Chapter 1 Algebraic Thinking Answer Key

Chapter 1 – Algebraic Thinking Answer Key

CK-12 Middle School Math Concepts - Grade 7 1

1.1 Equations that Describe Patterns

Answers

1. x 3 + 3 2. – 15 3. + 7 4. ÷ 4 5. x 4 – 1

6. ÷ 3 7. X 3 + 1 8. X 5 + 1 9. X 6 10. – 10

11. x 2 – 1 12. ÷ 3 13. ÷ 2 – 1 14. X 7 15. ÷ 3

1.2 Extend Numerical Patterns

Answers

1. 6, 7 2. 10, 12 3. 47, 95 4. 12, 15 5. 1

6. 38. 78 7. 25, 12.5 8. 50, 60 9. 60, 75 10. 136, 148

11. 7 12. 13 13. 5 14. 6.25 15. 10.5

1.3 Visual Patterns

Answers

1. x 2 – 1 2. – 10 3. X 2 + 5 4. ÷ 10 5. 49

6. 136 7. 91 8. 1 9 A triangle 10. 20 dots

11. 9 dots 12. 10 triangles 13. a square 14. 3 squares 15. 2 ¼ circles

1.4 Single Variable Expressions

Answers

1. 3 2. 54 3. 99 4. 25 5. 36

6. 18 7. 54 8. 107 9. 34 10. 78

11. 39 12. 14 13. 48 14. 84 15. 48



1.5 Expressions with One or More Variables

Answers

1. 24 2. 20 3. 39 4. 48

5. 132 6. 100 7. 40 8. 35

9. 65 10. 85 11. 2 12. 4

13. 6 14. 6 15. 10 16. 46

1.6 Expressions for Real Life Situations

Answers

1. 19 – n 2. 4x – 4 3. n + 30 4. 3x + 12 5. x/7

6. (x + 7)/2 7. 16x 8. x/8 9. 2(x + 7) 10. (x+5)/5

11. 22 – n 12. 3x – 17 13. 48 mysteries 14. 12 15. $70.00

1.7 Whole Number Exponents

Answers

1. b = 4, e = 5 4 x 4 x 4 x 4 x 4

2. b = 3, e = 2 3 x 3

3. b = 5, e = 8 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5

4. b = 4, e = 3 4 x 4 x 4

5. b = 6, e = 3 6 x 6 x 6

6. b = 2, e = 5 2 x 2 x 2 x 2 x 2

7. b = 1, e = 10 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1

8. b = 2, e = 4 2 x 2 x 2 x 2

9. b = 3, e = 4 3 x 3 x 3 x 3

10. b = 5, e = 2 5 x 5

11. b = 4, e = 4 4 x 4 x 4 x 4

12. b = 8, e = 10 8 x 8 x 8 x 8 x8 x8 x8 x8 x8 x8

13. b = 9, e = 3 9 x 9 x 9

14. b = 12, e = 2 12 x 12

15. b = 13, e = 3 13 x 13 x 13



1.8 Algebraic Expressions with Exponents

Answers

1. 8 2. 16 3. 25 4. 1 5. 125

6. 64 7. 27 8. 25 9. 129 10. 44

11. 11 12. 12 13. 80 14. m7 15. x7

16. y8 17. b9 18. a7 19. x12 20. y9

21. x8 22. y15 23. a20 24. x16 25. b12

1.9 Numerical Expression Evaluation with Basic Operations

Answers

1. 17 2. 27 3. 5 4. 14 5. 23

6. 12 7. 29 8. 29 9. 14 10. 34

11. 23 12. 55 13. 15 14. 50 15. 54

1.10 Expression Evaluation with Powers and Grouping Symbols

Answers

1. 18 2. 11 3. 15 4. 80 5. 16

6. 14 7. 27 8. 25 9. 36 10. 11

11. 13 12. 147 13. True 14. False 15. False

1.11 Mental Math for Addition/Subtraction Equations

Answers

1. 5 2. 5 3. 13 4. 5 5. 22

6. 12 7. 4 8. 15 9. 6 10. 12

11. 12 12. 5 13. 7 14. 7 15. 42

16. 14 17. 28 18. 3 19. 7 20. 16



1.12 Mental Math for Multiplication/Division Equations

Answers

1. 5 2. 8 3. 9 4. 7 5. 4

6. 2 7. 2 8. 3 9. 6 10. 20

11. 33 12. 60 13. 56 14. 72 15. 36

1.13 Appropriate Tools for Measurement of Squares and Rectangles

Answers

1. feet/meters 2. Centimeters/inches 3. Feet/meters 4. Feet/meters

5. kilometers/miles 6. Inches/centimeters 7. Feet/meters 8. Centimeters/inches

9. centimeters/inches 10. Feet/meters 11. Inches/centimeters 12. Feet/meters

13. feet/meters 14. Kilometers/miles 15. Kilometers/miles 16. Kilometers/miles

1.14 Area and Perimeter of Rectangles

Answers

1. P = 30 in. A = 50 in2 2. P = 40 ft. A = 96 ft2

3. P = 32 ft. A = 55 ft.2 4. P = 70 mi. A = 306 mi2

5. P = 84 ft A = 440 ft2 6. P = 28 cm A = 48 cm2

7. P = 74 cm A = 340 cm2 8. P = 10 ft A = 6 ft2

9. P = 52 yds A = 165 yds2 10. P = 32 yds A = 60 yds2

11. P = 24 ft A = 36 ft2 12. P = 32 ft. A = 64 ft2

13. P = 36 in. A = 81 in2 14. P = 16 in A = 16 in2

15. P = 48 in. A = 144 in2 16. P = 28 ft A = 49 ft2

17. P = 20 cm A = 25 cm2 18. P = 12 m A = 9 m2

19. P = 40 m A = 100 m2 20. P = 44 yds A = 121 yds2



1.15 Unknown Dimensions Using Formulas

Answers

1. 4 ft 2. 8 m 3. 10 miles 4. 11 inches 5. 12 ft

6. 6 ft 7. 4 ft 8. 6.4 ft 9. 3 m 10. 10 ft

11. 2 inches 12. 12 inches 13. 16 inches 14. 22.5 inches 15. 8.75 ft.

1.16 Problem Solving Models

Answers

1. 7 2. 124 pounds 3. 1 meter 4. $1.50 per ride 5. 5 rows

6. 119 sq. ft 7. 152 miles per day 8. 57 points 9. $6.25 sandwich 10. l = 9 meters

11 – 15 Answers will vary

1.17 Comparison of Problem Solving Models

Answers

1. $43.75 2. 224 3. 40 ft.

4. 39 rows 5. Yes, both are smaller than 14 inches 6. Ned = 416, Ella = 208, Peter = 104

