Ch. 9 Study Guide
1. I can’t draw the dot plot. The data are clustered around 39. There is a peak at 39. There is a gap between 33 and 38.
2. I can’t draw the dot plot. The data are clustered around 81. There is a peak at 81. There is a gap between 76 and 80.
3. Mean: 6.4; median: 7; mode: 7; range: 10
4. Mean: 6.875; median: 6.5; modes: 5 and 9; range: 6
5. Mean: 11.4; median: 6; mode: none; Sample answer: The median is besst because there is no mode, the mean is greater than most of the data and the median is close to 3 of 5 data values.
6. Mean: about 54.86; median: 53; mode: none; The mean or median is best because there is no mode and the mean and median are close to each other.
7. 74
8. 90
9. median: 36; Q1 = 22.5; Q3 = 57.5; IQR: 35
10. median: 37; Q1 = 30; Q3 = 39.5; IQR: 9.5
11. about 39.3; The distances driven differ from the mean distance by an average of about 39.3 miles.
12. 3.7; The prices of sunglasses differ from the mean price by an average of $3.70.
13. a. Range = 36 guests; IQR = 10 guests
13. b. The outlier is 90 guests; range = 18; IQR = 7; range
14. Greg’s hours: mean: 11.25; median: 10.5; modes: 9 and 12; range: 18; IQR: 7.5; MAD: 4.5
Tom’s hours: mean: 15; median: 15; modes: 12, 15 and 18; range: 6; IQR: 4; MAD: 1.75
Sample answer: The measures of center for Tom’s hours are greater than the measles of center for Greg’s hours. The measures of variation for Tom’s hours are less than the measures of variation for Greg’s hours.
9.5 Exercises #7-10, 12-16 (even), 18-20
7. 4.9; The capacities differ from the mean capacity by an average of 4.9 thousand, or 4900 people
8. 25.4; The numbers of visitors differ from the mean by an average of 25.4 or about 25 visitors
9. When calculating the mean absolute deviation, you need to divide by 6, not 5. Even though the distance from the mean of one of the values (38) is 0, it is still included in the calculation. So, the values differ from the mean by an average 3.0.
10. range: 14; The prices vary by no more than $14. IQR: 8; The middle half of the prices vary by no more than $8.; mean absolute deviation: 4; The admission prices differ from the mean price by an average of $4.
12. Derek’s collection: mean: 1929; median: 1930; no mode; range: 54; IQR: 48; MAD: 23.75
Paul’s collection: mean: 1929; median: 1929; no mode; range: 15; IQR: 6; MAD: 3.5
Sample answer: The measures of center for the data sets are almost identical. But the measures of variation for Paul’s coin collection are much less than the measures for Derek’s coin collection. This means that the years of the coins in Paul’s collection are closer together than the years of the coins in Derek’s collection.
14. The guesses for gumballs are greater and have a much larger range than the guesses for baseballs. So you can reason that the MAD for gumballs is greater than the MAD for baseballs. In general, guesses for gumballs will deviate more because there are many more in the jar, making it harder to guess and producing a larger range of guesses.
16. Sample answer: The range only uses 2 data values from a set and is greatly affected by outliers. The IQR ignores outliers, but only uses a few data values from a set. When calculating the MAD of a data set, you use all of the values in its calculation.
18. mean: 6.5; median: 6; mode: 6
19. mean: 1.6; median: 1.7; modes: 1.2, 1.7
20. C
9.4 Exercises #14, 15, 19, 23-25
14. median: 58.5; Q1 = 55; Q3 = 65; IQR: 10
15. range = 21 ¾ ft; The distances traveled by the paper airplane vary by no more than 21 ¾ feet; IQR = 11 ft; The middle half of the distances traveled by the paper airplane bary by no more than 11 ft.
