About

Understanding how negative numbers interact is a fundamental hurdle in early mathematics education. The concept that "subtracting a negative is equivalent to adding a positive" can be abstract and confusing. This Integer Operations Calculator bridges the gap between abstract rules and visual reality.

Designed for students, teachers, and parents, this tool does not just give the answer; it maps the operation onto a number line. This visual feedback reinforces the directionality of numbers—positive movements to the right, negative movements to the left—providing a concrete mental model for arithmetic with integers.

Formulas

The core logic of integer arithmetic relies on the interaction of signs:

a - (-b) = a + b

When multiplying or dividing:

+ × - = -

Reference Data

Operation	Rule	Example	Result
Add Positive	Move Right	3 + 2	5
Add Negative	Move Left	3 + (-2)	1
Subtract Positive	Move Left	3 - 2	1
Subtract Negative	Move Right (Double Negative)	3 - (-2)	5
Multiply Signs	Same Signs = Positive	-2 × -3	6
Multiply Signs	Different Signs = Negative	-2 × 3	-6

Frequently Asked Questions

Think of a negative number as 'debt'. If you subtract (remove) debt from someone, they are financially better off (positive). On a number line, subtracting reverses the direction. Since a negative number already points left, reversing it points right (addition).

The magnitude of the result is the same as normal division, but the sign follows the rule: positive divided by negative equals negative. The tool visualizes this result accurately.

This tool is optimized for Integers (whole numbers) to maintain a clean visual number line for educational purposes, but it will calculate decimals if entered.

Zero is neither positive nor negative. It is the neutral origin point on the number line.