Outline of arithmetic

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Arithmetic is an elementary branch of mathematics that is widely used for tasks ranging from simple day-to-day counting to advanced science and business calculations.

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