Addition, multiplication, subtraction, and division are the operations of arithmetic. Addition of the two real numbers `a` and `b` is designated by `a+b`. If `a+b=c`, then `c` is the sum and the real numbers `a` and `b` are called terms.

Multiplication of the real numbers `a` and `b` is designated by `ab` or `a*b`. If `ab=c`, then `c` is the product and the real numbers `a` and `b` are called factors.

The number `-b` is referred to as the additive inverse of `b`. Subtraction of the real numbers `a` and `b` is designated by `a-b` and is defined as the sum of `a` and the additive inverse of `b`. That is,

`a-b=a+(-b)`
If `a-b=c`, then `c` is called the difference of `a` and `b`.

The multiplicative inverse or reciprocal of the nonzero number `b` is `1/b`. The division of `a` and `b`, designated by `a-:b` with `b!=0`, is defined as the product of `a` and the reciprocal of `b`. That is,

`a-:b=a(1/b)` provided that `b!=0`
If `a-:b=c`, then `c` is called the quotient of `a` and `b`. The notation `a-:b` is often represented by the fractional notation `a//b` or `a/b`. The real number `a` is the numerator, and the nonzero real number `b` is the denominator of the fraction.

Properties of Real Numbers
Let `a`, `b`, and `c` be real numbers.
	Addition Properties	Multiplication Properties
Closure	`a+b` is a unique real number	`ab` is a unique real number
Commutative	`a+b=b+a`	`ab=ba`
Associative	`(a+b)+c=a+(b+c)`	`(ab)c=a(bc)`
Identity	There exists a unique real number `0` such that `a+0=0+a=a`	There exists a unique real number `1` such that `a*1=1*a=a`
Inverse	For each real number `a`, there is a unique real number `-a` such that `a+(-a)=(-a)+a=0`	For each nonzero real number `a`, there is a unique real number `1/a` such that `a*1/a=1/a*1=1`
Distributive		`a(b+c)=ab+ac`

An equation is a statement of equality between two numbers or two expressions. There are four basic properties of equality that relate to equations.

Properties of Equality
Let `a`, `b`, and `c` be real numbers.
Reflexive	`a=a`
Symmetric	If `a=b`, then `b=a`
Transitive	If `a=b` and `b=c`, then `a=c`.
Substitution	If `a=b`, then `a` may be replaced by `b` in any expression that involves `a`.