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

• Elementary arithmetic
• Decimal arithmetic
• Decimal point
• Numeral
• Place value

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
  • Associative property
  • Distributive property
  • Commutative property
• Factorial – Multiplication of numbers from the current number to 0

Types of numbers

• Real number
  • Rational number
    • Integer
      • Natural number
    • Composite number
  • Irrational number
• Odd number
• Even number
• Positive number
• Negative number
• Prime number
  • List of prime numbers
• Highly composite number
• Perfect number
• Algebraic number
• Transcendental number
• Hypercomplex number
• Transfinite number
• Indefinite and fictitious numbers

Elementary statistics

• Mean
  • Weighted mean
• Median
• Mode
• Range

Other basic concepts

• Combinations
• Percentage
• Permutations
• Proportion
• Rounding
• Scientific notation

Modern arithmetic

• Outline of number theory
• Riemann zeta function
• L-functions
• Multiplicative functions
• Modular forms

See also

• Elementary mathematics
• Table of mathematical symbols

External links

• MathWorld article about arithmetic
• The New Student's Reference Work/Arithmetic (historical)
• Maximus Planudes' the Great Calculation an early western work on arithmetic at Convergence