Adding Integers Calculator - Mathematical Calculations & Solutions
How It Works
Enter Integers
Input any two whole numbers (positive or negative)
Get Solution
See instant result with step-by-step explanation
Common Examples
Positive + Positive
Example: 15 + 8
Rule: Add normally
Result: 23
Negative + Negative
Example: (-7) + (-4)
Rule: Add and keep negative
Result: -11
Mixed Signs
Example: 12 + (-5)
Rule: Subtract smaller from larger
Result: 7
What is Adding Integers Calculator?
What
A free online tool that adds any two integers (positive, negative, or zero) and shows step-by-step solutions.
Why
Essential for learning math basics, homework help, and understanding integer operations with clear explanations.
Applications
Math education, homework solving, test preparation, and building strong foundation in arithmetic operations.
Integer Addition Rules & Examples
📊 Detailed Examples with Solutions
Integer Addition Table
| First Integer | Second Integer | Sum | Rule Applied | Type |
|---|---|---|---|---|
| 15 | 8 | 23 | Add directly | Both positive |
| -12 | -7 | -19 | Add and keep negative | Both negative |
| 20 | -13 | 7 | Subtract smaller from larger | Mixed signs |
| -25 | 18 | -7 | Subtract and keep larger sign | Mixed signs |
| 0 | 35 | 35 | Identity property | Zero addition |
| 14 | -14 | 0 | Additive inverse | Opposites |
*These examples show the three main rules for adding integers
Understanding Integer Addition
What are Integers?
Integers are whole numbers that include:
- • Positive numbers: 1, 2, 3, 4, 5...
- • Negative numbers: -1, -2, -3, -4, -5...
- • Zero: 0
Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
Addition Rules
Frequently Asked Questions
What are integers and how do I add them?
Integers are whole numbers including positive numbers (1, 2, 3...), negative numbers (-1, -2, -3...), and zero. To add integers, follow simple rules based on their signs.
How do I add two positive integers?
When adding two positive integers, simply add them together like regular numbers. For example: 15 + 8 = 23. This is the easiest type of integer addition.
How do I add two negative integers?
When adding two negative integers, add their absolute values and keep the negative sign. For example: (-7) + (-4) = -(7 + 4) = -11.
What happens when I add integers with different signs?
When adding integers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. Example: 12 + (-5) = 7.
What is the identity property of addition?
The identity property states that adding zero to any integer gives the same integer: 7 + 0 = 7. Zero is called the additive identity because it doesn't change the value.
What are additive inverses or opposite numbers?
Additive inverses are pairs of numbers that add up to zero. For example: 8 + (-8) = 0. Every integer has an additive inverse: the positive version for negative numbers and vice versa.
Can I use this calculator for homework and tests?
Yes! This calculator is perfect for checking your homework answers, understanding step-by-step solutions, and practicing integer addition. It shows the work so you can learn the process.
Why is learning integer addition important?
Integer addition is fundamental for algebra, solving equations, working with coordinates, understanding temperature changes, financial calculations, and many real-world applications in science and engineering.