Operation/Property	Rule	Note
Additive Inverse	The additive inverse of a is -a
Double Negative	-(-a) = a
Absolute Value		Absolute value is distance from 0 on the number line.
Adding two numbers with the same sign	Add their absolute values and put the common sign in front.
Adding two numbers with opposite signs	Subtract their absolute values. Answer "+" if positive number has larger absolute value. Answer "-" if negative number has larger absolute value.	Sum of 2 positive numbers is positive. Sum of 2 negative numbers is negative. In a + b = c, a, b, and c are terms.
Subtraction	a - b = a + (-b)
Multiplication	Product of two numbers with like signs is positive. Product of two numbers with opposite signs is negative.	Product is the result from multiplying. In a x b = c, a and b are factors and c is the product.
Multiplicative property of zero	a x 0 = 0 0 x a = 0
Division	Quotient of two numbers with like signs is positive. Quotient of two numbers with opposite signs is negative.	Quotient is the result from dividing.

Property	Addition	Multiplication
Commutative	a + b = b + a	ab = ba
Associative	(a + b) + c = a + (b + c)	(ab)c = a(bc)
Identity	a + 0 = a 0 + a = 0 0 is the additive identity element	a x 1 = a 1 x a = a 1 is the multiplicative identity element
Inverse	a + (-a) = 0 (-a) + a = 0 0 is the additive inverse or opposite of a	1 is the multiplicative inverse or reciprocal of a, a nonzero
Distributive (of multiplication over addition)	a(b + c) = ab + ac a(b + c + d + ... + n) = ab + ac + ad + ... + an

For real numbers a, b, c, and d:

	Note
	Invert and Multiply