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Extra info for Algebra I (Cliffs Quick Review)

Example text

Example 2: Find the intersection. {1, 2, 3} + {3, 4, 5} = {3} The intersection of a set with members 1, 2, 3 and a set with members 3, 4, 5 is a set with only member 3. Variables and Algebraic Expressions A variable is a symbol used to denote any element of a given set—often a letter used to stand for a number. Variables are used to change verbal expressions into algebraic expressions. Example 3: Give the algebraic expression. F 38 4/27/01 9:37 AM Page 38 CliffsQuickReview Algebra I ■ Key words denoting addition: sum plus more than greater than larger than gain increase enlarge rise grow ■ Key words denoting subtraction: difference minus lose less than smaller than fewer than decrease drop lower diminish reduced ■ Key words denoting multiplication: product multiplied by times twice of ■ Key words denoting division: quotient divided by ratio half Evaluating Expressions To evaluate an expression, just replace the unknowns with grouping symbols, insert the value for the unknowns, and do the arithmetic.

F 34 4/27/01 9:37 AM Page 34 CliffsQuickReview Algebra I Chapter Checkout Q&A 1. –12 + 9 = 2. (–2)(–3)(6) = 1+2= 4 3 25 3 4. # 5 36 = 1 1 5. 5 ' 2 = 5 6 3. - 1 6. Change to decimal: 8 7. 8 8. 15 is what % of 60? 9. (3 × 10 )(2 × 10 ) = 4 8 5 4. 5 5. 12 or 2 2 6. 125 7. 8 8. 25% Answers: 1. –3 2. 36 3. 12 9 12 5 5 12 9. F 4/27/01 9:37 AM Page 35 Chapter 3 TERMINOLOGY, SETS, AND EXPRESSIONS Chapter Check-In ❑ Set theory ❑ Algebraic expressions ❑ Evaluating expressions nderstanding the language of algebra and how to work with algebraic expressions will give you a good foundation for learning the rules of U algebra.

54 = 49 50 Important equivalents that can save you time Memorizing the following can eliminate computations. 50 = 350% Percent A fraction whose denominator is 100 is called a percent. The word percent means hundredths (per hundred). So 37% = 37⁄100 Changing decimals to percents To change decimals to percents, 1. Move the decimal point two places to the right. 2. Insert a percent sign. 85 = 185% Changing percents to decimals To change percents to decimals, 1. Eliminate the percent sign. 2. Move the decimal point two places to the left (sometimes, adding zeros will be necessary).