0 : nuilsee/^p^^ \ \-bs J"" Chapter R SUMMARY View the interactive Summary on the Pass the Test CD.

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1 44 CHAPTER i Review of the Real Number System Chapter R SUMMARY View the interactive Summary on the Pass the Test CD. KEY TERMS elements fmembers) Unite set infinite set empty ser (null set) variable set-builder notation number line coordinate graph additive inverse (opposite, negative) 1.2 signed numbers absolute value equation inequality interval interval notation thret-part inequality sum difference product quotient reciprocal mutltipliealive inverse) factors exponent (power) base exponential expression square root principal (positive) square root negative square root algebraic expression identity element for addition identity element for multiplication term coefficient (numerical coefficient) like terms unlike terms combining like terms NEW SYMBOLS set containing (*] r has property P) infinity «7,A] the elements a.set-builder notation 3C negative and h M absolute value of x infinity a" $ or { \ eniply set < is less than f-ao, =c) set of all real V is an element of < is less than or equal numbers (a set) to the interval is not an > is greater than element of > is greater than or ( so, a) the inierval i.s not equal to equal to {x\x < a} {x\a < X < b) m factors of a radical sign positive (or principal) square root of a TEST YOUR WORD POWER See how well vou have learned the vocabulary in this chapter. Answers, with examples, follow the Quick Review. J. The empty set is a set A. with 0 as its only element B. with an infinite number of elements C. with no elements I), of ideas. 2. A variable is A. a symbol used to represent an unknown number B. a value that makes an equation true C. a solution of an equation I), the answer in a division problem. 3. The absolute value of a number is A. the graph of the number B. the reciprocal of the number C. the opposite of the number 1). the disiance between f) and the number on.i number line. G> 4. The reciprocal of a nonzero number a is A. a B. 5. A factor is C. -a D. 1. A. the answer in an addition problem B. the answer in a multiplication problem 0. one of two or more numbers that are added to get another number I), any number that divides evenly into a given number. 6. An exponential expression is A. a number (hat is a repeated factor in a product B. ;i number or a variable written with an exponent C. a number (hat.shows how many times a factor is repealed in a product D. an expression that involves addition. 7. A term is A. a numerical factor B. a number or a product of a number and one or more variables raised to powers C. one of several variables with the same exponents I). a sum of numbers and variables raised to powers. 8. A numerical coefficient is A. the numerical factor in a term B. the number of terms in an expression C. a variable raised to a power D. the variable factor in a term. 0 : nuilsee/^p^^ \ \-bs J""

2 CHAPTER i Summary 45 QUICK REVIEW <5> Concepts Examples 1.1 BASIC CONCEPTS Sets of Numbers Natural Numbers {I, 2, 3, 4,...) Whole Numbers (0, , 4 } Integers { , 0, 1, 2,...} ,4,9 Rational Numbers [f\p and q are integers. $ oj (all terminating or repealing decimals!.-0.14, 0.6., Irrational Numbers {x\x is a real number that is not rational} 77. V'3. -V22 tali nonterminating. nonrepeating decimals) Real Numbers {x\x is a rational or an irrational number} a if a is positive or 0 Absolute Value \a = \ a if a is neg Hive 1.2 OPERATIONS ON REAL NUMBERS Addition Same Sign: Add the absolute values. The sum has the same sign as the given numbers. Different Signs: Find the absolute values of the numbers, and subtract the smaller absolute value from the larger. The sum has the same sign as the number with the larger absolute value. Subtraction For all real numbers a and a - b = a + (-b) ] (-71 = -(2 + 7) = S = 8-5 = = -(12-4) = -8-5 < 3) = -5-3 = -2 c-c,c) A ^HhV -c_ C (-to, oo) \y_\l-c 4 Multiplication and Division Same Sign: The answer is positive when multiplying or dividing two numbers with the same sign. Different Signs: The answer is negative when multiplying or dividing iwo numbers with different.signs. Division 1-or all real numbers a and h (where b ^ 0). -3I-8) = 24-7(5) = a - b 5_2^ 6 6 ~ 3 5 (continued) ( r jjr+-- (0)0 ) (-00,0) 1> ^ ivi4e^a^ 2 = H v * 1 x ' iv"r<^h(fkc4 ^ b * ^

