These are a series of phenomena that we see particularly in addition and multiplication operations that allow us to make many different moves in both algebra and calculus. They really seem likes common sense, but they are so helpful when we need to move things around in an equation or expression. The most common property we observe and use to our advantage is the commutative property. The basic premise is that the order of the real numbers does not affect the overall solution. The second premise, called the associative property, builds off of the first premise. This applies to when parenthesis around sums or products, in this case the order you perform them does not affect the outcome. The identity property tells us that any value you add to zero is itself. The distributive property talks to multiplying a factor to group of real numbers. If we are adding several real numbers found in parenthesis and multiplying the sum, it is the same as multiplying the outside by each number and adding their products.
The worksheets on this page focus on real numbers. They are values that are representative of some value that can be found on a number line. The most commonly taught properties in the Commutative Property of both addition and multiplication. Those properties basically reinforce the common mathematically rule that order does not matter as long as the operations have not changed. Another well discussed property is the Associative Property of addition and multiplication. This expands the concept of regrouping with parenthesis (normally). The minute students begin to learn multiplication the zero property of multiplication is instantly engrained in their memory. When we begin to learn negative numbers and operations with them, the Additive Inverse Property appears. We seldom hear that property being named in classrooms today. Below you worksheets that highlight the use of the Associative, Commutative, Distributive, Operations and Numeracy rules, and the Division Principle.