# Properties of Real Numbers

May 28th, 2015
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1. Commutative property : Changing the order of terms/factors in addition/multiplication will not change the sum/product, i.e a + b = b + a for addition & ab = ba for multiplication 2. Associative property: Changing the grouping of

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ALGEBRABlock Diagram of the Number SystemDefinitions:Complex numbers numbers which take the form x + yi where x and y are real numbers.x is the real party is the imaginary parti is the imaginary unit which is equal to Examples: 2 + 3i, 3 4i, -2 + 5iRational number a number which can be expressed as the ratio of two integers such as , , 3, 0.25.Irrational number - a number which can not be expressed as the ratio of two integers such as , , , e.Integer any whole number which can be either negative, zero or positive such as 3, 0, 7.Natural numbers- are positive whole numbers including zero such as 0, 1, 2, 3, 4, . . . .Properties of Real Numbers1. Commutative property : Changing the order of terms/factors in addition/multiplication will not change the sum/product, i.e.a + b = b + a for addition &ab = ba for multiplication2. Associative property: Changing the grouping of terms/factors to be added/multiplied will not change the sum/product, i.e.a + (b + c) = (a + b) + c for additiona(bc) = (ab)c for multiplication3. Distributive property: a(b + c) = ab + ac4. Reflexive property: Any number is equal to itself, i.e. a = a.5. Symmetric property: If a = b, then b = a.6. Transitive property: If a = b and b = c, then a = c.Factors and Special Products1. Difference of two squares: 2. Sum of two cubes: 3. Difference of

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