Adding Subtracting Integers Calculator - Mathematical Calculations & Solutions
Adding & Subtracting Integers Calculator
Step-by-Step Solution:
How It Works
Enter Integers
Input any positive or negative whole numbers (e.g., -5, 0, 7)
Choose Operation
Select addition (+) or subtraction (-) operation
Apply Rules
Calculator applies integer arithmetic rules automatically
Get Result
View step-by-step solution with detailed explanation
Common Examples
Adding & Subtracting Integers Calculator
What
Perform addition and subtraction operations with positive and negative integers.
Why
Foundation for algebra, number theory, and understanding positive/negative number relationships.
Applications
Temperature changes, financial calculations, elevation differences, and basic algebra.
📊 Integer Rules
Integer Operations Reference Table
| Operation Type | Rule | Example | Result |
|---|---|---|---|
| Positive + Positive | Add normally | 8 + 5 | 13 |
| Negative + Negative | Add absolute values, keep negative | (-6) + (-4) | -10 |
| Positive + Negative | Subtract smaller from larger | 9 + (-4) | 5 |
| Negative + Positive | Subtract smaller from larger | (-7) + 3 | -4 |
| Positive - Positive | Subtract normally | 10 - 3 | 7 |
| Positive - Negative | Add the opposite | 6 - (-2) | 8 |
| Negative - Positive | Add negative values | (-5) - 3 | -8 |
| Negative - Negative | Add the opposite | (-4) - (-7) | 3 |
Frequently Asked Questions
What are the fundamental rules for adding integers?
When adding integers with the same sign, add their absolute values and keep the common sign. When adding integers with different signs, subtract the smaller absolute value from the larger and use the sign of the number with the larger absolute value.
How do I subtract integers correctly?
Subtraction of integers follows the rule: a - b = a + (-b). This means subtracting a number is the same as adding its opposite. For example, 5 - 3 = 5 + (-3) = 2, and 5 - (-3) = 5 + 3 = 8.
What happens when adding positive and negative integers?
When adding a positive and negative integer, find the difference between their absolute values. The result takes the sign of the integer with the larger absolute value. For example: 7 + (-3) = 4 (positive), and (-7) + 3 = -4 (negative).
Can integer operations result in zero?
Yes! Zero results occur when: (1) adding opposites like 5 + (-5) = 0, (2) subtracting a number from itself like 7 - 7 = 0, or (3) when the absolute values are equal in addition with different signs.
What are practical applications of integer operations?
Integer operations are used in: temperature calculations (above/below freezing), financial transactions (credits/debits), elevation changes (above/below sea level), sports scoring, inventory management, and any scenario involving gains and losses or opposing directions.
How do I remember the rules for integer operations?
Use these memory aids: "Same signs, add and keep" for addition with same signs. "Different signs, subtract and keep the larger's sign" for mixed signs. "Subtraction means add the opposite" for all subtraction problems. Practice with a number line visualization.