The properties of numbers refer to the basic rules that govern how numbers behave in mathematics. These include the commutative property, which states that the order of addition or multiplication does not change the result, and the associative property, which indicates that the way numbers are grouped does not affect the sum or product. Another important property is the distributive property, which combines addition and multiplication, showing that multiplying a number by a sum is the same as multiplying each addend separately and then adding the results. Understanding these properties helps simplify calculations and solve mathematical problems more efficiently.