# Arithmetic Index

Arithmetic is a subject in math that covers the basic manipulation and properties of numbers.

## Notation

A dot between two numbers denotes multiplication in mathematics.

In mathematics there are multiple different ways to represent division. The obelus is often used in elementary mathematics, then later the horizontal bar is adopted for convenience, and the forward slash is used because of the prevelence of computers and calculators.

In mathematics parentheses are used to group expressions to be evaluated together and organize the order of operations. Everything within the parantheses is evaluated, then the rest of the calculation is carried out.

Two expressions placed next to eachother and separated by parenthesis are assumed to be multiplied together.

In mathematics when two variables are next to each other the implied operation is multiplication. This makes many equations and formulas more simple.

In mathematics the plus symbol represents addition between two numbers. Addition is the process of combining two things together.

The decimal point is used to separate the whole part of a number from the decimal part. The whole part is represented using number digits to the left of the decimal point. The decimal part is also represented using digits to the right of the decimal point.

A fraction is represented using a horizontal bar between two expressions. The expression on top is called the numerator and the expression on bottom is called the denominator.

The syntax for a ratio is two numbers separated by the colon symbol.

In mathematics the minus symbol represents the subtraction operator. The expression on the right is subtracted from the expression on the left.

## Operators

Addition is a basic operation in mathematics for combining two numbers together. It is a binary operation denoted with the plus symbol with an expression on the left and an expression on the right.

Subraction is a basic arithmetic operation of taking away one number from another number.

Multiplication is a basic arithmetic operation performed on two numbers. Multiplying a number by another number is the same as taking n groups of the other number.

The division operator returns the result of dividing one number by another number.

The modulus operator returns the remainder of dividing the first expression by the second expression.

## Concepts

Counting is the process of calculating the quantity of a group of objects.

Base ten is the representation of numeric values using the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In combination with the decimal system it forms the basis for how people write and use numbers.

The fundamental theory of arithmetic states that every number greater than 1 is either a prime number or composed by a unique product of prime numbers.

In math an interval represents the valid values between an upper limit and a lower limit.

There are three propreties of addition: the commutative property, associative property, and the identity property.

There are four properties of the multiplication operation in mathematics: the commutative property, associative property, identity property, and distributive property.

## Examples

To find the factors of a number, test if the number is divisible by all of the numbers from one up to the number, if it is divisible then it is a factor.

## Functions

The exponential function models exponential growth. The output of the function at any given point is equal to the rate of change at that point. For real number input, the function conceptually returns Euler's number raised to the value of the input.

The absolute value returns the distance from zero of the input.

Returns the integer part of the number n.

Returns the greatest common denominator of the two numbers a and b.

Returns true if the number n is prime, false otherwise.

Returns the logarithm with a base of b of the number x.

Returns the remainder of dividing x by n.

Returns the natural logarithm of the number x.

Returns the result of b raised to the y power.

Returns the square root of n.