Ch. 4 Study Guide
1. 13,000 cm2
2. 154 in2
3. 4 cm2
4. 120 ft2
5. 51 m2
6. 128 in2
7-8. I can’t draw the graphs.
9. 16 units; 16 units2
10. 28 units; 48 units2
11. 35 ft2
12. a. 4605 ft b. 1,459,063 ft2
13. 400 ft2
4.4 Exercises #8-24 (even), 25, 27-31
8-10. I can’t draw the graphs. Check with your neighbor.
12. 12 units; 9 units2
14. 16 units; 15 units2
16. The x and y coordinates are reversed.
18-20. I can’t draw the graphs. Check with your neighbor.
22. (6, 1) and (8, 9)
24. 41 mi2
25. 2.5 times larger
27. 2
28. 8 ⅘
29. 5/16
30. 3 19/27
31. D
4.3 Exercises # 4-18 (even), 21, 23-27
4. 12 units2
6. 27 units2
8. 10 cm2
10. The height was not included in the formula. A = ½(6 + 14)(8) = 80 m2
12. 16 units2
14. 16 ft2
16. 253 cm2
18. 301 m2
21. The area of the floor covered by the larger speaker is 4 times greater than the area of the floor covered by the smaller speaker.
23-26. I can’t draw the graphs. Check your placement with your neighbor!
27. C
4.2 Exercises # 3-9, 11, 14, 17, 21-24
3. 6 cm2
4. 40 ft2
5. 1620 in2
6. 154 yd2
7. 1125 cm2
8. 132 m2
9. The side length of 13 meters was used instead of the height. A = ½(10)(12) = 60 m2
11. 324 cm2
14. 189 mm2
17. x2 times greater
21. Multiplication Property of One
22. Commutative Property of Multiplication
23. Associative Property of Addition
24. C
4.1 Exercises #3-13 (odd), 14-16, 18, 22-26
3. 18 ft2
5. 187 km2
7. 243 in2
9. 15 meters was used for the height instead of 13 meters. A = 8(13) = 104 m2
11. 12 units2
13. 24 units2
14. 64 cm2
15. 72 m2
16. 96 ft2
18. 22 times
22. 13
23. 1640
24. 480
25. 118
26. B
Ch 3 Study Guide
1. 10
2. 0
3. 48
4. 2x or x • 2
5. 25 + 50 or 50 + 25
6. 40 5
7. 11.7 + m
8. 70n
9. 45w
10. 4x + 32
11. 12y - 60
12. 4q + 2
13. 15r + 17
14. 8s
15. 2t + 5
16. 6(3 + 4)
17. 8(5 - 2)
18. 5(3x + 4)
19. 8(4x - 5y)
20. 94 min
21. 90x
22. 9n; 3(1/4n)
3.4 Exercises #22-32 (even), 33, 34, 39-49 (odd)
22. 18n +9
24. 90 - 54w
26. 70 + 7x
28. 78 + 6z
30. 25x -25y
32. 13n + 52 + 91m
33. The 6 was not distributed to the 8 inside the parentheses. 6(y + 8) = 6y + 48.
34. a. 30(8 + x) = 240 + 30x b. Sample answer: $2. It is less than the regular price to the exhibit. c. Sample answer: $300; yes
39. 6x + 25
41. 68 + 28k
43. 19y + 5
45. 3d + 1
47. 5v
49. 2.7w - 14.04
3.4 Exercises #5-8, 66-70
5. 63
6. 684
7. 516
8. 440
66. 10.641
67. 34.006
68. 135.213
69. 0.387
70. B
3.3 Exercises #11-23 (odd), 24-28 (even)
11. The groupings of the numbers did not change. The statement illustrates the Commutative Property of Addition because the order of the terms changed.
13. y + 17
15. 63w
17. a + 8
19. 18.6d
21. 4n + 11.4
23. 0
24. x + 16
26. When x = 0.25, the object is the ruler (B). When x = 12.5, the object is the square floor tile (C). When x = 144, the object is the siding for a house (A).