7. $8.00 per hour 8. 40.5 pounds 9. Figure A

10. 280 miles 11. 5 12. $24.00

13. 87 people 14. 116 people 15. 106 people

Chapter 2 – Using Decimals Answer Key


2.1 Decimal Comparisons without Rounding

Answers

1. < 2. > 3. >

4. < 5. > 6. <

7. < 8. < 9. >

10. 373.129, 373.192, 373.219, 373.291

11. .4674, .4754, .4755, .4764

12. 7.06, 7.16, 7.2, 7.21

13. 25.074, 25.407, 25.417, 25.741

14. 15.0001, 15.001, 15.067, 15.100

15. 6.008, 6.087, 6.780, 6.870

2.2 Decimal Rounding Given Place Value

Answers

1. 622 2. 1,318 3. 17 4. 50 5. 124

6. 350 7. 16, 789 8. 13 9. 146 10. 32.30

11. .1062 12. 2.40047 13. 4,062.0 14. .1238 15. 3.457

2.3 Decimal Comparisons with Rounding

Answers

1. = 2. = 3. <

4. > 5. > 6. <

7. = 8. = 9. <

10. 2.033, 2.034, 2.035, 2.039

11. 16.088, 16.089, 16.089, 16.100

12. 3.821, 3.822, 3.828, 3.829

13. .056, .057, .058, .060

14. .7, .8, .9, 1.0, 2.0

15. $54.00 two person, $68.00 Three Person, $90 Four person

The best estimate is for 2 – three person units to be rented



2.4 Decimal Addition

Answers

1. 740.811 2. 1.9445 3. 55.92 4. 79.604 5. 72.556

6. 112.5 7. 1521.2 8. 11.1 9. 1.9 10. 10.4

11. 610.61 12. 8.46 13. 335.78 14. 2.05 15. 4.77

2.5 Decimal Addition Using Front- End Estimation

Answers

1. 6.8 2. 6.2 3. 10.9 4. 11 5. 6.9

6. 17.5 7. 15.5 8. 14.5 9. 39 10. 43.7

11. 37.3 12. 39.4 13. 1.0 14. 13.1 15. 1.6

2.6 Commutative Property of Addition with Decimals

Answers

1. Associative 2. Commutative 3. Associative

4. Commutative 5. Commutative 6. Associative

7. Commutative 8. Associative 9. .292

10. 2.115 11. .306 12. 6.174

13. 1.08 14. $50.50 15. 61.2 yards

2.7 Decimal Subtraction

Answers

1. .82 2. .0386 3. 12.5034 4. 11.94 5. 191.4

6. 8.146 7. 75.75 8. .7669 9. 788.244 10. 101.76

11. 12.88 12. .18 13. 699.97 14. .33 15. .97



2.8 Decimal Subtraction Using Front- End Estimation

Answers

1. 2.2 2. 1.0 3. 6.9 4. 6.4 5. 1.2

6. 9.1 7. 1.1 8. 10.2 9. .2 10. .5

11. .6 12. .4 13. .3 14. 4.1 15. .1

2.9 Inverse Property of Addition in Decimal Equations

Answers

1. 4.62 2. 11.58 3. 10.05 4. 2.952 5. 65.82

6. 45.32 7. 78.35 8. 5.78 9. 69.11 10. 204.495

11. 45.68 12. 1.6 pounds 13. 6.495 km 14. $32.49 15. 8.5 Liters

2.10 Decimal Multiplication

Answers

1. 10.16 2. .1656 3. 20.3406 4. 18.432 5. 19.2814

6. 1.935 7. 9.6252 8. 172.12 9. 6.51 10. 22.54

11. 100 12. 65.7 13. 10.56 14. 61.88 15. 80.91

2.11 Estimation to Check Decimal Multiplication

Answers

1. 6.9 2. 124.2 3. .0624 4. 539.5 5. 5.488

6. 9.49 7. 5.44 8. .51 9. .4611 10. .3724

11. 24.75 12. 132 13. 294 14. .0099 15. 70.3



2.12 Commutative Property of Multiplication with Decimals

Answers

1. 37.048p 2. 100.068q 3. 330.12x 4. 14.84r 5. 21.28x

6. 6.72y 7. 20.77x 8. 20.493r 9. 15.876y 10. 9.966x

11. 15.68x 12. 29.44y 13. 10.35x 14. 197.12x 15. 259.86y

2.13 Decimal Division

Answers

1. 1.2 2. 1.3 3. 1.5 4. 2 5. 14.7

6. 1.6 7. 8.8 8. 10.3 9. 7.5 10. 4.9

11. 4.50 12. 12.79 13. 244.90 14. 2.04 15. 3.57

2.14 Estimation to Check Decimal Division

Answers

1. 70 2. .3 3. 20 4. 4 5. 14.4

6. 2.8 7. 2.9 8. 2 9. 3.7 10. 5.1

11. 3.9 12. 5.4 13. 5 14. 8.7 15. .2

2.15 Division to Solve Decimal Equations

Answers

1. 2.1 2. 3.3 3. 4.1 4. 4.2 5. 5.6

6. 2.5 7. 6.3 8. 6.3 9. 6.8 10. 9.6

11. .581 12. 11.7 13. 5.5 km 14. 6.8 m 15. 96.54 kilometers per hour



2.16 Scientific Notation

Answers

1. 5.6 x 10-9 2. 2.4 x 1010 3. 9.6 x 1017

4. 1.2 x 10-7 5. 3.6 x 107 6. 9.8 x 10-4

7. 3.4 x 10-8 8. 3.45 x 108 9. 380,800,000,000

10. .0000021 11. 591,200,000 12. .00000678

13. 5,700,000,000 14. .000045 15. 32,100,000

2.17 Comparison of Numbers in Scientific Notation

Answers

1. > 2. < 3. > 4. < 5. > 6. >

7. > 8. < 9. > 10. < 11. >

12. 2.1 x 1020, , 6.4 x 1015, 1.7 x 1015, 9.2 x 1010

13. 8.71 x 10-3, 4.16 x 10-3, 5.63 x 10-5, 3.42 x 10-6

14. .000202, .0000221, .000212, .0000202

15. 8.61 x 108, 86,120,000, 86,102,000, 8.61 x 107

2.18 Operations with Numbers in Scientific Notation

Answers

1. 8.8 x 103 2. 4.1 x 104 3. 12.1 x 105

4. 8 x 103 5. 32.64 x 106 6. 6.2 x 102

7. 9.8 x 105 8. 2.1 x 103 9. 10.1 x 103

10. 3.96 x 106 11. 4.1 x 102 12. 274.6 x 10-6

13. 1.64 x 104 14. 9.728 x 103 15. .71 x 103



2.19 Metric System

Answers

1. 10 m 2. 1,000,000 cL 3. 1000 cg

4.10 cL 5. .0002 kg 6. .2 m

7. .002 kL 8. .02 kg 9. 1.8076 m

10. 1807.6 mm 11. .0018076 km 12. 490.9 L

13. 49,090 cL 14. 490,900 ML 15. 1000

2.20 Appropriate Tools for Metric Measurement

Answers

1. graduated cylinder 2. Metric tape 3. Scale

4. Graduated cylinder 5. kilometer 6. Gram

7. Centimeter 8. Milliliter 9. kilograms

10. Kilograms 11. Meter 12. 113.4 meters

13. 3.525 liters 14. Max, Taboo, Arnaud, Josie 15. 1800 grams

2.21 Conversions of Length, Mass and Capacity in Metric Units

Answers

1. 100 mm 2. 100,000 m 3. .453 km

4. 1,567,000 m 5. 67 m 6. 780 cm

7. 65,570 mL 8. 282.03 mL 9. 9761 mL

10. 2946.7 centigrams 11. .00562 centigrams 12. 4505.84 centigrams

13. .08996 kiloliters 14. .045217 kiloliters 15. 31.20700 kiloliters



2.22 Comparison of Metric Measurement

Answers

1. > 2. < 3. > 4. < 5. < 6. > 7. >

8. > 9. < 10. < 11. > 12. = 13. >

14. 7,938,200 mg, 7,838,200 cg, 79,382 g, 79,282 kg

15. 21.06 kL, 21,061 L, 21,161,000 mL, 2,261,000

2.23 Estimation of Conversion to Metric Units

Answers

1. 1.18 Liters 2. 4.57 meters 3. 152.4 mm

4. 6.08 kg 5. .24 Liters 6. .004 km

7. 152.4 cm 8. 365.76 cm 9. 203.2 mm

10. 807.96 grams 11. 298.45 mm 12. 7.57 Liters

13. 6.80 kilograms 14. 1.05 km 15. Computer

Chapter 3 – Using Fractions Answer Key


3.1 Equivalent Fractions

Answers

1. ¾, 9/12, 18/24, 27/36 2. 21/8 3. 17/5 4. 8/7 5. 49/9

6. 1 1/28 7. 2 2/5 8. 4 ½ 9. 2 1/8 10. 7 1/3

11. 4/6, 8/12, 16/24

12. 3/7, 9/21, 6/14

13. 6/8, 9/12, 18/24

14. 18/20, 27/30, 36/40

15. 14/16, 21/24, 28/32

3.2 Mixed Number and Fraction Estimation

Answers

1. 1 2. ½ 3. 0 4. 1 5. 0

6. 0 7. 1 8. ½ 9. ½ 10. 1

11. 3 12. 6 13. 44 14. 8 15. 7

3.3 Fraction and Mixed Number Comparison

Answers

1. < 2. > 3. > 4. < 5. =

6. > 7. > 8. = 9. < 10. =

11. 1/3, 4/9, 5/6

12. ¼, 2/3, 6/7

13. 2/3, 4/5, 6/6

14. ½, 3/5, 2/3

15. 2/7, ¼, 3/6

16. 1/6, 2/9, 2/5

17. parsley, cheese, asparagus

18. Wall A



3.4 Addition of Fractions

Answers

1. 1/2 2. 1 1/12 3. 7/10 4. 5/18 5. 3 9/20

6. 10 11/12 7. 3 5/12 8. 7 2/15 9. 6 1/3 10. 16 3/5

11. 6 5/6 12. 9 23/45 13. 2 5/6 14. 19 3/10 15. 31 23/36

3.5 Estimation of Sums of Mixed Numbers and Fractions

Answers

1. 1 2. 1 ½ 3. 1 ½ 4. 0 5. 1

6. 1 7. 1 8. 1 ½ 9. 1 10. 1

11. 7 12. 14 ½ 13. 6 14. 2 15. 19

3.6 Commutative Property of Addition with Fractions

Answers

1. ½ + y 2. x + 5 3. 7/9 + y 4. 4 + x

5. x + 8 5/6 6. 1 1/8 + x 7. 1/3 + x 8. x + 5 11/14

9. 4 11/12 + x 10. 5 13/30 + x 11. 6 2/3 + x 12. 5 11/18 + x

13. 13/21 14. 4 23/40 15. 15 17/84 16. ¼ + 4/7 + x

3.7 Subtraction of Fractions

Answers

1. 9/20 2. 0 3. 11/21 4. 5/8

5. 2 9/10 6. 1 1/8 7. 5/6 8. 2 5/14

9. 1 10. 0 11. 1 12. ½

13. 11 14. 0 15.0 16. 3 ½



3.8 Estimation with Mixed Number/Fraction Subtraction

Answers

1. 1 2. 0 3. 1 4. ½ 5. 1

6. 11 7. 0 8. ½ 9. 3 ½ 10. 0

11. 2 12. 9 13. 6 14. 17 ½ 15. 8

3.9 Inverse Property of Addition in Fraction Equations

Answers

1. 3/5 2. ½ 3. 1/9 4. 1/7 5. 1/12

6. 7/15 7. 3/13 8. 3/7 9. 2/5 10. 5/12

11. 5 ½ 12. 1 ½ 13. 3 5/8 14. 15 ¼ 15. 27/56

3.10 Products of Mixed Numbers

Answers

1. 3/28 2. 5/9 3. ¼ 4. 8/21

5. 8/9 6. 3 9/35 7. 5 7/40 8. 36/55

9. 9 ¼ 10. 1/42 11. 6 7/18 12. 7/60

13. 3/7 14. 9/20 15. 5/42 16. 1 13/15

