The basic properties of real numbers, including the associative, commutative, identity, inverse and distributive properties, are important to understand when learning addition and multiplication. They are also the building blocks for beginning algebra. Once you understand each property, you can use them to solve many different mathematical problems. Using the name of each property to remember the property itself is the easiest way to keep them straight.
Associate the associative property with the word associate. The associative property describes how you can group different sets of numbers together when adding or multiplying with the same result. Remember that in addition and multiplication, numbers or variables can associate with each other in different groups for the same result.
Connect the commutative property to the word commute, or travel. According to the commutative property, when adding or multiplying numbers or variables the order does not matter. The numbers or variables can "commute" from one position to another and the result will be the same.
Remember the identity property is a number that can be added to or multiplied by a number without changing its identity. In addition, the identity property is zero, because adding zero to any number results in the original number. In multiplication, the identity property is one.
Think of the reverse to help you remember the inverse property. The inverse property of addition means that for every number (x) there is a negative (-x) that will result in zero when added. The inverse property of multiplication shows that for every number (x) there is a number (1/x) that when multiplied by x will result in one.
Think of handing out or distributing a number throughout a quantity when multiplying to remember the distributive property. For example, if you have an equation of 2(x+y) you can distribute the 2 to write the equation as 2x+2y.