28. 72y
3.3 Exercises #5-8, 35-43
5. Commutative Property of Multiplication
6. Associative Property of Addition
7. Associative Property of Multiplication
8. Commutative Property of Addition
35. 98
36. 108
37. 90
38. 200
39. 37 is already prime
40. 24 • 32
41. 3 • 72
42. 5 • 41
43. B
3.2 Exercises #2, 13-19 (odd), 22, 27-31 (odd)
2. The coefficient represents the cost to print each photo, 25 cents.
13. 7 + w or w + 7
15. y + 4 or 4 + y
17. 2 • z or z • 2
19. The expression is not written in the correct order; 8/y
22. a. 1,19; 2, 38; 3, 57; 4, 76; 5, 95 b. 19n
27. y/4 - 3; 2
29. 8x + 6; 46
31. a. 1, $5; 2 $8; 3, $11; 4, $14; 5, $17 b. 2 + 3g c. $26
3.2 Exercises #3-12, 36-40
3. 8 - 5
4. 3 • 12 or 12 • 3
5. 28/7
6. 6 + 10 or 10 + 6
7. 18 - 3
8. 15 + 17 or 17 + 15
9. x - 13
10. 5 • d or d • 5
11. 18/a
12. s - 6
36. 45
37. 59
38. 390
39. 140
40. D
3.1 Exercises # 8-10, 16-22 (even), 25-31 (odd), 43, 45
8. Terms: 7h, 3; Coefficient: 7; Constant: 3
9. Terms: g, 12, 9g; Coefficients: 1, 9; Constant: 12
10. Terms: 5c2, 7d; Coefficients: 5, 7; Constant: none
16. b3
18. 8w4
20. a2c2
22. The coefficient and the exponent are reversed. 3 • n • n • n • n = 3n4
25. 9
27. 11
29. 10
31. 6
43. 23
45. 2 5/6
3.1 Exercises # 4-7, 56-60
4. 8/2; $4
5. 20 • 6; $120
6. 95 - 82; 13 points
7. 20 - 12; $8
56. 243
57. 512
58. 2401
59. 256
60. C
Ch. 2 Study Guide
1. ⅜
2. 1/12
3. 9 4/7
4. ½
5. 25
6. 3 1/23
7. 8.71
8. 7.762
9. 3.374
10. 53.6
11. 0.28
12. 35.2101
13. 0.8
14. 130
15. 2.33
16. 21.84
17. 5 for $58.99
18. ½ hour
19. $4.66
20a. 1.2 times faster
20b. 4 more pictures
2.6 Exercises #18-34 (even), 40, 42, 61-65
18. 6.2
20. 5.58
22. 0.15
24. They brought down 2 zeros instead of 1.
26. $0.12
28. 7.945
30. 25.2
32. 2.35
34. The 12-pack; The price per unit is $0.74 for the 4-pack, $0.72 for the 12-pack, and $0.73 for the 24-pack. So, the 12-pack is the best buy.
40. 352.5
42. 7200
61. 1 ⅙
62. 1 3/20
63. 1/20
64. 1/24
65. B
2.5 Exercises #27, 36-42, 54-56
27. 30.06 lb
36. 0.0000032
37. 0.000012
38. 2.48
39. 109.74
40. 5.6952
41. 3.886
42. 117.96438
54. 4.355
55. 23.112
56. 2.016
2.5 Exercises #13-20, 70-74
13. 33.6
14. 31.5
15. 115.04
16. 18.27
17. 21.45
18. 29.45
19. 13.888
20. 98.256
70. 26
71. 5
72. 3
73. 7
74. D
2.4 Exercises #1, 2, 8, 10, 14-34 (even), 36-40
1. Estimating allows you to check that your answer is reasonable.
2. Line up the decimals points and insert zeros if needed.
8. 34.098
10. 34.313
14. 3.561
16. 2.884
18. You need to regroup and subtract 8 from 10. 9.5 - 7.18 = 2.32
20. $1.40
22. 6.772
24. 10.343
26. 21.582
28. Sample answer: 9.55, 10.6, 7.755
30. 3.6 hours
32. 28.546 AU
34. 10.26 AU
36. ½
37. ¼
38. ⅙
39. 1/20
40. C
2.3 Exercises #5-23 (odd), 26-36 (even), 41-45
5. 3
7. 9 ¾
9. 3 18/19
11. 9/10
13. 12 ½
15. 1 ⅕
17. 2/7
19. 1 5/18
21. The mixed number 1 ⅔ was not written as an improper fraction before inverting.
23. 14 hamburgers
26. 3
28. 3
30. 6 9/26
32. 13 ⅕
34. 3 ⅓
36. 7/108
41. 0.43
42. 0.013
43. 3.8
44. 7.009
45. C
2.2 Exercises #19-25 (odd), 28, 30, 43-51 (odd), 54, 55
19. 3
21. 2/27
23. 27/28
25. 20 ¼
28. You invert the second fraction, not the first.
30. 3/25
43. 1/216
45. 1 ⅙
47. 2
49. 3/26
51. ⅔
54. When the fraction has, or can be simplified to have, a 1 in the numerator; the reciprocal will have, or can be simplified to have, a 1 in the denominator, so it is a whole number.
55. a. 3 ¾ times b. 3 ⅓ times c. ¼
2.2 Exercises #11-18, 58-62
11. ½
12. 2 11/12
13. 16
14. 20
15. 1/14
16. 3/25
17. ⅓
18. ⅔
58. 8
59. 6
60. 16
61. 5
62. D
2.1 Exercises #1-3, 20-38 (even), 45,55
1. Multiply numerators and multiply denominators, then simplify the fraction.
2. 4
3. Sample Answer: 3 ½ • 3 ¼
20. You did not multiply the denominators. You also did not NEED to find a common denominator.
22. ¼
24. > because 22/15 is more than 1 and when you multiply a number by more than 1, it is going to get bigger.