3 46 CHAPTER i Review of the Real Number System Concepts Examples 1.3 EXPONENTS, ROOTS, AND ORDER OF OPERATIONS The product of an even number of negative factors ( 5) is positive: ( 5) : = ( 5)1 5) = 25 is positive. The product of an odd number of (-5, is negative: (-5)-' - (-5X-5X-5) = -125 negative factors is negative. Order of Operations Work separately above and below any fraction 5.3 ~ It) 2 bar. \ 2. If parentheses, brackets, or absolute value I 6)[2" 4)] + 3 bars are present, start with the innermost set and work outward. 3. Evaluate all exponents, roots, and absolute = (-6)[2 : - 7] + 3 = t-6);4-7] + 3 values. ~ (-6);-3] Multiply or divide 111 order from left to right 5. Add or subtract in order from led to right. 1.4 PROPERTIES OF REAL NUMBERS _ For real numbers a. b. and c. W~^)J>)C fe~h\^ Distributive Property = = 21 ai.b + c) = ah + ac ;..(4 + 2) = Inverse Properties a + (-</) = 0 and -a + a = ( = I I. a - - =! and - - «= ).-> = 1 (-3)= I «a 5 3 Identity Properties a + 0 = () + a = a and a 1 = 1 «= a I Commutative Properties a + b = b + a and ab = ba >* + (-3) > n(-4) - (-4)6 Associative Properties a + (b + c) = Ui + b) + c and ai.bc) = <ab)c : + (5 + J) - (7 + 5) + > 4(6 3) < 4-6)3 Multiplication Property of 0 a 0 = 0 and 0 a = = 0 01,-3) = 0 Answers to Test Your Word Power I. C; Examine:TTte set of whole numbers 2. A; Examples: n. b.c 3. D; Examples: \2\~ 2 and j 21 2 less irian 0 is the empty sei. u ritten t). 4. B: Examples; 1 is the recipiocal of 4: 5. t>: Examples: 2 and 5 are (actors of B: Examples: 3 J and j - '-. is ihe recipiocal of - i. since both divide evenly (without remainder) into Id. other integer factors of 10 are - III I. I. and 10 l l J 7. B: Examples: u* J S. A: Examples: The term 8r lias nunierical coefficient IS. and Hh'v has nunierical coefficient - 10.

4 CHAPTER i Review Lxercises 47 REVIEW EXERCISES [T.lj* Graph the elements of each set an a number line. 1. i-a. -1.2, ( -5,, -0.5, Find the value of each expression Let S = {-9. - f. - V , V7.V-9.-y}. Simplify the elements of S as necessary, and then list those elements of S which belong to the specified sel. 6. Whole numbers 7. Integers 8. Rational numbers 9. Real numbers Write each sel by listhlg its elements. 10. {.vj.v is a natural number between 3 an J 9) 11. 'yjv is a whole number less than 4} Write true orfalsefor each inetjuitlit): i (3 + 7) 401 The graph shines the percent change in annual domestic car sales fmm January 2004 to January 2005 for various automakers. Use this graph to work Exercises 15-IS. 15. Which automaker had the greatest change in sales? What was that change? 16. Which automaker had the least change in sales'' What was that change? 17. True or false: The absolute value of the percent change for Ford was greater than the absolute value of the percent change for General Motors. Car Sales, 2005 Chrysler General Motors 5 Honda Hyundai Mazda Toyota 137% IS 5.2% -5.6% B -25% J m 8.5% g 3.0% 9HB 13-4% Percent Change from 2004 Source: Chicago Tribune, February Trite at false: The percenl chance for Toyota was more than four times greater than the percent change for Mazda. Write each set in interval notation and graph the interval. 19. {x\x < -5j 20. {.T!-2 < T < 3} 11.2] Add or subtract as indicated. "-i-(-t) 5 \ 10/ F<M help wiili the Review Lxcrcises in this text, icier to the, appropriate section given in rmiukcis.