3.11 Product Estimation of Mixed Numbers/Fractions

Answers

1. 1 2. 12 3. ½ 4. ½ 5. 17 ½

6. 18 7. 7 ½ 8. 35 9. 35 10. 4

11. 49 12. 18 13. 35 14. 84 15. 192



3.12 Commutative Property with Products of Fractions

Answers

1. 6/14 2. 9/20 3. 5/42 4. 1 13/15 5. 1/7

6. 9/50 7. 2/81 8. 7/10x 9. 2 2/9x 10. 1 1/24x

11. 1/2x 12. 1/2x 13. 6/25x 14. $22.50 15. 2 1/6 ft

3.13 Division of Fractions

Answers

1. 2/15 2. 1 2/3 3. 8/25 4. 2 2/3 5. 4

6. 32/75 7. 4 5/6 8. 15 ¾ 9. 2 5/16 10. 6/7

11. 2 3/10 12. 10 22/35 13. 12/35 14. 36 4/5 15. 4 29/40

3.14 Quotient Estimation with Mixed Numbers/Fractions

Answers

1. 1 2. 1 3. ½ 4. 2 5. 4

6. 2 7. 12 8. 3 9. 4 10. 3

11. 5 12. 8 13. 2 14. 3 15. 13

3.15 Fractions as Decimals

Answers

1. .6 2. .5 3. .8 4. .75 5. .375

6. .875 7. 2.25 8. 5.4 9. 6.5 10. 11.625

11. 10.5 12. 18.75 13. 12.8 14. 19.75 15. 22.25



3.16 Repeating Decimals

Answers

R is for repeating decimal

1. .66 R 2. .83 R 3. 5.3 R 4. .33 R 5. .75

6. .166 R 7. .125 8. .4285714286 9. .33 R 10. 4.66 R

11. 7.33 R 12. 6.83 R 13. 8.5 14. 9.66 R 15. 11.2

3.17 Decimals as Fractions

Answers

1. 3/10 2. 2/5 3. 1/5 4. 53/100

5. 55/100 6. 2/25 7. ¼ 8. 23/100

9. 219/250 10. 64/125 11. 74 17/50 12. 3 22/25

13. 5 3/5 14. 12 4/5 15. 23 3/50 16. 987/1000

3.18 Positive and Negative Fraction and Decimal Comparison

Answers

1. < 2. < 3. > 4. < 5. =

6. > 7. < 8. = 9. < 10. <

11. 1/3, .25, .54

12. .55, .613, ¾

13. 1/9, .252, .31

14. .05, .546, 7/8

15. .09, .1, .88



3.19 United States Customary Units

Answers

1. 3 quarts 2. 32 Tablespoons 3. 56 ounces

4. 2640 feet 5. 3.5 pounds 6. 2 feet

7. 66 inches 8. 8 ounces 9. 36 inches

10. 3 feet 11. 64 Tablespoons 12. 192 teaspoons

13. 2.086 pounds 14. 32 ounces 15. 2 pints

3.20 Appropriate Tools for Customary Measurement

Answers

1. Scale 2. Measuring spoon 3. Measuring cup

4. Tape measure 5. measuring spoon 6. Measuring cup

7. Scale 8. Feet/yards 9. gallons

10. Inches 11. Pounds 12. Miles

13. gallons 14. Gallons 15. Inches

3.21 Conversion of Customary Units of Measurement

Answers

1. 5.4 yards 2. 352 yards 3. 29.3 yards

4. 30 yards 5. 300 yards 6. 131.5 pounds

7. 6 pounds 8. 375 pounds 9. 30,000 pounds

10. 204 pints 11. 3.56 pints 12. 76 pints

13. 8 pints 14. 36 pints 15. 536 pints

3.22 Conversion Estimation between Systems of Measure

Answers

1. 8.8 pounds 2. 24.6 feet 3. 25.38 cupts

4. 8.215 miles 5. 3.72 miles 6. 33.84 cuts

7. 44 pounds 8. 39.36 feet 9. 3.78 liters

10. 963.8 gallons 11. 23.58 kilograms 12. 22.86 centimeters

13. 4.26 meters 14. 3.78 Liters 15. 8.04 kilometers

Chapter 4 – Using Integers Answer Key


4.1 Integers that Represent Different Situations

Answers

1. -10 2. +50 3. -$20.00

4. -35 5. -120 6. +15,000

7. -20 + 15 8. 15 – 20 9. 20 + 35

10. -19 – 30 11. 30,000 + 15,000 12. -15,000 – 12,000

13. -60 + 15 14. -15 – 20 15. 1500 + 1000

4.2 Absolute Value of Integers

Answers

1. -20 2. 7 3. -22 4. 34 5. 0

6. 9 7. -14 8. -25 9. 13 10. 11

11. 5 12. 17 13. 9

4.3 Comparison of Integers with Absolute Value

Answers

1. > 2. > 3. > 4. < 5. >

6. > 7. > 8. = 9. < 10. =

11. = 12. > 13. < 14. < 15. =

4.4 Sums of Integers on a Number line

Answers

1. 7 2. 0 3. -6 4. 2 5. -14

6. -8 7. 12 8. 1 9. 7 10. -3

11. -9 12. -5 13. -13 14. 10 15. -4



4.5 Sums of Integers Using Absolute Value

Answers

1. 11 2. -15 3. -5 4. -31 5. -7

6. -24 7. -70 8. -14 9. -2 10. -28

11. -2 12. -2 13. -3 14. -27 15. -20

4.6 Simplify Variable Expressions Involving Integer Addition

Answers

1. 4z 2. 2z 3. 2x 4. 10y 5. –x

6. 0 7. 11a 8. -11y 9. -11d + 2 10. 4x – 5

11. 4y 12. -6x 13. 11a 14. 3,000 ft. 15. -5 degrees F

4.7 Differences of Integers Using a Number Line

Answers

1. 2 2. -8 3. 3 4. 7 5. -9

6. 11 7. 0 8. -9 9. 9 10. -11

11. -61 12. -27 13. -7 14. -75 15. -161

4.8 Differences of Integers Using Absolute Value

Answers

1. 8 2. -19 3. -4 4. 22 5. -25

6. 37 7. -3 8. -10 9. 36 10. -5

11. -13 12. 29 13. 14 14. -13 15. 38



4.9 Simplify Variable Expressions Involving Integer Subtraction

Answers

1. -11m 2. -6c 3. -15a

4. 16a 5. 2a 6. -5a

7. 17z 8. -34x 9. -37a

10. 34x 11. 28y 12. 88z – (-44x) or 88z + 44x

13. -15a – 8x 14. -15a – 8x – 2 15. -15a – 7y

4.10 Integer Multiplication

Answers

1. -27 2. -72 3. 96 4. -28 5. 22

6. -75 7. 30 8. 56 9. 24 10. -9

11. 18 12. 24 13. 54 14. -48 15. 44

4.11 Simplify Variable Expressions Involving Integer Multiplication

Answers

1. 42k 2. 24ab 3. -6abc 4. -48ab 5. 36xy

6. -32x 7. 20ab 8. -24abc 9. -144abc 10. 96xz

11. 28ac 12. -132abc 13. 44abc 14. 216ab 15. 63ab

4.12 Integer Division

Answers

1. -3 2. 3 3. 6 4. -8 5. 7

6. -5 7. 20 8. -5 9. 9 10. -7

11. -8 12. 4 13. -4 14. 2 15. -6



4.13 Simplify Variable Expressions Involving Integer Division

Answers

1. -4t 2. 8n 3. 2 4. -4n 5. 9y

6. -8t 7. -6x 8. 6 9. 4 10. 4a

11. 11y 12. 11ab 13. 12xy 14. 13xy 15. -45xyz

4.14 Properties of Rational Numbers

Answers

1. -11/1 2. 19/6 3. 9/1 4. 8/100 5. -34/100

6. 678/1000 7. 4/5 8. -19/1 9. 25/1 10. 17/100

11. 2347/10,000 12. -17/1 13. 347/1 14. 87/1 15. -97/1

4.15 Comparison of Rational Numbers

Answers

1. = 2. < 3. > 4. < 5. <

6. > 7. = 8. > 9. > 10. <

11. = 12. > 13. > 14. < 15. .9 , .9, ½, 0

4.16 Expressions and the Distributive Property

Answers

1. 42 2. 25 3. 96 4. 90 5. 18

6. 9 7. 24 8. 10 9. 28 10. 36

11. 5x + 15 12. 6y – 12 13. 5x + 45 14. 8a + 8b 15. 7x – 7y



4.17 Points in the Coordinate Plane

Answers

1. N (-3, 2) M(0, -6) P(3, -2)

2. (-9,7) 3. (-7,-8) 4. (8,7) 5. (7, -9) 6. (-5, 1) 7. (3, 4)

8. (0, -5) 9. (-9, 10) 10. (-7, 1) 11. (-2, -10) 12. (3, 1) 13. (5, 10)

14.

15.

4.18 Scatter Plots

Answers

1. No Correlation 2. 1 3. 2 4. 1 5. 2

6. 3 7. 2 8. True 9. False 10. False

11. Scatter plots – answers vary 12. True 13. False 14. False 15. 8

Chapter 5 – Using Ratios, Rates and Proportions Answer Key


5.1 Equivalent Ratios

Answers

1. yes 2. No 3. No 4. Yes 5. Yes

6. No 7. yes 8. No 9. No 10. Yes

11. Yes 12. No 13. yes 14. Yes 15. No

5.2 Ratios in Simplest Form

Answers

1. 1 to 2 2. 1 : 4 3. 9 to 11 4. 9/10 5. 5/11

6. 1 to 7 7. 9 to 5 8. 3 to 1 9. 2 : 1 10. 3 to 2

11. 1 to 2 12. 6 to 1 13. 3 : 1 14. 8 to 1 15. 3/2

5.3 Comparison of Ratios in Decimal Form

Answers

1. .25 2. .5 3. .75 4. 1.6 5. .25

6. .8 7. .09 8. .75 9. .36 10. .3

11. .75 12. .43 13. > 14. < 15. =

5.4 Identification and Writing of Equivalent Rates

Answers

1. 1 for $5 2. 1 for $5 3. 1 for $2.50

4. 1 for $2.50 5. 1 for $9.00 6. 1 for $4.00

7. 1 mile in 2 minutes 8. 5 miles in 1 hour 9. 5 feet in 1 minute

10. 2 pounds in 1 week 11. 1/5 12. 1/5

13. 1/5 14. ½ 15. 9/1



5.5 Unit Rates

Answers

1. 1 for $5 2. 1 for $5 3. 1 for $2.50

4. 1 for $4 5. 9 for $1 6. 1 for $4

7. 1 mile in 2 minutes 8. 5 miles in 1 hour 9. 5 feet in 1 minute

10. 2 pounds in 1 week 11. 2 pounds for $1.00 12. 6 miles in 1 hour

13. 3” for $1.00 14. 15 miles per gallon 15. 50 miles in 1 hour

5.6 Comparison of Unit Rates

Answers

1. yes 2. No 3. Yes

4. $3.00 per gallon 5. .69 for 1 6. 160 per hour

7. $1.25 per square foot 8. 62 per minute 9. .30

10. .28 11. 12 ounce/2 cents 12. 47 mph

13. 51 mph 14. Amy 15. 4 mph

5.7 Slope

Answers

1. Positive 2. 0 3. Negative 4. 0 5. Positive

6. 0 7. Negative 8. Positive 9. Negative 10. Negative

11. no 12. False 13. True 14. True 15. True



5.8 Slope of a Line Using Two Points

Answers

1. 3/2 2. 0 3. -7/3 4. 0

5. 3/2 6. 0 7. -7/3 8. 4/5

9. -2/1 10. -7/5 11. -4/3

12.