19. a. range = 172 points; IQR = 42 points b. The outlier is 193 points; range = 101; IQR = 34; range
23. 11
24. 56
25. D
9.4 Exercises #6-9, 11-13
6. 12
7. 23
8. 57
9. 7.3
11. median: 37; Q1 = 33.5; Q3 = 40.5; IQR: 7
12. median: 88; Q1 = 84; Q3 = 92; IQR: 8
13. median: 133.5; Q1 = 128; Q3 = 139; IQR: 11
9.3 Exercises #7-12, 14, 17, 21, 29, 33-37
7. median: 7; mode: 3
8. median: 15; modes: 14, 16
9. median: 92.5; mode: 94
10. median: 33; no mode
11. median: 17; mode: 12
12. median: 51.5; modes: 44, 55
14. black, blue
17. mean: 35.875; median: 44; mode: 48; Sample answer: The median is probably best because it is close to most of the data. The mean is less than most of the data and the mode is the greatest value.
21. With Outlier: mean: 48.5; median: 53; mode: none; Without Outlier: mean: 53; median: 54; mode: none; The outlier reduces the median slightly, but reduces the mean more. There is no mode with or without the outlier.
29. With 30 year-old: mean: 22.5 years; median: 23.5 years; modes: 14 and 25; With 15 year-old: mean: 21.25 years; median: 21.5 years; modes: 14 and 25; The mean and median were lowered. The modes were unchanged.
33. 13
34. 65
35. 119
36. 2875
37. D
9.2 Exercises #7, 8, 10-12, 14, 15, 19-23
7. 3 brothers and sisters
8. 103 sit ups
10. a. about 7th b. 26 and 37 are outliers because they are much greater than the other values
11. a. yes; There will be variability in the lengths of the commercial breaks. B. 3.45 minutes
12. 3.245 inches
14. a. The 288 minutes used in September is much less than the other values, so it is an outlier.
b. With outlier: 488.4 Without outlier: 538.5 The outlier caused the mean to be about 50 minutes or less
c. Sample answer: School could have caused you to spend less time talking on your cell phone.
15. 3.9 inches; No, neither team has a height that is much shorter or taller than the other heights. So, you can say that the Tigers are taller than the Dolphins on average.
19. 9
20. 30
21. 18.5
22. 15.5
23. B
9.1 Exercises #4-12, 16, 18, 22, 26-29
4. 12 in; yes
5. Sample answer: 2 pets; no
6. Sample answer: 9th; no
7. 100 senators; yes
8. Statistical; there are many different answers
9. Not statistical; there is only one answer
10. Statistical; there are many different answers
11. Statistical; there are many different answers
12. I can’t draw the dot plot. Most of the data are clustered around 1. There are peaks at 1 and 2. There is a gap between 2 and 6.
16. a. yes; It is a statistical question because you would anticipate variability in the hours spent on homework each night by students.
b. I can’t draw the dot plot. Most of the hours cluster around 2. The peak is 2. There is no gap.
c. Most students spend about 2 hours on homework during a school night.
18. a. 18 players
b. Sample answer: Use a tape measure. The units are in inches.
c. Sample answer: What are the heights of players on an NBA championship team?; The heights are spread out, but most of the heights (in inches) are in the mid-to-low 80s.
22. Sample answer: 45 mph; Most of the data cluster around 45 and 45 mph is a common speed limit.
26. yes
27. no
28. yes
29. D
Ch. 8 Study Guide
1. 8 faces, 18 edges, 12 vertices
2. 8 faces, 14 edges, 8 vertices
3. 28 ft2
4. 270 ft2
5. 5 in2
6. 299.75 m2
7. 35/8 cm2 or 4 ⅜ cm2
8. 21/2 ft3 or 10 ½ ft3
9. I can’t draw the solid here.
10. 138 in2
11. 13 quarts of paint
12. 8 times greater
8.4 Exercises #4-13, 16, 19-22
4. 3/10 in3
5. 1 5/16 cm3
6. 8/125 ft3
7. 15/16 m3
8. 3 ⅛ cm3
9. 12 ½ m3
10. 1620 = 9 • 9 • h; 20 cm
11. 220.5 = 7 • w • 7; 4.5 cm
12. 532 = 19 • w • 1 ¾; 16 in
13. 234 pounds
16. a. Sample answer: 297 in3 b. No; the container only holds 196 cubic inches.
