Most of these problems are the commutative property:
Addition
a + b = b + a
Multiplication
a * b = b * a
and the associative property:
Addition
(a + b) + c = a + (b + c)
Multiplication
(a * b) * c = a * (b * c)
There's also the Identity property:
Addition \ Subtraction:
a + 0 = a \ a - 0 = a
Multiplication \ Division:
a * 1 = a \ a / 1 = a