13. Positive

14.

15. Negative



5.9 Proportions

Answers

1. yes 2. Yes 3. No 4. Yes 5. No

6. No 7. yes 8. No 9. a = 5 10. x = 1

11. n = 14 12. z = 4 13. t = 36 14. k = 30 15. x = 16

5.10 Proportions with Variables in the Numerator

Answers

1. 4 2. 10 3. 12 4. 4 5. 8

6. 10 7. 7 8. 9 9. 5 10. 6

11. 9 12. 2 13. 9 14. 18 15. 2.25

5.11 Proportions Using Cross Products

Answers

1. 3 2. 6 3. 20 4. 3.5

5. 2.5 6. 18 7. 5 8. 4.5

9. 12 10. 15 11. 25 12. 18

13. 9 14. 49 15. 4 16. 42.5

5.12 Proportions with Variables in the Denominator

Answers

1. 10 2. 30 3. 14 4. 42 5. 99

6. 48 7. 34 8. 30 9. 45 10. 7.5

11. 9.5 12. 12.5 13. 54 14. 24 15. 11.5



5.13 Scale Distances or Dimensions

Answers

1. 5” 2. 20” 3. 30” 4. 7 cm 5. 14 cm

6. 21 cm 7. 3” 8. 6” 9. 2 cm 10. 1 cm

11. 4” x 3.5” 12. 12 m 13. 344 miles 14. 18 mm 15. 1670 ft.

5.14 Unit Scale to Find Actual Distances

Answers

1. 200 miles 2. 300 miles 3. 25 miles





5.15 Scale Factor to Find Actual Dimensions

Answers

1. 10 cm 2. 20 cm 3. 20 cm

4. 10 cm 5. 1.5” 6. 3”

7. 4000 cm 8. 80 mm 9. 8 cm

10. 4” 11. 1.5 mm 12. 108 ft.

13. 6660 ft. 14. a. 7.5 m b. 5.1 m 15. a. 5 m x 4 m b. 20 sq. m



5.16 Problem Solving Plan, Proportions

Answers

1. 4 2. Lionel 3. 44 miles 4. .83 m 5. 125 students

6. Brand x 7. 6 miles 8. 20 miles 9. 2” 10. 6”

11. 8 ft. 12. 6 ft. 13. 9 ft. 14. 4 ft. 15. 3”

