Put three apples on a table. Add two more, and you have five. That simple act—combining quantities to get a total—is addition, the most basic operation in arithmetic and the foundation for nearly everything else in mathematics.

The result of adding two or more numbers is called the sum. Addition obeys familiar rules: order doesn't matter (3 + 5 equals 5 + 3), and grouping doesn't matter ((2 + 3) + 4 equals 2 + (3 + 4)). These properties—commutativity and associativity—let us rearrange problems without changing the answer. Adding zero leaves a number unchanged.

Children learn addition with counters, fingers, or number lines. Later, the same operation extends to fractions, decimals, negative numbers, and algebraic expressions. In everyday life, addition balances checkbooks, calculates grocery bills, and measures distances. In higher mathematics, it appears as vector addition, matrix addition, and the addition of complex numbers. Each extends the same core idea: putting things together.

• Combines two or more numbers into a sum
• Commutative and associative
• Adding zero leaves a number unchanged
• Extends to fractions, vectors, matrices, and more