45 Chapter 1 / REVIEW Real Numbers and Algebraic Expressions What’s the big idea? Chapter 1 provides us with the skills to simplify numerical expressions by applying the rules for signed numbers, the properties of real numbers, and the order of operations. These rules and properties also provide the framework for us to simplify and evaluate algebraic expressions. Translating phrases to their mathematical form was also shown. These skills form the foundation for algebra and will be used in every section of this text. Success in this course depends on mastering these skills. The Tools Study Tips Listed below are the key terms, skills, and formulas, and properties you should know for this chapter. The page reference is provided if you need additional help with the given topic. The Study Tips will assist in your preparation for an exam. 1. Learn all of the terms, formulas, and properties. Make flash cards and have someone quiz you. 2. Rework problems from the exercises and also the ones you worked in class. Work additional problems from the review exercises. 3. Review the summaries of key concepts. 4. Work the chapter test. 5. Be sure to review the online resources for additional study materials. Terms Absolute value 9 Additive identity 33 Additive inverse 8, 33 Algebraic expressions 23 Associative property 34 Base 20 Circumference 26 Coefficients 35 Commutative property 34 Empty set 2 Equation 37 Evaluate an algebraic expression 24 Exponent 20 Finite set 2 Identity element 33 Inequality 37 Infinite set 2 Integers 4 Intersection of sets 3 Inverse 33 Irrational numbers 5 Like terms 35 Member or element 2 Multiplicative identity 33 Multiplicative inverse 33 Natural numbers 4 Net worth 25 Opposite 8 Origin 7 Rational numbers 5 Real number line 7 Real numbers 5 Reciprocal 19 Roster method 2 Set 2 Set-builder notation 2 Simplify an expression 35 Square root 5 Subscripts 24 Subset 2 Term 35 Union of sets 3 Variable 2 Whole numbers 4 Formulas and Properties • Associative properties 34 • Commutative properties 34 • Distributive property 34 • Division properties with zero 19 • Dividing rule 19 • Exponential notation 20 • Identity properties 33 • Inverse properties 33 • Order of operations 22 • Product property of zero 18 • Subtraction rule 16
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