5 48 CHAPTER t Review of the Real Number System 23. I - i I) (- 13) + ( (-10) + (-7) 1 1 ' 4 ' I2-9 + (-4) In Krispy Kreme Doughnuts reported a profit of $13.1 million. In the low-carb diet craze was responsible for a firsl-quarier loss in doughnut sales of $24.4 million. Find the difference beiween these two amounts. (Source: Krispy Kreme Douahnuts. I Multiply or divide as indicated i.-5)(-3)(-3) _ I - _ J Concept Chuck Which one of the following is undefined: , [I.3 Evaluate each expression ) : ' Fin,! each square root. If it is not t/ real number, say so. [M 39. V \ 41. -V0.S1 V V Simplify each expression l4j) + 6 * =-[5(- I) 4'] (3 ; ) + 9(V'4) ) Evaluate each expression if k ~ -4. nt = 2, and n = k - 7/ir Vli + m + 5k 4/n 3 3n 49. The following expression for body mass index (BM1) can help determine ideal body weight. 704 x (weight in pounds) * (height in inches) 2 A BM1 of 19 to 25 corresponds to a healthy isource: Washington Post.) weight. (a) Baseball player Carlos Beltran is 6 ft, I in., lall and weighs 190 lb. {Source; Street & Smith's Baseball 2004 yearbook.) Find his BM] (to the nearest whole number). (b) Calculate your BMI.

6 CHAPTER i Review Exercises ! Simplify each expression. 5(1. 2i\ + 19$ ; - 17z 52. -m + 6m 53. Sp - /) 54. -It I; + 3) 55. 6(r + 3) 56. 9(2»/ 1 3n) 57. -(-/> + 6q) - (2p - 3(/) y v a a (4/i/ - 2) + 2(3/i/ - 1) - 4(3* + 1) Complete each slaiemem so thai the indicated property is illustrated. Simplify each answer if possible r + 3v = (distributive properly) (identity property) 63. 2(4A-) =. _ =. (associative property I (commutative property) = (,.v + r.) =. (inverse property) (distributive property) _ = (identity properly) (inverse property) MIXED REVIEW EXERCISES* The table gives U.S. exports and imports with Canada, in millions of U.S. dollars. Year Exports Imports , , , , ,870 Source: U.S. Census Bureau. Determine the absolute value of the. difference between imports and exports for each year. Is the balance of trade (exports minus imports) in each year positive or negative? Perform the indicated operations (-40)?2 + V i V 4-3 V H 7(-3) V * '["he order of exercises in ihis final pinup does not toncspond in the order in which topics occur in the chapter. This liindoin 01 Jennc should help yon prepaie for the chapter test in yet another way.

7 50 CHAPTER i Review of the Real Number System (k - I) + U - t 83. -V'-KX) 84. -(31-4h) I2.4S] ( 15) + ( ) 2 5 i' 3 9 I Evaluate ml 31" + 5m) if (a) it =» -4 and HI = 2 and (b) k j and m J. 90. tuwrr.t C To evaluate (3 + 2) :. should you work within the parentheses first, or should you square 3 and square 2 and (hen add? Chapter TEST View the complete solutions to all Chapter Test exercises on the Pass the Test CD. Graph \ ,. 5, 6.3 > on a number line. Let A = {- VS. - I. -0.5, V'25, 7.5. =y. V 4). hirst simplify each element as needed, and then list the elements from A that belong to each set. 2. Whole numbers 3. Integers 4. Rational numbers 5. Real numbers Write each set in interval notation and graph the interval 7. {y -4 < vs 2} Perform the indicated operations (-11) - (-3) : + 2(6) + -4) 3!, -2[3 - (-1-2) + 2] V9I-3) - (-2) (-4) (-6) 11. V161-5) : 5-2(-l K.' table shows the heights in feel of some selected mountains and the depths in feet (as negative numbers) of some selected ocean trenches. 14. What is the difference between the height of Ml. Foraker and the depth of the Philippine Trench? Mountain Height Trench Depth Foraker 17,400 Philippine -32,995 Wilson 14,246 Cayman -24,721 Piles Peak 14,110 Java -23,376 Source: World Alumnae and Bunk o)'tacts 2(X)f). 15. What is the difference between the height of Pikes Peak and the depth of the Java Trench? 16. How much deeper is the Cayman Trench than the Java Trench?

Classify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers.

Real Numbers and The Number Line Properties of Real Numbers Classify, graph, and compare real numbers. Find and estimate square roots Identify and apply properties of real numbers. Square root, radicand,