Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 5.5 Real Numbers and Their Properties.

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Presentation transcript:

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 5.5 Real Numbers and Their Properties

Copyright 2013, 2010, 2007, Pearson, Education, Inc. What You Will Learn Properties of Real Numbers Closure Commutative Associative Distributive 5.5-2

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Real Numbers The set of real numbers is formed by the union of the rational and irrational numbers. The symbol for the set of real numbers is

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Relationships Among Sets Irrational numbers Rational numbers Integers Whole numbers Natural numbers Real numbers 5.5-4

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Relationships Among Sets Real Numbers Rational Numbers Integers Natural Numbers Irrational Numbers Fractions Terminating or repeating decimal numbers Zero Negative Integers 5.5-5

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Properties of the Real Number System Closure If an operation is performed on any two elements of a set and the result is an element of the set, we say that the set is closed under that given operation

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Properties of the Real Number System Commutative Property for any real numbers a and b. Addition a + b = b + a Multiplication a b = b a 5.5-7

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Properties of the Real Number System Associative Property for any real numbers a, b and c. Addition (a + b) + c = a + (b + c) Multiplication (a b) c = a (b c) 5.5-8

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Properties of the Real Number System Distributive Property of Multiplication over Addition for any real numbers a, b and c. a (b + c) = a b + a c 5.5-9

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 2: Identifying Properties of Real Numbers Name the property illustrated. a)2 + 5 = Commutative property of addition b)(x + 3) + 5 = x + (3 + 5) Associative property of addition c)4 (3 y) = (4 3) y Associative property of multiplication

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 2: Identifying Properties of Real Numbers Name the property illustrated. d)9(w + 3) = 9 w Distributive property of multiplication over addition e)5 + (z + 3) = 5 + (3 + z) Commutative property of addition

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 2: Identifying Properties of Real Numbers Name the property illustrated. f)(2p) 5 = 5 (2p) Commutative property of multiplication

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Simplify by Using the Distributive Property Simplify

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 4: Distributive Property Use the distributive property to multiply 2(x + 5). Then simplify the result