5.17 Conversion Using Unit Analysis

Answers

1. 5280 ft. 2. 97,680 ft. 3. 3750 mL

4. 18,250 mL 5. 6000 pounds 6. 5000 pounds

7. 9,500 pounds 8. 54 feet 9. 48 inches

10. 105 inches 11. 29,500 mL 12. 4 ounces

13. 108 inches 14. $4.50 15. 8 pints

Chapter 6 – Using Percents Answer Key


6.1 Percents

Answers

1. 10/100 2. 6/100 3. 22/100

4. 41/100 5. 33/100 6. 70/100

7. 77/100 8. 19/100 9. 25/100

10. 15/100 11. 7/100 12. 29/100

13. 88/100 14. 92/100 15. 90/100

6.2 Percents as Fractions

Answers

1. 1/10 2. 3/50 3. 11/50 4. 41/100 5. 33/100

6. 7/10 7. 77/100 8. 19/100 9. 3/25 10. 1/5

11. 1/20 12. ¼ 13. 2/5 14. 3/5 15. 9/10

6.3 Fractions as Percents

Answers

1. 50% 2. 25% 3. 75% 4. 11% 5. 20%

6. 50% 7. 17% 8. 125% 9. 250% 10. 233%

11. 54% 12. 50% 13. 42% 14. 40% 15. 50%

6.4 Percent of a Number

Answers

1. 2.5 2. 6 3. 20 4. 27 5. 150

6. .8 7. 10 8. 3.8 9. 4.5 10. 3.6

11. 6.75 12. 21.25 13. 27 14. 100 15. 165



6.5 Proportions to Find Percent, P

Answers

1. 50% 2. 20% 3. 25% 4. 20% 5. 33.3%

6. 50% 7. 20% 8. 25% 9. 60% 10. 75%

11. 13.3% 12. 33.3% 13. 20% 14. 80% 15. 12.5%

6.6 Proportions to Find Part a

Answers

1. 4.5 2. 2 3. 7.2 4. 8.8 5. 30

6. 15 7. 32 8. 24 9. 60 10. .6

11. 1 12. 12.8 13. 5.75 14. 8.5 15. 9.9

6.7 Proportions to Find Base b

Answers

1. 50 2. 70 3. 50 4. 40 5. 32

6. 28 7. 500 8. 5 9. 72 10. 300

11. 75 12. 138.46 13. 120 14. 32.72 15. 400

6.8 Percents as Decimals

Answers

1. .12 2. .15 3. .03 4. .67 5. .18

6. .78 7. .34 8. .07 9. .06 10. .36

11. .28 12. .335 13. .185 14. .1325 15. .0675



6.9 Decimals as Percents

Answers

1. 45% 2. 30% 3. 67.5% 4. 90% 5. 8%

6. 78.5% 7. 22% 8. 9.5% 9. 54% 10. 27.5%

11. 4% 12. 4.5% 13. 11.2% 14. 460% 15. 67.2%

6.10 Small and Large Percents as Decimals

Answers

1. .0034 2. .005 3. 3.5 4. 6.5 5. .0030

6. .0010 7. .0009 8. .0022 9. 2.3 10. 5

11. 7 12. .00012 13. .0004 14. .006 15. .0016

6.11 Percent Equation to find Part a

Answers

1. 3.6 2. 3 3. 4.5 4. 3.24 5. 5.4

6. 44 7. 9 8. 67.5 9. 8.8 10. 15

11. 1.2 12. 198 13. 10.8 14. 42.55 15. 32.8

6.12 Percent Equation to Find Percent

Answers

1. 50% 2. 50% 3. 25% 4. 25% 5. 40%

6. 50% 7. 50% 8. 25% 9. 50% 10. 92%

11. 14% 12. 45% 13. 66% 14. 70.4% 15. 10%



6.13 Percent Equation to Find the Base b

Answers

1. 50 2. 50 3. 90 4. 24 5. 37.5

6. 70 7. 320 8. 200 9. 112.5 10. 64

11. 333.3 12. 83.3 13. 140 14. 550 15. 335

6.14 Percent of Increase

Answers

1. 60% 2. 100% 3. 178% 4. 264% 5. 12.5%

6. 233% 7. 17.6% 8. 20% 9. 38.5% 10. 25%

11. 50% 12. 40% 13. 14.3% 14. 12.5% 15. 22.2%

6.15 Percent of Decrease

Answers

1. 60% 2. 63% 3. 55.5% 4. 6.6% 5. 33.3%

6. 16.6% 7. 25% 8. 7% 9. 19.6% 10. 87%

11. 50% 12. 12% 13. 33% 14. 15% 15. 95%

6.16 Percent of Change

Answers

1. 22.5 2. 25.5 3. 16.2 4. 27.3 5. 10.56

6. 77.4 7. 40 8. 86.33 9. 42 10. 12

11. 209 12. 67.5 13. 147.6 14. 1320 15. 13,680



6.17 Prices Involving Discounts

Answers

1. $22.80 2. $14.40 3. $21.60

4. $30.00 5. $16.20 6. $11.94

7. $54.00 8. $108.00 9. $102.00

10. $20.40 11. $46.75 12. $30.18 or $30.17

13. $15.30 14. $7.44 15. $21.25

6.18 Prices Involving Sales Tax

Answers

1. $3.00 2. $5.60 3. $5.00 4. $7.00 5.$9.00

6. $10.00 7. $18.00 8.$24.00 9. $25.00 10. $22.00

11. $26.00 12. $27.00 13. $19 – 20.00 14. $18.00 15. $20.00

6.19 Total Bill Involving Tip and Tax

Answers

1. $70.37 2. $53.63 3. $80.60 4. $31.62 5.$23.25

6. $73.16 7. $26.66 8. $55.18 9. $15.50 10. $53.32

11. $110.98 12. $123.19 13. $292.33 14. $372.62 15. $841.03

6.20 Simple Interest Equation to Find Interest Rate

Answers

1. $40 2. $30 3. $200 4. $60 5. $96

6. $45 7. $92 8. $40 9. $625 10. $330

11. $525 12. $2100 13. $3510 14. $8050 15. $25,000



6.21 Simple Interest

Answers

1. $45 2. $92 3. $40 4. $625 5. $330

6. $525 7. $2100 8. $138 9. $1787.50 10. $2400

11. 4 years 12. 2.5 years 13. $6.25 14. Avi, $2.60 more 15. $12,916.67

6.22 Interpretation of Circle Graphs

Answers

1. Baseball 2. Ice Hockey 3. 15% 4. 60 people 5. 27 people

6 – 8 Answers Vary

9. 0 10. Pizza 11. Chicken Sandwich or Tacos 12. 10% 13. 90%

14. 70% 15. 70% 16. 30%

17 – 18. Answers Vary

6.23 Circle Graphs to Display Data

Answers


4. 43.2° 5. 90°

6. 100.8° or 101° 7. 151.2° or 151°

8. 68.4° or 68° 9. 288°

10. 324° 11. 122.4° or 122°

12. 54° 13. 18°

14. 36° 15. 280.8° or 281°

Chapter 7 – Equations, Inequalities and Functions Answer Key


7.1 Addition and Subtraction Phrases as Equations

Answers

1. x + 5 2. x + 6 3. y + 8

4. n – 7 5. 8 – 4 6. n + 9

7. n – 5 = 10 8. 8 – 4 = x 9. 5 + y = 12

10. x – 16 = 80 11. 20 + x = 55 12. x + 15 = 40

13. n + 12 = 60 14. n – 15 = 90 15. x – 60 = 80

7.2 Multiplication and Division Phrases as Equations

Answers

1. 4x = 12 2. 6x = 30 3. 12y = 48 4. 14x = 28 5. 5y = 30

6. 8x = 64 7. 20/y = 4 8. 80/x = 4 9. 19x = 95 10. 13y = 39

11. 12/x = 6 12. x/2 = 8 13. x/7 = 14 14. 5x = 35 15. x/12 = 12

7.3 Single Variable Equations from Verbal Models

Answers

1. 10x = 30 2. 5x = 15 3. x + 7 = 11 4. x/3 = 12 5. x + 18 = 30

6. x/12 = 14 7. 7y = 49 8. x/13 = 7 9. 8y = 64 10. j – 8

11. c/3 12. 2s 13. w + 3 = l 14. n/3 = 6 15. 30 – 20 = c

7.4 Simplify Sums or Differences of Single Variable Expressions

Answers

1. 13a 2. 5x 3. 18y 4. 20a 5. 5y

6. 23a 7. 4b 8. 41x 9. 33y 10. 43a

11. 10x 12. 20a 13. 54b 14. 83x 15. 44y



7.5 Simplify Products or Quotients of Single Variable Expressions

Answers

1. 24a2 2. 18x 3. 28y2 4. 16a2 5. 44x2

6. 36b 7. 3a 8. 11 9. 25 10. 9

11. 5 12. 2y 13. 2 14. 5x/y 15. 41

7.6 Simplify Variable Expressions Involving Multiple Operations

Answers

1. 10a – 2b 2. 24b 3. 25a 4. 9x 5. 10y

6. 12a – 12b 7. 40a + 14b 8. 40a + 3b 9. 22a + 12y 10. 80a + 2b

11. 20y – 2x 12. 12x + 4y – 19z 13. 20y 14. 35y 15. 52y

7.7 Single Variable Addition Equations

Answers

1. 7 2. 17 3. 7 4. 17 5. 8

6. 6 7. 36 8. 35 9. 21 10. 226

11. 226 12. 206 13. 308 14. 8 15. 236

7.8 Single Variable Subtraction Equations

Answers

1. 17 2. 47 3. 38 4. 34 5. 41

6. 63 7. 80 8. 42 9. 41 10. 51

11. 5.1 12. 7.4 13. 15.6 14. 4.77 15. 14.64



7.9 Single Variable Multiplication Equations

Answers

1. 4 2. 12 3. -12 4. -8 5. 8

6. 9 7. -2 8. 2 9. -7 10. -3

11. -2 12. 2 13. -3 14. 3 15. 3

7.10 Single Variable Division Equations

Answers

1. 10 2. 21 3. -36 4. -80 5. 160

6. 30 7. -360 8. 81 9. -132 10. -9

11. -40 12. 3.9 13. 9.6 14. 7.2 15. 4.5

7.11 Two Step Equations from Verbal Models

Answers

1. 2x + 7 = 19 2. 3x + 5 = 20 3. 6x + 10 = 46

4. 2x – 7 = 21 5. 3x – 8 = 16 6. x/2 + 7 = 10

7. x/3 + 6 = 11 8. x/4 – 2 = 10 9. 4x + 8 = 20

10. 5x – 3 = 12 11. 2x + 7 = 29 12. 4x + 2 = 26

13. -3x – 4 = -10 14. -2x + 8 = -12 15. -5x – 8 = 17

7.12 Two – Step Equations and Properties of Equality

Answers

1. 4 2. 4 3. 3

4. 7 5. 7 6. 9

7. 4 8. 2 9. 6

10. 10 11. 9 12. 7

13. 7 14. 2m – 7 = 3, Monday = 5 shirts 15. 19 = 1/2r + 6, red = 26



7.13 Inequalities on a Number Line

Answers

1.

2.

3.

4.

5.

6.

7.

8.



9.

10.

11.

12.

13.

14.

15.



7.14 One – Step Inequalities

Answers

1. x < 6 2. x ≥ 10 3. b ≤ 10 4. a ≥ 21 5. y > 5

6. x ≤ 3 7. y > 3 8. x > 4 9. x = 20 10. x ≤ 30

11. x ≥ 1 12. y ≤ 2 13. a > 6 14. b < 15 15. x < 25

7.15 Domain and Range of a Function

Answers

1. No 2. Yes 3. Yes 4. No 5. No

6. {1, 2, 2, 3} 7. {2, 3, 4, 5} 8. {6, 7, 8} 9. {5} 10. {81, 75, 76, 77}

11. {3, 6, 5, 7} 12. {5, 6, 7, 8} 13. {1, 2, 3} 14. {2, 3, 4, 5} 15. {19, 18}

7.16 Input – Output Tables for Function Rules

Answers

1. (0, 2)(1, 9)(2, 16)(3, 23)(4, 30) 2. (0,-6)(6,0)(13,7)(22,16)

3. (8,3)(14, 6) 4. No

5. Yes 6. No

7. Yes 8. Yes

9. Yes 10. Yes


7.17 Function Rules for Input-Output Tables

Answers

1. Add 2 each time 2. y = x + 2 3. Multiply by 2 4. y = 2x 5. Multiply by 2 and add 1

6. y = 2x + 1 7. 48, 60 8. Multiply by 12 9. y = 12x 10. 60

11. (0, 10)(1, 30)(2, 50)(3, 70)(4, 90)

12. {0, 1, 2, 3, 4}

13. Zero doesn’t make sense because it isn’t a row

14. Add 3

15. y = x + 3



7.18 Graphs of Linear Equations

Answers

1. y = x + 3

2. y = 2x



3. y = 3x

4. y = x – 2



5. y = x + 4

6. y = 7x



7. y = 2x + 1

8. y = 2x – 1



9. y = 3x – 1

10. y = 4x



7.19 Linear and Non – Linear Function Distribution

Answers

1. Non Linear 2. Linear 3. Non linear

4. Missing a table 5. Can’t answer – missing information

6. (-4, 2)(-2, 3)(0, 4)(2, 5)(4, 6)

7.

8. Linear

9. (-2, 6)(-1, 3)(0, 2)(1, 3)(2, 6)

10.

11. Non Linear



12. y = x + 1

13.

14. y = 2x – 2

15.



7.20 Linear and Non – Linear Patterns of Change

Answers

1. Non-Linear 2. Linear 3. Linear 4. Linear 5. Non-Linear

6. Linear 7. Linear 8. Non-Linear 9. Linear 10. Non-Linear

11. y = 3x

12.

13. $9.00

14. (0, 10)(1, 8)(2, 6)(3, 4)

15.

