Arithmetic

Arithmetic is the branch of mathematics concerned with numbers and operations such as addition, subtraction, multiplication, and division.

Natural number: A number used for counting, commonly beginning with zero or one depending on convention. Natural numbers provide the basic counting quantities on which elementary arithmetic is built.
Addition: The operation that combines quantities into a sum. Addition combines numbers and serves as the inverse of subtraction.
Mental calculation: Calculation performed without external tools, using memory and numerical strategies. Arithmetic properties enable shortcuts for computing sums, products, and quotients mentally.
Elementary algebra: A branch of mathematics that uses symbols to represent numbers and express relationships among them. Algebra generalizes arithmetic by allowing unknown quantities and variable rules.
Integer: A whole number, its negative, or zero. Integers extend counting numbers so subtraction can produce negative results.
Subtraction: The operation that finds a difference between quantities or removes one quantity from another. Subtraction reverses addition and may require negative numbers.
Long division: A written algorithm for dividing numbers one digit at a time. It applies place value and repeated subtraction to larger division problems.
Number theory: The branch of mathematics that studies integers and their properties. Number theory investigates patterns and structure in the numbers arithmetic calculates with.
Place-value notation: A numeral system in which a digit's value depends on its position and the system's base. Position lets a small set of digits represent large numbers and supports written calculation.
Multiplication: The operation that scales a number or combines equal-sized groups into a product. Repeated equal groups connect multiplication to addition while extending it to scaling.

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