Outline of arithmetic

The following outline is provided as an overview of and topical guide to arithmetic:

Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms, and the use of such operations to perform more complicated calculations.

Arithmetic is fundamental for both pure mathematics and its practical application to science and daily life. In pure mathematics, arithmetic is defined formally for various types of numbers, such as integers, fractions of integers (rational numbers), and real numbers. In practical application, arithmetic is usually approximate, operating on decimal or binary numbers, with rounding.

Essence of arithmetic

History of arithmetic

Arithmetic operations and related concepts

Order of operations
Addition
- Summation – Answer after adding a sequence of numbers
- Additive inverse
Subtraction – Taking away numbers
Multiplication – Repeated addition
- Multiple – Product of multiplication
  - Least common multiple
- Multiplicative inverse
Division – Repeated subtraction
- Modulo – The remainder of division
- Quotient – Result of division
- Quotition and partition – How many parts are there, and what is the size of each part
- Fraction – A number that is not whole, often shown as a division equation
  - Decimal fraction – Representation of a fraction in the form of a number
  - Proper fraction – Fraction with a numerator that is less than the denominator
  - Improper fraction – Fractions with a numerator that is any number
  - Ratio – Showing how much one number can go into another
  - Least common denominator – Least common multiple of two or more fractions' denominators
- Factoring – Breaking a number down into its products
  - Fundamental theorem of arithmetic
  - Prime number – Number divisible by only 1 or itself
    - Prime number theorem
    - Distribution of primes
  - Composite number – Number made of two smaller integers
  - Factor – A number that can be divided from its original number to get a whole number
    - Greatest common factor – Greatest factor that is common between two numbers
    - Euclid's algorithm for finding greatest common divisors
Exponentiation (power) – Repeated multiplication
- Square root – Reversal of a power of 2 (exponent of 1/2)
- Cube root – Reversal of a power of 3 (exponent of 1/3)
Properties of Operations
Factorial – Multiplication of numbers from the current number to 0