16. $2.00

Chapter 8 – Geometry Answer Key


8.1 Angle Classification

Answers

1. Straight 2. Obtuse 3. Acute 4. Acute 5. Right

6. Obtuse 7. Right 8. Obtuse 9. Acute 10. Obtuse

11. Right 12. Straight 13. acute 14. Acute 15. Obtuse

8.2 Angle Pairs

Answers

1. Complementary 2. Complementary 3. Supplementary

4. Supplementary 5. Neither 6. Supplementary

7. Supplementary 8. Neither 9. Neither

10. Complementary 11. Neither 12. Neither

13. Complementary 14. Neither 15. Neither

8.3 Supplementary and Complementary Angle Pairs

Answers

1. 27° 2. 7° 3. 87° 4. 67° 5. 20°

6. 61° 7. 24° 8. 3° 9. 147° 10. 77°

11. 107° 12. 102° 13. 81° 14. 70° 15. 53°

8.4 Vertical Angles

Answers

1. Intersecting 2. Parallel 3. Intersecting 4. Perpendicular

5. Parallel 6. Perpendicular 7. Intersecting 8. Vertical

9. Adjacent 10. Adjacent 11. Vertical 12. Vertical

13. Adjacent 14. Vertical 15. Adjacent 16. 95°

17. 55° 18. 107° 19. 98° 20. 67°



8.5 Parallel and Perpendicular Lines

Answers

1. True 2. False 3. False 4. True 5. False

6. True 7. True 8. True 9. True 10. Intersecting

11. Intersecting 12. Parallel 13. Parallel 14. Intersecting 15. Parallel

8.6 Corresponding Angles

Answers

1. Angles next to each other

2. Angles opposite each other with the same measure

3. Lines that will never intersect

4. Lines that intersect at a 90 degree angle

5. An angle pair whose sum is 180°

6. An angle pair whose sum is 90°

7. Angles formed when two parallel lines are intersected

8. vertical

9. Angle P

10. Angle Q

11. True

12. False

13. False

14. 4

15. No



8.7 Triangle Sum Theorem

Answers

1. 90° 2. 60° 3. 75° 4. 35° 5. 65°

6. 15° 7. 30° 8. 10° 9. 25° 10. 80°

11. 60° 12. 55° 13. 85° 14. 95° 15. 50°

8.8 Triangle Classification

Answers

1. 80° 2. 72° 3. 55° 4. Obtuse 5. Acute

6. Acute 7. Right 8. Scale 9. Equilateral 10. Scalene

11. Isosceles 12. Obtuse 13. false 14. True 15. True

16. True 17. False 18. False 19. true 20. True

8.9 Quadrilateral Classification

Answers

1. Trapezoid 2. Parallelogram 3. Square

4. Rhombus 5. Rectangle 6. square

7. Parallelogram 8. Trapezoid 9. Rhombus

10. Quadrilateral 11. trapezoid 12. Square

13. Rectangle or square 14. Square or rhombus 15. rectangle

8.10 Polygon Classification

Answers

1. square, trapezoid

Angle F = 90°, Angle E = 90°, Angle G = 90°, Angle H = 55°, Angle I = 90°

2. True 3. True 4. True 5. False 6. False 7. True

8. Yes 9. No 10. No 11. No 12. Yes 13. No

14. Yes 15. Yes



8.11 Regular and Irregular Polygons

Answers

1. Trapezoid 2. Rectangle 3. Square 4. Square

5. square, trapezoid

Angle F = 90°, Angle E = 90°, Angle G = 90°, Angle H = 55°, Angle I = 90°

6. True 7. True 8. True

9. False 10. False 11. True

12. True 13. False 14. Regular hexagon

15. Irregular heptagon 16. Regular pentagon 17. Irregular octagon

8.12 Congruent Figures

Answers

1. Angle S

2. ST

3. Angle Q

4. 2 cm

5. 85°

6. 85°

7. True

8. No

9. Yes

10. No

11. No

12. No

13. Yes, congruent figures have the same measure

14. Congruent figures have the same size and shape

15. False



8.13 Similarity

Answers

1. Congruent

2. Similar

3. Similar

4. Neither

5. Congruent

6. Neither

7. True

8. False

9. False

10. Two equal ratios form a proportion

11. True

12. Similar figures have the same shape but different size

13. Congruent

14. Having exactly the same size, shape and measure

15. True

8.14 Scale Factor of Similar Polygons

Answers

1. 1/5 2. 1/6 3. 1/2.5 4. 1/3.5 5. 3/1

6. 4/1 7. ¼ 8. 2/1 9. 3/1 10. 8/1

11. 5/1 12. 6/1 13. 2/1 14. 3/1 15. 1/3



8.15 Unknown Measures of Similar Figures

Answers

1. 3 cm 2. 56 inches 3. 21 4. 3

5. 4/3 6. 8/1 7. 9/1 8. 24 cm

9. 19.5 in 10. 4500 ft 11. 9000 ft 12. 7500 ft

13. 2250 ft 14. 3750 ft 15. 5250 ft 16. 7500 ft

8.16 Rigid Transformations

Answers

1. Translation 2. Rotation 3. Translation 4. Reflection

5. Rotation 6. Translation 7. Reflection 8. Rotation

9. Line 10. Rotational 11. Line 12. Line


8.17 Lines of Symmetry

Answers

1. False 2. True 3. False 4. True 5. True 6. False

7. True 8. True 9. Line 10. Rotational 11. Line 12. Line


8.18 Transformation Classification

Answers

1. Translation 2. Rotation 3. Translation

4. Reflection 5. Rotation 6. Translation

7. Reflection 8. Translation 9. True

10. (5, 3)(7,7)(8,2) 11. (3,3)(7,7)(8, 2) 12. (6, 3)(7,7)(8, 2)

13. (10, -1)(7,7)(8, 2) 14. (11, 4)(7,7)(8, 2) 15. (10, 5)(7,7)(8, 2)



8.19 Translations, Rotations and Reflections

Answers

1. (-1, 5)(-5, 1)(-1, -3)

2. (3, 2)(-1, -2)(3, -6)

3. (-4, 2)(-10, -2)(-6, -6)

4. (-7, 2)(-11, -2)(-7,-6)

5. (1,1)(-3, -3)(1, -7)

6. (-2, 4)(-6, 0)(-2, -4)

7. (0, 5)(-4, 1)(0, -3)

8. (2, 1)(-2, 5)(-6, 1)

9. (1, -2)(5, 2)(1, 6)

10. (-1, -2)(-5, 2)(-1, 6)

11. (1, 2)(5, -2)(1, -6)

12. (2, 7)(-2, 3)(2, -1)

13. (-5, -4)(-11, -8)(-5, -12)

14. True

15. False

Chapter 9 – Distance and Area Answer Key


9.1 Evaluation of Square Roots

Answers

1. 4 2. 5 3. 1 4. 7 5. 12

6. 9 7. 13 8. 11 9. 10 10. 16

11. 3 and 4 12. 3 and 4 13. 5 and 6 14. 6 and 7 15. 7 and 8

16. 8 and 9 17. 8 and 9 18. 10 and 11 19. 2 and 3 20. 3 and 4

9.2 Evaluation of Perfect Square Roots

Answers

1. 6 2. 7 3. 8 4. 9 5. 10

6. 11 7. 12 8. 14 9. 20 10. 30

11. 100 12. 15 13. 16 14. 18 15. square roots are each a whole number

9.3 Simplification of Radical Expressions

Answers

1. 18 2. 25 3. 26 4. 120 5. 9

6. 35 7. 21 8. 24 9. 21 10. 23

11. 3 12. 47 13. 31 14. 9 15. 25

9.4 Equations with Square Roots

Answers

1. 3 2. 7 3. 10 4. 8 5. 15

6. 16 7. 3 8. 5 9. 6 10. 8

11. 9 12. 99 13. 6 14. 2 15. 3



9.5 Estimation of Square Roots

Answers

1. 2.8 2. 3.3 3. 4.9 4. 5.6 5. 6.1

6. 6.6 7. 7.7 8. 8.2 9. 8.5 10. 8.9

11. 9.7 12. 9.9 13. 10 14. 12.2 15. 11.7

9.6 Properties of Rational versus Irrational Numbers

Answers

1. Irrational 2. Rational 3. Rational 4. Rational 5. Irrational

6. Rational 7. Rational 8. Irrational 9. Irrational 10. Rational

11. Irrational 12. Rational 13. Irrational 14. Rational 15. Irrational

9.7 Pythagorean Theorem and Its Converse

Answers

1. 10 2. 15 3. 20 4. 25 5. 30

6. 40 7. 8.6 8. 14.2 9. 15.6 10. 14. 4

11. 13.6 12. 12.04 13. 16.55 14. 14.31 15. 14.42

9.8 Solving Equations Using the Pythagorean Theorem

Answers

1. 10.4 2. 12

3. 3 4. 15.6

5. 20 6. 6.6

7. 8.7 8. 7.5

9. 1.52 + 22 = c2 10. 2.5 m tall

11. 32 + 42 = c2 12. 5 miles

13. 5.52 + b2 = 14.52 14. 13.4 inches



9.9 Area of a Parallelogram

Answers

1. 45 sq. in. 2. 12 sq. in. 3. 72 sq. ft.

4. 88 sq. meters 5. 130 sq. yds. 6. 10 sq. ft.

7. 19.25 sq. in 8. 58.5 sq. ft. 9. 396 sq. miles

10. 348 sq. meters 11. 242 square meters 12. 585 sq. meters

13. 1000 sq. meters 14. 4,400 sq. meters 15. 1106 sq. meters

9.10 Unknown Dimensions of Parallelograms

Answers

1. 5 ft 2. 2.5 in. 3. 9 ft 4. 10 in. 5. 2.5 ft. 6. 12 in.

7. 18 ft. 8. 16 m 9. 2 in. 10. 5 miles 11. 6 in. 12. 2 meters

13. 15 ft. 14. 11 ft. 15. 11 ft. 16. 8 miles 17. 3 meters 18. 4 feet

9.11 Estimation of Parallelogram Area in Scale Drawings

Answers

1. 96 sq. ft. 2. 192 sq. ft. 3. 64 sq. ft.

4. 80 sq. ft. 5. 144 sq. ft. 6. 320 sq. ft.

7. 528 sq. ft. 8. 540 sq. ft. 9. 720 sq. ft.

10. 26 cm 11. 42 in. 12. 398.94 sq. cm

13. 2210 sq. ft. 14. Kara’s, 3.3 inches 15. 223 cm

9.12 Triangle Area

Answers

1. 18 in2 2. 9 in2 3. 14 in2 4. 31.5 m2 5. 60 ft2

6. 35 ft2 7. 91 ft2 8. 44 m2 9. 55.25 ft2 10. 51.75 m2

11. 135 m2 12. 162.75 ft2 13. 99 ft2 14. 158.88 m2 15. 440 ft2



9.13 Unknown Dimensions of Triangles

Answers

1. 3 m 2. 6 m 3. 3 m 4. 6 ft 5. 5 ft

6. 12 ft 7. 9 in 8. 18 in 9. 9 ft. 10. 6 in.

11. 10 in 12. 14 ft. 13. 18 in 14. 17 ft. 15. 13 in.

9.14 Area of Composite Shapes Involving Triangles

Answers

1. 66.5 sq. in. 2. 99 sq. in. 3. 126 sq. in.

4. 45 sq. ft. 5. 45 sq. ft 6. 120 sq. ft.

7. 102 sq. ft. 8. 150 sq. in. 9. 132.5 sq. in

10. 220.25 sq. in. 11. 82.5 sq. in 12. 24 cm

13. 13 in. 14. 432 sq. ft. 15. 16.5 sq. in.

9.15 Circle Circumference

Answers

1. 12.56 in. 2. 12.56 in. 3. 28.26 in.

4. 25.12 m 5. 75.36 in. 6. 37.68 mm

7. 87.92 mm 8. 40.82 ft. 9. 62.8 in

10. 23.55 ft. 11. 15.7 in 12. 35.17 ft.

13. 11.78 ft. 14. 14.13 ft. 15. 33.76 m

9.16 Diameter or Radius of a Circle Given Circumference

Answers

1. 5 ft 2. 6.5 in. 3. 7 m 4. 1.5 cm 5. 15 ft. 6. 7 in.

7. 2.5 m 8. 2.25 in. 9. 3.25 cm 10. 2 ft. 11. 102.05 m 12. 420.76 cm

13. 45.40 ft. 14. 55 inches 15. 100 cm 16. 6.5 ft. 17. 3548.2 m 18. 138.16 in.



9.17 Area of a Circle

Answers

1. 28.26 sq. in 2. 78.5 sq. in 3. 50.24 sq. ft.

4. 153.86 sq. m 5. 113.04 sq. cm 6. 38.47 sq. in

7. 200.96 sq. in 8. 153.86 sq. cm 9. 314 sq. in

10. 176.63 sq. m 11. 379.94 sq. cm 12. 452.16 sq. mm

13. 1808.64 sq. in. 14. 854.87 sq. in 15. 2082.02 sq. in

9.18 Radius or Diameter of a Circle Given Area

Answers

1. 2 in 2. 5 m 3. 8 cm 4. 9 in 5. 1.5 ft.

