Outline of arithmetic

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

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