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. We also learned how to express relationships in mathematical form. 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, 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. Formulas and Properties • Associative property of addition 72 • Associative property of multiplication 72 • Average 64 • Commutative property of addition 72 • Commutative property of multiplication 72 • Complementary angles 52 • Distributive property 73 • Fundamental property of fractions 16 • Identity property of addition 71 • Identity property of multiplication 71 • Inverse property of addition 71 • Inverse property of multiplication 71 • Order of operations 29, 51 • Percent change 64 • Supplementary angles 53 Terms Absolute value 9 Additive identity 71 Additive inverse 71 Algebraic expression 30 Average 64 Base 27 Coefficient 77 Composite 14 Constant terms 77 Dividend 61 Divisor 61 Equation 31 Ellipsis 2 Equivalent fractions 21 Exponential expression 27 Factor 13 Factor tree 14 Finite 2 Fraction 15 Identity element 71 Improper fraction 15 Infinite 2 Integer 3 Inverse 71 Irrational number 3 Least common denominator (LCD) 21 Like terms 78 Lowest terms 16 Member or element 2 Mixed number 15 Multiplicative identity 71 Multiplicative inverse 71 Natural number 3 Numerator and denominator 15 Opposite 8 Perimeter 34 Prime factorization 14 Prime number 14 Proper fraction 15 Rational number 3 Real number 3 Real number line 5 Reciprocal 19 Right angle 52 Roster method 2 Set 2 Set-builder notation 2 Simplified 16 Solve an equation 31 Solution of an equation 31 Square root 3 Straight angle 53 Term 77 Unlike terms 78 Variable 2 Variable term 77 Whole number 3 85
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