Properties of addition, subtraction, multiplication, division and exponentiation
a + 0	a	addition property of 0
0 + a	a	addition property of 0
a + b	b + a	commutative property of addition
(a + b) + c	a + (b + c)	associative property of addition
a · 0	0	multiplication property of 0
0 · a	0	multiplication property of 0
a · 1	a	multiplication property of 1
1 · a	a	multiplication property of 1
a b	b a	commutative property of multiplication
(a b) c	a (b c)	associative property of multiplication
a (b + c)	a b + a c	distributive property
a / 0	not in my class!	division property of 0
a / 1	a	division property of 1
a 0	1	exponentiation property of 0
a 1	a	exponentiation property of 1
a b a c	a b + c	multiplying with common base
a bc	a b c	raising an exponent to an exponent
(a b) c	a c b c	raising multiple values in parentheses to a common power
a c + b c	a + b c	addition of fractions
a b	a · c b · c	multiplication of both terms of a fraction
a b	a ÷ c b ÷ c	division of both terms of a fraction
a b · c d	a · c b · d	multiplication of two fractions
a b ÷ c d	a b · d c	division of two fractions
a b · b a	1	multiplication of reciprocal fractions
a = b	a + c = b + c	addition property of equality
a = b	a - c = b - c	subtraction property of equality
a = b	a · c = b · c	multiplication property of equality
a = b	a c = b c	division property of equality

Negative numbers and addition, subtraction, multiplication and division
+(+a)=+a +(-a)=-a -(+a)=-a -(-a)=+a	addition and subtraction of a number
(+) · (+) = (-) · (-) = (+) (-) · (+) = (+) ·y (-) = (-)	multiplication of two numbers
(+) ÷ (+) = (-) ÷ (-) = (+) (-) ÷ (+) = (+) ÷ (-) = (-)	division of two numbers
(+) (+) (+) = (+) (-) (-) = (-) (-) (+) = (-) (+) (-) = (+) (+) (-) (-) = (-) (+) (+) = (+) (+) (-) = (+) (-) (+) = (-)	division of a fraction