6. 3 m 7. 4 in 8. 10 m 9. 16 cm 10. 18 in

11. 3 ft 12. 6 m 13. 28 ft. 14. 15 m 15. 12 ft

9.19 Areas of Combined Figures Involving Circles

Answers

1. 168.49 sq. mm 2. 100.61 sq. in. 3. 73.19 sq. in.

4. 235.33 sq. ft. 5. 334.55 sq. ft. 6. 49.81 sq. ft.

7. 65.13 sq. ft. 8. 72.29 sq. in. 9. 47.23 sq. ft.

10. 24.06 sq. ft. 11. 19.81 sq. in 12. 40.23 sq. in.

13. 22.87 sq. in 14. 452.16 sq. ft. 15. 138,474 sq. ft.

Chapter 10 – Surface Area and Volume Answer Key


10.1 Classification of Solid Figures

Answers

1. Rectangular Prism 2. Hexagonal prism 3. Cone

4. Cylinder 5. Triangular pyramid 6. pentagonal prism

7. Cube 8. Sphere 9. Octagonal prism

10. Hexagonal prism 11. prism 12. Sphere

13. Cone 14. Pyramid 15. Prism

10.2 Faces, Edges and Vertices of Solids

Answers

1. 2 faces

2. 5 faces, 1 vertex, 8 edges

3. 1 face, 1 vertex

4. 6 vertices, 5 faces, 9 edges

5. 6 faces, 8 vertices, 12 edges





10. none



13. sphere

14. cylinder

15. 12

16. 8

17. 9



10.3 Cross-Sections and Nets

Answers

1. Square pyramid 2. Rectangular prism

3. Pentagonal prism 4. Triangular pyramid

5. triangular prism 6. Cylinder

7. Cone 8. Cube

9. Cylinder 10. hexagonal prism

11 - 20 Answers will vary

10.4 Surface Area of Rectangular Prisms

Answers

1. 340 sq. in 2. 352 sq. in 3. 288 sq. m

4. 344 sq. in 5. 392 sq. m 6. 318 sq. ft.

7. 232 sq. m 8. 126 sq. ft. 9. 72 sq. ft.

10. 96 sq. ft. 11. 510 sq. ft. 12. 808 sq. ft.

13. 1392 sq. ft. 14. 1592 sq. m 15. 2082 sq. m

10.5 Surface Area of Triangular Prisms

Answers

1. cm 2. 15 cm 3. 4 cm

4. Rectangle 5. 4 cm x 3 cm 6. SA = 2(1/2bh) + 3lw

7. 192 cm2 8. 57 in2 9. 110 ft2

10. 45 in2 11. 150 m2 12. 510 ft2

13. 252 in2 14. 318 in2 15. 157 ft2



10.6 Surface Area of Cylinders

Answers

1. 25.12 m2 2. 75.36 cm2 3. 602.88 in2

4. 251.2 in2 5. 471 in2 6. 703.36 ft2

7. 1570 m2 8. 1186.92 cm2 9. 527.52 m2

10. 62.8 cm2 11. 376.8 m2 12. 1036.2 in2

13. 602.88 cm2 14. 1356.48 m2 15. 2237.25 in2

10.7 Heights of Cylinders Given Surface Area

Answers

1. 2 in 2. 2 in 3. 1.5 in 4. 2 cm 5. 2.5 m

6. 4 cm 7. 3 cm 8. 1 m 9. 2 cm 10. 1.5 cm

11. 3 cm 12. 2 cm 13. 2 cm 14. 2 cm 15. 3 cm

10.8 Surface Area and Volume of Pyramids

Answers

1. 640 in2 2. 768 in2 3. 3,456 in2 4. 1,750 in2 5. 6,174 in2

6. 10,240 m2 7. 16,038 cm2 8. 34,606 m2 9. 3,888 in2 10. 24,000 cm2

11. 8,640 in2 12. 19,200 ft2 13. 144 in2 14. 59,136 m2 15. 45,000 in2

10.9 Surface Area and Volume of Cones

Answers

1. 113.04 in2 2. 188.4 m2 3. 84.78 cm2

4. 204.1 mm2 5. 452.16 in2 6. 863.5 cm2

7. 1055.04 in2 8. 104.495 cm2 9. 162.495 mm2

10. 263.76 cm2 11. 388.575 cm2 12. 690.8 cm2

13. 1708.16 cm2 14. 1347.06 cm2 15. 1654.78 cm2



10.10 Volume of Rectangular Prisms

Answers

1. 60 in3 2. 210 m3 3. 288 cm3 4. 384 cm3 5. 300 ft3

6. 792 m3 7. 82.5 in3 8. 231 cm3 9. 168 ft3 10. 1200 m3

11. 462 m3 12. 1152 ft3 13. 1024 in3 14. 1728 m3 15. 864 in3

10.11 Volume of Triangular Prisms

Answers

1. 60 in3 2. 157.5 in3 3. 360 m3 4. 780 m3 5. 216 cm3

6. 252 cm3 7. 44 mm3 8. 396 cm3 9. 3230 ft3 10. 2700 ft3

11. 2754 ft3 12. 4788 ft3 13. 3528 ft3 14. 297,000 ft3 15. 440,000 ft3

10.12 Volume of Cylinders

Answers

1. 628 in3 2. 351.68 in3 3. 141.3 ft3

4. 226.08 ft3 5. 452.16 cm3 6. 1356.48 m3

7. 2154.04 in3 8. 785 m3 9. 138.16 m3

10. 339.12 cm3 11. 1243.44 cm3 12. 703.36 m3

13. 13,797.16 cm3 14. 2813.44 in3 15. 1049.15 cm3

10.13 Heights of Cylinders Given Volume

Answers

1. 8 in 2. 9 in 3. 15 ft. 4. 20 ft 5. 10 ft

6. 14 m 7. 16 m 8. 18 m 9. 25 in 10. 8 ft.

11. 5 in 12. 6 in 13. 9 m 14. 9 ft 15. 7 in



10.14 Volume of Pyramids

Answers

1. 108 ft3 2. 213.33 m3 3. 524.33 in3 4. 378 ft3 5. 33.75 in3

6. 20 in3 7. 40 ft3 8. 84 m3 9. 20 in3 10. 84 ft3

11. 85.33 ft3 12. 40 in3 13. 26.54 ft3 14. 119.71 ft3 15. 60 ft3

10.15 Volume of Cones

Answers

1. 65.94 in3 2. 235.5 ft3 3. 376.8 m3

4. 1256 in3 5. 2110.08 mm3 6. 314 ft3

7. 148.37 in3 8. 70.52 in3 9. 666.73 cm3

10. 736.85 cm3 11. 647.63 in3 12. 2076.33 in3

13. 2453.13 ft3 14. 527.52 m3 15. 126.60 in3

Chapter 11 – Data and Statistics Answer Key


11.1 Mean

Answers

1. 5 2. 7.2 3. 15.22 4. 22.38 5. 30

6. 36.57 7. 41.17 8. 126.56 9. 222.67 10. 545.17

11. 780.86 12. 348.67 13. 220.43 14. 1140.5 15. 2393.17

11.2 Median

Answers

1. 3 2. 13 3. 21 4. 18.5 5. 54

6. 3 7. 5 8. 12 9. 22.5 10. 30

11. 37 12. 43.5 13. 128 14. 223 15. 545.5

11.3 Mode

Answers

1. 7 2. 6 3. No mode 4. 121 5. 600

6. 4 7. 7 8. 11 9. 21 10. 33

11. 34 12. 43 13. 110 14. No mode 15. 550

11.4 Range of Spread/Dispersion

Answers

1. 34.71 2. 35 3. 40 4. 17

5. 157.2 6. 152.5 7. 200 8. 105

9. 25.6 10. 25 11. 25 12. 7

13. 8.9 14. 9 days 15. 9 days 16. 1 day



11.5 Bar Graphs

Answers

1. 5 2. 20 3. Carrots

4. Tomatoes or potatoes 5. 30 6. 10

7. 15 8. 35, it would be the most 9. 60,20,50,30,20

10. 15, 5, 12.5, 7.5, 5 11. 90 12. 5

13. 0 – 35 14. units of 5 15. 20

11.6 Multiple Bar Graphs

Answers

1. 13 2. 28 3. 4

4. Florida and Pennsylvania 5. NY 6. Answers vary

7. Television 8. Television or DVD player 9. Television

10. Video Camera 11. Game system 12. Video camera

13. 7 14. 3 15. True

11.7 Line Graphs

Answers

1. 100 2. 300 3. 200 vegetables 4. 300

5. 0, no charge 6. 400 vegetables 7. 300 vegetables 8. 700 vegetables

9. 350 vegetables 10. 500 vegetables 11. 200 vegetables 12. False 13. True

14 – 15 Answer Vary

11.8 Multiple Line Graphs

Answers

1. Answers vary 2. Seattle 3. Seattle

4. 2007 5. 2007 6. Seattle zoo

7. increase 8. Increase 9. 30,300 tickets

10. 34,700 11. Line graph 12. Answers vary

13. False 14. Multiple line graph 15. Answers vary



11.9 Stem-and-Leaf Plots

Answers

1. 2 2 5 7 9

3 1 4 4 9

4 0 4

2. 6 5

7 2

8 6 8 9

9 0 1 6

10 0 1

3. 0 4 6 6 7 8 9

1 1 2 5

2 0

4. 9.8

5. 7.5

6. 6

7. 16

8. 2 1 5 6 7 9 9

3 1 4 6 8 9

4 0

9. 31.25

10. 30



11. 29

12. 19

13. 1, 2, 3

14. 7th

15. 16 = 8th, 11 = 7th

16. 8th

17. 4, 5, 6

18. 49°

19. 40°

20. Seattle

21. 18

22. 16

23. 56° = Austin, 40° = Seattle



11.10 Box – and – Whisker Plots

Answers

1. 22 2. 15 3. 28 4. 12 5. 31

6.

