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Prealgebra

A | Cumulative Review

PrealgebraA | Cumulative Review
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

Note: Answers to the Cumulative Review can be found in the Supplemental Resources. Please visit http://openstaxcollege.org to view an updated list of the Learning Resources for this title and how to access them.

Chapter 1 Whole Numbers

No exercises.

Chapter 2 The Language of Algebra

Simplify:

1.5(3+2·6)821.5(3+2·6)82

Solve:

2.17=y132.17=y13

3.p+14=233.p+14=23

Translate into an algebraic expression.

4.114.11 less than the product of 77 and x.x.

Translate into an algebraic equation and solve.

5.5.Twice the difference of yy and 77 gives 84.84.

6.6.Find all the factors of 72.72.

7.7.Find the prime factorization of 132.132.

8.8.Find the least common multiple of 1212 and 20.20.

Chapter 3 Integers

Simplify:

9.|89||38|9.|89||38|

10.−2+4(−3+7)10.−2+4(−3+7)

11.27(−47)11.27(−47)

12.28÷(−4)712.28÷(−4)7

Translate into an algebraic expression or equation.

13.13.The sum of −5−5 and 13,13, increased by 11.11.

14.14.The product of −11and8.−11and8.

15.15.The quotient of 77 and the sum of −4andm.−4andm.

16.16.The product of −3−3 and is −51.−51.

Solve:

17.−6r=2417.−6r=24

Chapter 4 Fractions

18.18.Locate the numbers on a number line. 78,53,314,5.78,53,314,5.

Simplify:

19.21p57q19.21p57q

20.37·(2845)20.37·(2845)

21.−634÷9221.−634÷92

22.−335÷622.−335÷6

23.−423(67)23.−423(67)

24.−2143824.−21438

25.7·8+4(712)9·62·925.7·8+4(712)9·62·9

26.2336+172026.2336+1720

27.12+13341327.12+133413

28.35821228.358212

29.23r=2429.23r=24

Chapter 5 Decimals

Simplify:

30.24.767.2830.24.767.28

31.12.9+15.63331.12.9+15.633

32.(−5.6)(0.25)32.(−5.6)(0.25)

33.$6.29÷1233.$6.29÷12

34.34(13.449.6)34.34(13.449.6)

35.64+22535.64+225

36.121x2y236.121x2y2

37.37.Write in order from smallest to largest: 58,0.75,81558,0.75,815

Solve:

38.−8.6x=34.438.−8.6x=34.4

39.39.Using 3.143.14 as the estimate for pi, approximate the (a) circumference and (b) area of a circle whose radius is 88 inches.

40.40.Find the mean of the numbers, 18,16,20,1218,16,20,12

41.41.Find the median of the numbers, 24,29,27,28,3024,29,27,28,30

42.42.Identify the mode of the numbers, 6,4,4,5,6,6,4,4,4,3,56,4,4,5,6,6,4,4,4,3,5

43.43.Find the unit price of one t-shirt if they are sold at 33 for $28.97.$28.97.

Chapter 6 Percents

44.44.Convert 14.7%14.7% to (a) a fraction and (b) a decimal.

Translate and solve.

45.6345.63 is 35%35% of what number?

46.46.The nutrition label on a package of granola bars says that each granola bar has 180180 calories, and 8181 calories are from fat. What percent of the total calories is from fat?

47.47.Elliot received $510$510 commission when he sold a $3,400$3,400 painting at the art gallery where he works. What was the rate of commission?

48.48.Nandita bought a set of towels on sale for $67.50.$67.50. The original price of the towels was $90.$90. What was the discount rate?

49.49.Alan invested $23,000$23,000 in a friend’s business. In 55 years the friend paid him the $23,000$23,000 plus $9,200$9,200 interest. What was the rate of interest?