19. Yes
20. No
21. No
22. C
8.3 Exercises #6-11, 13-15, 18-20
6. 119 in2
7. 172.8 yd2
8. 552 cm2
9. 224.4 ft2
10. 195.6 in2
11. 55 m2
13. 21,274.4 ft2
14. Yes; The weight of the glass is 29.4 pounds, which is less than the limit of 35 pounds for the chain.
15. 4
18. 7 : 3, 14 : 6, 28 : 12
19. 10 : 4, 5 : 2, 30 : 12
20. B
8.2 Exercises #6-11, 12-16 (even), 18-21
6. 130 ft2
7. 198 cm2
8. 76 yd2
9. 17.6 ft2
10. 740 m2
11. 57.1 mm2
12. 448 in2; The surface area of the box is 448 square inches so that is the least amount of paper needed to cover the box.
14. 83 ft2
16. 2qt
18. 48 m2
19. 165 ft2
20. 15 in2
21. C
8.1 Exercises #10-28 (even), 30-33
I can’t put the drawings on here. You will be turning in your homework when you get to class tomorrow.
Ch. 7 Study Guide
1. 7s = 84
2. 13 = ⅓ • m
3. b = 8
4. v = 22
5. x = 14
6. b = 15
7. m = 35
8. k = 12
9. Yes
10. No
11. m ≤ 300
12. h ≥ 48
13. Closed circle on 5 and arrow colored to the right.
14. Closed circle on -2 and arrow colored to the left.
15. x < 10; open circle on 10 and arrow colored to the left.
16. n ≤ 6; closed circle on 6 and arrow colored to the left.
17. b ≤ 9; closed circle on 9 and arrow colored to the left.
18. p < 6; open circle on 6 and arrow colored to the left.
19. 4x = 332; 83 students
20. a. c = 20 + 10t (I can’t draw the graph her, but you SHOULD) b. Sample answer: The ordered pair (3, 50) represents 3 shirts being ordered for $50.
21. w ≥ 74 miles per hour
7.7 Exercises #10-20, 25, 27, 30, 31, 39-42
10. x < 8; open circle on 8 and arrow colored to the left
11. x ≥ 5; closed circle on 5 and arrow colored to the right
12. w ≤ 9; closed circle on 9 and arrow colored to the left
13. p ≤ 6; closed circle on 6 and arrow colored to the left
14. b > 20; open circle on 20 and arrow colored to the right
15. x < 15; open circle on 15 and arrow colored to the left
16. s ≥ 12; closed circle on 12 and arrow colored to the right
17. v ≤ 81; closed circle on 81 and arrow colored to the left
18. t > 18; open circle on 18 and arrow colored to the right
19. w ≤ 32; closed circle on 32 and arrow colored to the left
20. m < 11; open circle on 11 and arrow colored to the left
25. 8n < 72; n < 9
27. 225 ≥ 12w; 18.75 ≥ w
30. a. 12x ≥ 15,000; x ≥ 1250 (at least 1250 rides are needed)
b. The park is open 12 hours a day. To have 1250 rides in a day, the thrill ride would have to operate about 104.2 times per hour (1250/12). That means the thrill ride would have to operate once every 35 seconds. It seems unreasonable to unload 12 people and load 12 people and conduct a ride in 35 seconds.
