Reals Operations Properties Base 5 Divisibility Prime Numbers GCD & LCM

Properties of Real Numbers

The set of real numbers has many properties. Some of the subsets we have studied have these properties too. A property is something that always holds true, no matter which number or operation you choose.

To determine whether a subset has these properties, choose a set of numbers (such as the Whole Numbers), an operations (such as Addition), and a property (such as Closure). Check to see if the property holds for all numbers in the set under that operation.

  • Closure property -- operating on any two elements of the set yields a number in the set
  • Commutative property -- operating on two elements of the set can be done in any order
  • Associative property -- operating on three or more elements of the set can be done in any order
  • Identity element property -- operating on any number of the set with the identity element yields the original number
  • Zero multiplication property -- multiplying by zero always gives zero
  • Distributive property -- distribution of multiplication over addition/subtraction in the parentheses
  • Inverse property -- operating on a number and its "inverse" gives the identity element

Blank properties chart for taking notes

Properties charts