26. 8/9
28. 2
30. 5
32. 1
34. 3 ½
36. 23 ⅖
38. 7 ⅞
45. a. 7 ft2 b. 10 ⅓ ft2
55. 4 miles
2.1 Exercises #4-11, 60-64
4. 2/21
5. 5/16
6. 1/10
7. 3/28
8. 8/21
9. ⅝
10. 1/24
11. ⅓
60. 23 • 3
61. 32 • 5
62. 53 is prime.
63. 22 • 3 • 5
64. B
Ch. 1 Study Guide
1. 6342
2. 3836
3. 4784
4. 9
5. 8
6. 225
7. 625
8. 85
9. 5
10. 10
11. 1, 52; 2, 26; 4, 13
12. 1, 66; 2, 33; 3, 22; 6, 11
13. 2 • 23
14. 22 • 7
15. 6
16. 8
17. 13
18. 9
19. 42
20. 72
21. 78
22. 84
23. 4 bracelets
24. 48 of each color marble
25. 2740 lb.
1.6 Exercises #12-18, 20, 25-31 (odd)
12. 63
13. 108
14. 90
15. 55
16. 180
17. 350
18. The product of 2 numbers is not necessarily the LCM. Use the ladder method to find the LCM is 2 • 3 • 3 = 18.
20. 4 packs of hot dogs and 5 packs of buns.
25. 120
27. 1260
29. Always
31. Never
1.6 Exercises #3-5, 37-40
3. 21
4. 24
5. 60
37. 32
38. 54
39. 175
40. B
1.5 Exercises #13-18, 20, 22-25
13.15
14. 9
15. 9
16. 12
17. 1
18. 1
20. Not all of the common prime factors are included. The GCF is 2 • 7 = 14.
22. 8 arrangements
23. 7
24. 6
25. 14
1.5 Exercises #4-6, 35-39
4. 6
5. 2
6. 12
35. Commutative Property of Addition
36. Associative Property of Addition
37. Commutative Property of Multiplication
38. Associative Property of Multiplication
39. B
1.4 Exercises #11-23 (odd), 24, 26, 27
11. 1, 39; 3, 13
13. 1, 54; 2, 27; 3, 18; 6, 9
15. 1, 61
17. 5 • 5 or 52
19. 2 • 13
21. 2 • 3 • 3 • 3 or 2 • 33
23. 7 • 11
24. 9 is not prime, it is equal to 3 • 3. 72 = 2 • 2 • 2 • 3 • 3 or 23 • 32
26. 180
27. 1575
1.4 Exercises #4-7, 40-44
4. 2, 3, 6, 9
5. 3, 5, 9
6. 2, 3, 5, 6, 9, 10
7. None, 1709 is a prime number
40. 145
41. 357
42. 2395
43. 1248
44. B
1.3 Exercises #7-15 (odd), 19-25 (odd), 26, 28
7. 5
9. 24
11. 88
13. 2
15. Addition was performed before multiplication. 9 + 2 • 3 = 9 + 6
19. 25
21. 47
23. 8
25. 22 people
26. 12
28. 3
1.3 Exercises #3-5, 34-38
3. 57
4. 2
5. 2
34. 5.7
35. 6.1
36. 9.6
37. 0.9
38. D
1.2 Exercises #7-13 (odd), 14-24 (even), 25-39 (odd)
7. 25
9. 84
11. 76
13. The base is written as the exponent and the exponent is written as the base. 4 • 4 • 4 = 43.
14. 25
16. 32
18.117,649
20. 20,736
22. The exponent is written as a factor, but it should have been used to indicate the number of times the base is used as a factor. 83 = 8 • 8 • 8 = 512
24. 24=16 in
25. Not a perfect square
27. Perfect square
29. perfect square
31. Not a perfect square
33. 40,000 cm2
35. 8 squares
37. As the exponent decreases the value of the power is divided by 4.
39. 13 blocks; add 72 - 62 blocks 19 blocks; add 102 - 92 blocks 39 blocks; add 202 - 192 blocks
1.2 Exercises #4-6, 40-44
4. 92
5. 132
6. 153
40. 84
41. 165
42. 8
43. 7
44. C
1.1 Exercises #1-7, 13, 15, 19, 21, 28-38 (evens)
1. addition
2. multiplication
3. division
4. subtraction
5. addition
6. subtraction
7. a. dividend b. quotient c. divisor
13. 7081
15. 2462
19. 6944
21. 31
28. Two digits were brought down instead of one after subtracting 12 from 13. The answer should be 109.
30. subtraction
32. multiplication
34. division
36. 42 ft; 108 sq. ft
38. 1165 tickets
1.1 Exercises #8-11, 47-51
8. 2118 + 3391+ 4785 + 6354; 16,648 people
9. 4785 - 3391; 1394 more people
10. 6354/2118; 3 times more people
11. 4785 • 2; 9570 people
47-50. I cannot show a graph here on my website. Please compare with a partner.
51. A