31. 80x > 2 • 272; x > 6.8 yards per play
39. Rectangle
40. Trapezoid
41. Parallelogram
42. C
7.6 Exercises #8-28 (even), 29-33
8. 8 ≤ c; closed circle on 8 and arrow colored to the right
10. z ≤ 17; closed circle on 17 and arrow colored to the left
12. g ≥ 34; closed circle on 34 and arrow colored to the right
14. 18 ≥ s; closed circle on 18 and arrow colored to the left
16. b > 5/12; open circle on 5/12 and arrow colored to the right
18. 22 + x ≤ 40; x ≤ 18
20. x + 5 < 17; x < 12
22. x ≤ 8; closed circle on 8 and arrow colored to the left
24. 4.8 ≥ c; closed circle on 4.8 and arrow colored to the left
26. a. 4200 + x ≤ 8500; x ≤ 4300 b. At most 2.6875 cubic yards; You can add at most 4300 pounds to your truck and each cubic yard of sand weights 1600 pounds. So, you can haul at most 4300/1600=2.6875 cubic yards.
28. 25
29. t = 48
30. 27 = s
31. x = 9
32. 6 = z
33. C
7.5 Exercises #5-35 (odd), 39, 47-51
5. k < 10
7. z < ¾
9. 1 + y ≤ -13
11. Yes
13. Yes
15. No
17. B
19. D
21. x < 1; A number x is less than 1.
23. x ≥ -4; A number x is at least -4.
25-35. I can’t draw the graphs here. Your graphs should match these descriptions.
25. Open circle on 4 and arrow colored to the right.
27. Closed circle on 3 and arrow colored to the left.
29. Open circle on 2/9 and arrow colored to the left.
31. Open circle on -5 and arrow colored to the right.
33. Open circle on 1.5 and arrow colored to the left.
35. Open circle on -1.6 and arrow colored to the right.
39. a. b ≤ 3; closed circle on 3 and arrow colored to the left.
b. l ≥ 18; closed circle on 18 and arrow colored to the right.
47. x = 9
48. x = 14
49. x = 28
50. x = 14.1
51. D
7.4 Exercises #4, 6-11, 18, 21- 23, 30, 31, 40-44
4. p = 2w + 10 where p is the perimeter in inches and w is the width in inches. p depends on w.
6. no
7. yes
8. yes
9. no
10. no
11. yes
18. Your score on the test is the dependent variable.
21. The number of hours you work is the independent variable.
22. c = 1.5t + 5 where t is the number of toppings and c is the total cost of the pizza. Please keep your homework out so I can show you the graphs.
23. c = 25m +35 where m is the number of months and c is the total cost of the gym membership. Please keep your homework out so I can show you the graphs.
30. 11
31. 1
40. 30%
41. 80%
42. 45%
43. 68%
44. A
7.3 Exercises #7-22, 25, 29, 33, 35, 36-38
7. s = 70
8. t = 30
9. x = 24
10. r = 32
11. a = 4
12. z = 7
13. y = 10
14. k = 6
15. x = 15
16. w = 12.5
17. d = 78
18. v = 45
19. c = 66
20. b = 7.2
21. n = 2.56
22. m = 6
25. 3x = 45; 15 teams
29. 8 units
33. x = 6; Because 5x is on both sides of the equation, 3x must be equal to 18 so that the equation is true.
35. Length: 20 in; Width: 5 in
36. b + 8 = 17
37. t/3 = 7
38. C
7.2 Exercises #6-11, 24-29, 32, 34, 41-47 (odd), 57-61
6. yes
7. yes
8. no
9. no
10. no
11. yes
24. f = 46
25. q = 11
26. j = 1 ¼
27. x = 7/30
28. m = 3.7
29. a = 11.8
32. 45 = h + 24; 21 in. The answer is reasonable because the rockhopper penguin looks like it is about half the height of the emperor penguin in the picture.
34. h - 6460 = 4181; 10,641 mi2
41. y = 15
43. v = 28
45. d = 54
47. x + 34 + 34 + 16 = 132; 48 in.
