in zero).