Mathematical properties are fundamental rules that describe how numbers and operations behave. These properties help simplify calculations and solve problems. Common properties 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 grouping of numbers does not affect the outcome. Another important property is the distributive property, which allows us to multiply a number by a sum or difference by distributing the multiplication across each term. Understanding these properties is essential for mastering basic arithmetic and algebra, making them valuable tools in mathematics.