57. 96
58. 208
59. 5
60. 24
61. C
7.1 Exercises #6-16, 19, 23-27
6. x + 4 = 12
7. y -9 = 8
8. 9b = 36
9. w/5 = 6
10. 54 = t + 9
11. 5 = 1/4c
12. 11 = y/6
13. n - 9 = 27
14. The word is indicates an equal sign, so the equal sign is in the wrong position. n = 12 + 5.
15. 6042 = 1780 + a
16. 90 = 3/4d
19. 326 = 12(14) + 6(5) + 16x
23. 13
24. 3
25. 28
26. 5
27. B
Ch. 6 Study Guide
1. -4, -2, 0, 1, 3
2. -8, -5, -3, 4, 5
3. I can’t draw the number lines, but you should have graphed 14 and -14 using equal intervals.
4. I can’t draw the number lines, but you should have graphed -40 and 40 using equal intervals.
5. I can’t draw the number lines, but you should have graphed -1 ⅓ and 1 ⅓ using equal intervals.
6. I can’t draw the number lines, but you should have graphed 1.75 and -1.75 using equal intervals.
7. 7
8. 11
9. <
10. >
11. >
12. <
13-16. I can’t show the graph.
13. Point J is on the x-axis between Quadrants I and II.
14. Quadrant II
15. Quadrant IV
16. Quadrant III
17. (-2, -4)
18. (5, -1)
19. a. 3; -2 b. 3; 2 c. the diver on the springboard
20. Sample answer: (1, 4), (6, 4)
21. Mercury has a higher melting point than Radon and a lower melting point than Bromine, Cesium, and Francium.
6.5 Exercises #4-30 (even), 35, 55-59
4. I can’t draw the graph, but you should see an arrow pointing to the right.
6. (-3, -2)
8. (1, 2)
10. (0, -4)
12. (-4, -4)
14. (4, -4)
16. I can’t draw the graph. Point is located in Quadrant II.
18. I can’t draw the graph. Point is located in Quadrant IV.
20. I can’t draw the graph. Point is located in Quadrant II.
22. I can’t draw the graph. Point is located in Quadrant III.
24. The numbers are reversed. To plot (4, 5), start at (0, 0) and move 4 units to the right and 5 units up.
26. I can’t draw the graph. The length of the line segment is 3 units.
28. I can’t draw the graph. The length of the line segment is 9 units.
30. I can’t draw the graph. The length of the line segment is 5 units.
35. a. about 142,000 b. 2011 and 2012 c. about 10,000
55. y - 4
56. 18b
57. x + 9
58. w/3
59. C
6.4 Exercises #12-22 (even), 26-38 (even), 40-44
12. 11
14. 68
16. The absolute value of a number cannot be negative. The absolute value of 14 = 14.
18. =
20. >
22. <
26. C; You owe less than $25, so debt <$25
28. -4, -3, l-3l, l-4l, l5l
30. -20, -19, -18, l-18l, l-22l, l30l
32. -6
34. a. -50 degrees C is closer to 0K than 32 degrees F. b. One thing that the Kelvin scale and absolute values have in common is that neither can have negative numbers. For both, the least possible number is 0.
36. always; The absolute value is the positive distance from zero on a number line.
38. a. I can’t draw the number line. b. racecar; yes c. Sample answer: Madam, I’m Adam
40-43. I can’t draw the graphs.
44. D
6.3 Exercises #8-18, 20-24 (even), 28-32
8-9. I can’t draw the number lines. Please check with a neighbor!
10. >
11. <
12. <
13. <
14. <
15. >
16. <
17. >
18. >
20. -3, -2 ½, -2 ⅖, -2 3/10, -2
22. -2, -1.8, -1.75, 0, 1.3
24. Sirius
28-31. I can’t draw the number lines. Please check with a neighbor!
32. D
6.2 Exercises #4-7, 8-12 (even), 13-21 (odd), 22-25, 29-33
4. >
5. <
6. >
7. >
8. <
10. <
12. The student compares 3 and 1, not -3 and -1. Negative numbers behave in an opposite manner to positive numbers. -3 < -1.