Solve:

50.9p=−61450.9p=−614

Chapter 7 The Properties of Real Numbers

51.51.List the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers,

(e) real numbers −5,−214,4,0.25¯,135,4−5,−214,4,0.25¯,135,4

Simplify:

52.(815+47)+3752.(815+47)+37

53.3(y+3)8(y4)53.3(y+3)8(y4)

54.817·49·17854.817·49·178

55.55.A playground is 5555 feet wide. Convert the width to yards.

56.56.Every day last week Amit recorded the number of minutes he spent reading. The recorded number of minutes he read each day was 48,26,81,54,43,62,106.48,26,81,54,43,62,106. How many hours did Amit spend reading last week?

57.57.June walked 2.82.8 kilometers. Convert this length to miles knowing 11 mile is 1.611.61 kilometer.

Chapter 8 Solve Linear Equations

Solve:

58.y+13=−858.y+13=−8

59.p+25=8559.p+25=85

60.48=23x60.48=23x

61.4(a3)6a=−1861.4(a3)6a=−18

62.7q+14=−3562.7q+14=−35

63.4v27=7v63.4v27=7v

64.78y6=38y864.78y6=38y8

65.264(z2)=665.264(z2)=6

66.34x23=12x5666.34x23=12x56

67.0.7y+4.8=0.84y5.367.0.7y+4.8=0.84y5.3

Translate and solve.

68.68.Four less than nn is 13.13.

Chapter 9 Math Models and Geometry

69.69.One number is 88 less than another. Their sum is negative twenty-two. Find the numbers.

70.70.The sum of two consecutive integers is −95.−95. Find the numbers.

71.71.Wilma has $3.65$3.65 in dimes and quarters. The number of dimes is 22 less than the number of quarters. How many of each coin does she have?

72.72.Two angles are supplementary. The larger angle is 24°24° more than the smaller angle. Find the measurements of both angles.

73.73.One angle of a triangle is 20°20° more than the smallest angle. The largest angle is the sum of the other angles. Find the measurements of all three angles.

74.74.Erik needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is 1212 feet tall and Erik has 1515 feet of wire. How far from the base of the antenna can he attach the wire?

No Alt Text

75.75.The width of a rectangle is 44 less than the length. The perimeter is 9696 inches. Find the length and the width.

76.76.Find the (a) volume and (b) surface area of a rectangular carton with length 2424 inches, width 1818 inches, and height 66 inches.

Chapter 10 Polynomials

Simplify:

77.(8m2+12m5)(2m27m1)77.(8m2+12m5)(2m27m1)

78.p3·p1078.p3·p10

79.(y4)379.(y4)3

80.(3a5)380.(3a5)3

81.(x3)5(x2)381.(x3)5(x2)3

82.(23m3n6)(16m4n4)82.(23m3n6)(16m4n4)

83.(y4)(y+12)83.(y4)(y+12)

84.(3c+1)(9c4)84.(3c+1)(9c4)

85.(x1)(x23x2)85.(x1)(x23x2)

86.(8x)086.(8x)0

87.(x3)5(x2)487.(x3)5(x2)4

88.32a7b212a3b688.32a7b212a3b6

89.(ab−3)(a−3b6)89.(ab−3)(a−3b6)

90.90.Write in scientific notation: (a)4,800,000(b)0.00637(a)4,800,000(b)0.00637

Factor the greatest common factor from the polynomial.

91.3x46x318x291.3x46x318x2

Chapter 11 Graphs

Graph:

92.y=4x392.y=4x3

93.y=−3x93.y=−3x

94.y=12x+394.y=12x+3

95.xy=695.xy=6

96.y=−296.y=−2

97.97.Find the intercepts. 2x+3y=122x+3y=12

Graph using the intercepts.

98.2x4y=898.2x4y=8

99.99.Find the slope of the line shown.

No Alt Text

100.100.Use the slope formula to find the slope of the line between the points (−5,−2),(3,2).(−5,−2),(3,2).

101.101.Graph the line passing through the point (−3,4)(−3,4) and with slope m=13.m=13.

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