26 27 29 30 32 35 41 42 44

7. 32

8. 28

9. 41.5

10. 26

11. 44

12.

100 105 107 109 110 120

13. 108 14. 105 15. 110 16. 100 17. 120



11.11 Frequency Tables to Organize and Display Data

Answers

1. 174 2. 5 days 3. 1 day

4. Days Frequency

0 15

1 13

2 30

3 21

4 35

5 60

5. 1 student

6. 175 total

7. Books Students

1 2

2 1

3 2

4

5 2

6 1

7 1

8 1

8. 4

9. 1, 3 or 5

10. Correct

11. Unorganized



12. 7

13. 4

14. 7

15. False

16. False



11.12 Histograms

Answers

1.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Series 1

Series 2

Series 3



2.

Number Frequency

2 1

3 1

4 1

5 4

6 1

7 3

8 2

9 2

10 1

11 1

12 1

13 0

14 1

15 1



3.

4.

Number Frequency

3 3

4 1

5 1

7 1

8 1

9 2

10 1

11 1

12 1

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

2 3 4 5 6 7 8 9 10 11 12 13 14 15

Series 1

Column1

Column2



5.

6. The number three is the most popular and the number 6 is not even represented in the data.

7 – 10. Answers Vary

11.

Number Frequency

1 5

2 2

3 5

4 1

5 1

6 1

12. 1 and 3

13. 4, 5, 6

14. 5

15. 2, 5

0

0.5

1

1.5

2

2.5

3

3.5

3 4 5 6 7 8 9 10 11 12

Series 1

Series 2

Series 3



11.13 Identification of Misleading Statistics

Answers

1. yes 2. Intervals aren’t consistent 3. Even out the intervals by using the same measures

4.

0

0.5

1

1.5

2

2.5

3

3.5

4

6th 7th 8th 9th 10th 11th 12th

Tim

e

Grade



5. ONE POSSIBLE ANSWER

6. 4 hours 7. 1.5 hours 8. True

1

3

5

7

9

11

13

15

6th 7th 8th 9th 10th 11th 12th

Tim

e

Grade



9.


11. New Jersey 12. No, because the purpose is to compare states that have sales tax.

0

1

2

3

4

5

6

7

8

Alaska Alabama Arizona California New Jersey

Sale

s Ta

x R

ate

(%

)

State

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

Alaska Alabama Arizona California New Jersey

Sale

s Ta

x R

ate

(%

)

State




14.

47

49

51

53

55

57

59

61

63

65

1 2 3 4 5 6 7 8 9 10

Tem

pe

ratu

re

Days

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7 8 9 10

Tem

pe

ratu

re

Days



15. 64

16. 49

17 – 20. Answers may vary



11.14 Data Display Choices

Answers

1. False 2. True 3. #1 4. $28,000

5. $31,000 6. #1 7. $28,000 8. Box and Whisker Plot

9.

36 42 45 48 49 50 56 58 59 62

10.

0

2

4

6

8

10

12

14

16

18

1 2 3 4 5 6

Series 1

Series 2

Series 3



11.

12. Number Frequency

5 1

8 1

10 2

12 1

15 2

18 2

20 1

23 1

25 2

27 1

30 1

0

2

4

6

8

10

12

14

16

18

1 2 3 4 5 6 7 8 9 10

Series 1

Series 2

Series 3



13.

30 should have a bar to the number 1. It wouldn’t fit on this chart.

14.

5 8 10 10 12 15 15 18 18 20 23 25 25 27 30

15.

3 .5 .6 .6 .8

4 .1 .2 .3 .5 .6

5 .1

0

0.5

1

1.5

2

2.5

5 8 10 12 15 18 20 23 25 27 30

Series 1

Series 2

Series 3



16.

0

1

2

3

4

5

6

1 2 3

Series 1

Series 2

Series 3

Series 4

Series 5



11.15 Displaying by Type of Data

Answers

1.

2. 85% 3. 32% 4. 65% 5. 46% 6. Waikiki 7. Denver

8. Frequency Table

9. 0 4

1 3

2 7

3 6

4 4

5 4

6 2

10. 23%

11. 10%

0

10

20

30

40

50

60

70

80

90

100

Series 1

Series 2

Series 3



12. 3

13. 4

14. 3%

15. 4%

16 – 20 Answers will vary

Chapter 12 – Probability Answer Key


12.1 Definition of Probability

Answers

1. 4 2. One favorable outcome 3. 1/6

4. 3, 4, 5,6 5. 4 favorable outcomes 6. 4/6

7. 5, 6 8. Two favorable outcomes 9. 2/6

10. 2, 4, 6, 8, 10, 12 11. 6 favorable outcomes 12. 6:12

13. 4, 5, 6, 7, 8, 9, 10, 11, 12 14. 9 favorable outcomes 15. 9:12

16. 5 17. 5/15 18. 9 19. 9:15 20. 6

21. 6:15 22. 6 23. 6:15 24. 2 25. 2:15

12.2 Measurement of Probability

Answers

1. 9 2. One favorable outcome 3. 1:10 4. 10%

5. 3, 4 6. Two favorable outcomes 7. 10 8. 20%

9. 1, 3, 5, 7, 9 10. 5 favorable outcomes 11. 10 12. 50%

13. 6, 8, 10 14. 3 15. 10 16. 30%

17. 33.3% 18. 50% 19. 50% 20. 83.3%

12.3 Empirical Probability

Answers

1. 17 2. 60 3. 28% 4. 24 5. 50

6. 48% 7. 78 8. 100 9. 78% 10. 8

11. 40 12. 20% 13. 16 14. 50 15. 32%



12.4 Mutually Exclusive Events

Answers

1. Overlapping 2. Disjoint 3. Disjoint

4. Overlapping 5. Disjoint 6. disjoint

7. Disjoint 8. Overlapping 9. Overlapping

10. Disjoint 11. overlapping 12. Overlapping

13. Disjoint 14. Overlapping 15. overlapping

12.5 Mutually Inclusive Events

Answers

1. 1:8 2. 3:8 3. 2:8 4. 2:8 5. 5:8

6. 2:8 7. 6:12 8. 6:12 9. 1:12 10. 1:12

11. 3:12 or 1:4 12. 6:12 13. 4:12 or 1:3 14. 5:12 15. 1:12

12.6 Complement Rule for Probability

Answers

1. .85 2. .2 3. 51%

4. 5/8 5. .93 6. .875

7. 3.9% 8. 4/5 9. Complement

10. Complement 11. Not a Complement 12 Not a Complement

13. Complement 14. Not a Complement 15. Not a complement

12.7 Counting Events

Answers

1. 6 2. 9 3. 12 options 4. 8 5. 18

6. 12 7. 36 8. 6 9. 8 10. 8

11. 10 12. 15 13. 18 14. 10 15. 14



12.8 Sample Spaces and Events

Answers

1. 6

2. 2

3. HT TT HH TH

4. HHH TTH TTT HTT HTH THH THT HHT

5. 3

6. 3

7. 4

8. 8

9. 12

10. 5

11. 0

12. 4

13. 4

14. True

15. False

12.9 Additive and Multiplicative Rules for Probability

Answers

1. 1/3 2. 1/3 3. 1/3 4. 1/3 5. 1/3

6. 2/3 7. 3/50 8. ½ 9. ¼ 10. ¼

11. 1/12 12. 1/6 13. ½ 14. ¾ 15. 2/3



12.10 Basic Counting Rules

Answers

1. 6 2. 8 3. 96 4. 18 5. 8

6. 54 7. 6 8. 104 9. 84 10. 52

11. 30 12. 15 13. 10 14. 20 15. 25

12.11 Counting Rule to Calculate Probabilities

Answers

1. ¾ 2. 3/8 3. ¼ 4. ¼ 5. ¼

6. ¼ 7. 1/6 8. 1/6 9. 1/6 10. 1/6

11. 1/6 12. ½ 13. ½ 14. 1/3 15. 1/3

12.12 Permutations

Answers

1. Order doesn’t matter – passwords 2. Order doesn’t matter because it is trios.

3. order does matter – combination locks 4. Order does matter – prizes are given out

5. Order doesn’t matter 6. Order does matter – awards given out

7. 6 8. 24 9. 24

10. 24 11. 24 12. 120

13. 720 14. 18,060 15. 40,320 – it more than doubles

12.13 Permutation Problems

Answers

1. 6 2. 24 3. 12 4. 60

5. 120 6. 720 7. 210 8. 840

9. 120 10. 6 11. 720 12. 24

13. 12 14. 24 15. 120 16. 120



12.14 Combinations

Answers

1. Combination 2. Combination 3. Combination

4. Permutation 5. Combination 6. Permutation

7. Combination 8. Permutation 9. Combination

10. Permutation 11. Combination 12. Combination

13. Permutation 14. Combination 15. Combination

12.15 Combination Problems

Answers

1. 120 2. 24 3. 6 4. 144,480 5. 362,880

6. 720 7. 21 8. 7 9. 70 10. 84

11. 56 12. 120 13. 220 14. 55 15. 120

12.16 Independent Events

Answers

1. Independent 2. Dependent 3. Independent

4. Independent 5. Independent 6. Dependent

7. Independent 8. Dependent 9. independent

10. Dependent 11. Dependent 12. Dependent

13. independent 14. Independent 15. Independent



12.17 Probability of Independent Events

Answers

1. 1/9 2. 1/9 3. 2/9 4. 4/9 5. .64

6. .04 7. .16 8. 8/104 9. 3/13 10. 8/104

11. 1/8 12. 1/16 13. 1/16 14. 1/32 15. 1/32

12.18 Dependent Events

Answers

1. ¼ 2. 3/8 3. ¼ 4. 1/4 5. 3/8

6. 1/56 7. 3/8 8. ¼ 9. 0/8 10. 3/8

11. 2/3 12. 1/5 13. 1/5 14. 3/10 15. 1/20

Documents

Chapter 1 Algebraic Thinking Answer Key