R 2 Real Numbers and Their Properties Sets
R. 2 Real Numbers and Their Properties Sets of Numbers and the Number Line ▪ Exponents ▪ Order of Operations ▪ Properties of Real Numbers ▪ Order on the Number Line ▪ Absolute Value Copyright © 2017, 2013, 2009 Pearson Education, Inc. 1
R. 2 Example 1 Identifying (page 10) Sets of Numbers List the elements of S that belong to each set. (a) natural numbers (b) whole numbers Copyright © 2017, 2013, 2009 Pearson Education, Inc. 2
R. 2 Example 1 Identifying (cont. ) Sets of Numbers List the elements of S that belong to each set. (c) integers (d) rational numbers All elements of S except Copyright © 2017, 2013, 2009 Pearson Education, Inc. 3
R. 2 Example 1 Identifying (cont. ) Sets of Numbers List the elements of S that belong to each set. (e) irrational numbers (f) real numbers Copyright © 2017, 2013, 2009 Pearson Education, Inc. All elements of S are real numbers. 4
R. 2 Example 2 Evaluating Exponential Expressions (page 11) Evaluate each expression and identify the base and the exponent. (a) Base: 10 Exponent: 3 (b) Copyright © 2017, 2013, 2009 Pearson Education, Inc. Base: – 3 Exponent: 4 5
R. 2 Example 2 Evaluating Exponential Expressions (cont. ) Evaluate each expression and identify the base and the exponent. (c) Base: 3 Exponent: 4 Base: 5 Exponent: 2 (d) (e) Copyright © 2017, 2013, 2009 Pearson Education, Inc. Base: 10 Exponent: 2 6
R. 2 Example 3(a) (page 12) Using Order of Operations Evaluate Copyright © 2017, 2013, 2009 Pearson Education, Inc. = 19 7
R. 2 Example (cont. ) 3(b) Using Order of Operations Evaluate Copyright © 2017, 2013, 2009 Pearson Education, Inc. 8
R. 2 Example (cont. ) 3(c) Using Order of Operations Evaluate Copyright © 2017, 2013, 2009 Pearson Education, Inc. 9
R. 2 Example (cont. ) 3(d) Using Order of Operations Evaluate Copyright © 2017, 2013, 2009 Pearson Education, Inc. 10
R. 2 Example 4(a) (page 13) Evaluate = – 6. Copyright © 2017, 2013, 2009 Pearson Education, Inc. Using Order of Operations using x = – 4, y = 3, and z Substitute 11
R. 2 Example (cont. ) 4(b) Using Order of Operations Evaluate z = – 6. Copyright © 2017, 2013, 2009 Pearson Education, Inc. using x = – 4, y = 3, and Substitute – 12
R. 2 Example (cont. ) Evaluate Copyright © 2017, 2013, 2009 Pearson Education, Inc. 4(c) Using Order of Operations using x = – 4, y = 3, and z = – 6. 13
R. 2 Example 5(a) Simplifying Expressions (page 15) Simplify (12 + 2 x) + 18 = (2 x + 12) + 18 Copyright © 2017, 2013, 2009 Pearson Education, Inc. = 2 x + (12 + 18) Commutative property Associative property = 2 x + 30 14
R. 2 Example 5(b) Simplifying Expressions (cont. ) Simplify Copyright © 2017, 2013, 2009 Pearson Education, Inc. Associative property 15
R. 2 Example 5(c) Simplifying Expressions (cont. ) Simplify Copyright © 2017, 2013, 2009 Pearson Education, Inc. Commutative property Associative property Commutative property 16
R. 2 Example 6 Using the Distributive Property (page 15) Rewrite using the distributive property and simplify. (a) (b) Copyright © 2017, 2013, 2009 Pearson Education, Inc. 17
R. 2 Example 6 Using the Distributive Property (cont. ) Rewrite using the distributive property and simplify. (d) Copyright © 2017, 2013, 2009 Pearson Education, Inc. 18
R. 2 Example 6 Using the Distributive Property (cont. ) Rewrite using the distributive property and simplify. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 19
R. 2 Example 7 Evaluating Absolute Values (page 16) Evaluate each expression: (a) (b) (c) (d) Copyright © 2017, 2013, 2009 Pearson Education, Inc. 20
R. 2 Example 8 Measuring Blood Pressure Difference (page 17) Find Pd for a patient with a systolic pressure, P, of 146. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 21
R. 2 Example 9 Evaluating Absolute Value Expressions (page 18) Let m = 13 and n = – 9. Evaluate each expression. (a) (b) Copyright © 2017, 2013, 2009 Pearson Education, Inc. 22
R. 2 Example 10 Finding the Distance between Two Points (page 19) Find the distance between – 8 and 14. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 23
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