Addition Calculator
Add two numbers together with step-by-step solutions and mathematical explanations
Calculate Addition
Enter any positive or negative number
Enter any positive or negative number
Addition Result
Example Calculations
Positive Numbers:
32,948 + 2,938,546 = 2,971,494
With Negative Numbers:
32,948 + (-2,938,546) = -2,905,598
Addition Properties
Commutative Property
A + B = B + A
Order doesn't matter
Associative Property
(A + B) + C = A + (B + C)
Grouping doesn't matter
Identity Property
A + 0 = A
Adding zero doesn't change the number
Addition Tips
When adding a negative number, you're essentially subtracting
The sum of two positive numbers is always positive
The sum of two negative numbers is always negative
Addition is the foundation of all arithmetic operations
Understanding Addition
What is Addition?
Addition is one of the four basic arithmetic operations, along with subtraction, multiplication, and division. It is the process of calculating the total of two or more numbers (called addends) to find their sum.
Key Terms
- •Addends: The numbers being added together (A and B)
- •Sum: The result of the addition operation (C)
- •Plus Sign (+): The symbol representing addition
Addition Formula
A + B = C
Where A and B are the addends (numbers being added) and C is the sum (result).
Special Cases
- Adding Zero: A + 0 = A (Identity Property)
- Adding Negatives: A + (-B) = A - B
- Same Numbers: A + A = 2A (Doubling)
Historical Context
Addition is one of the oldest mathematical operations, with evidence of its use dating back 20,000-18,000 years BC. The plus sign (+) was introduced relatively recently in the 14th century, evolving from the Latin conjunction "et" (meaning "and"). Before that, various symbols were used, including different notations by ancient civilizations like the Egyptians.