13. The explanation about where the integers are located on a number line is incorrect. -7 < -3; So, -7 is to the left of -3 on a number line.
15. -4, -3, -2, 1, 2
17. -7, -4, 2, 3, 6
19. -20, -10, -5, 15, 25
21. oxygen
22. least: -9; greatest: -3
23. always; The opposite of a positive integer is a negative integer. Positive integers are greater than negative integers.
24. never; If an integer is less than its opposite, it must be a negative integer, which is never greater than 0.
25. a. Florida, Louisiana, Arkansas, Tennessee, California
b. California, Louisiana, Florida, Arkansas, Tennessee
c. An elevation of 0 feet represents sea level.
29-32. I can’t draw the number lines. Please check with a neighbor!
33. B
6.1 Exercises #8-30 (even), 33-35
8. -42
10. 17
12. -350
14. 83; -47
16-22. I can’t draw the number lines. Please check with a neighbor.
24. The numbers shown are whole numbers. Positive integers are 1, 2, 3….; they do not include zero.
26. 5
28. -15
30. The average water level is 4 feet below high tide. So, the average water level relative to high tide is represented by the number -4.
33. ⅜, ½, ¾, ⅞
34. 4.312, 4.316, 4.32, 4.5
35. B
Ch. 5 Study Guide
1. 3 : 3; For every 3 scooters, there are 3 bikes.
2. 2 : 5; For every 2 starfish, there are 5 shells.
3. 4 : 2, 12 : 6, 36 : 18
4. 2 : 9, 4 : 18, 12 : 54
5. $18.00 per ticket
6. 70 miles per hour
7. 84%
8. 85%
9. 140%
10. 72
11. 15
12. 90
13. 85
14. 40
15. 5.26
16. 25.2
17. Soup A has more sodium because it has 150 mg of sodium compared to 120 mg of sodium per ounce.
18. The 48-fluid-ounce container is a better buy because it costs $0.05/ounce compared to $0.06/ounce.
19. 23/50
20. 8 students
5.7 Exercises #13-22, 26-32, 37-41
13. 0.19
14. 190.01
15. 37.78
16. 5.91
17. 14.49
18. The conversion factor is wrong. 8L/0.95L is about 8.42 qt.
19. a. about 60.67 m b. about 8.04 km
20. >
21. <
22. >
26. 8.07
27. 1320
28. 0.0175
29. 111.8
30. 1.13
31. 0.001
32. No; 2 L > 2 qt.
37. 30
38. 30.55
39. 18
40. 2.56
41. C
5.6 Exercises #2, 3-23 (odd), 28-36 (even), 39, 49, 54-58
2. The number (whole) will be less than 52 (part) because 130% (part) is greater than 100% (whole) so 52 will be greater than the number.
3. 12
5. 35
7. 9
9. 12.5
11. 21
13. 20.25
15. 24
17. 14
19. 84
21. 94.5
23. The percent was not written as a fraction before multiplying. 40% • 75 = ⅖ • 75 = 30.
28. 90
30. 36
32. 20
34. 20
36. 24
39. a. 50 students b. 18 students
49. a. 432 in2 b. 37.5%; Because the length is doubled, the width of the rectangle is now half of 75% of its length, or 37.5%.
54. 4.8
55. 16.5
56. 6.66
57. 26.28
59. D
5.5 Exercises #16-20 (even), 26-30, 34-36, 41-45
16. 2/25
18. 1/400
20. The 225 should be over 100. 225% = 225/100 = 2 ¼
26. 72%
27. 185%
28. 282%
29. The decimal point should not have been added to the percent expression. 14/25 = 56/100 = 56 %
30. 3/25; right-handed students; If 3/25 of the students are left-handed, then 22/25 of the students are right-handed and 22/25>3/25.
34. 56.25%
35. 82.5%
36. a. 7/16 b. 27.5%
41. ½
42. 12
43. 16
44. 1/12
45. D
5.4 Exercises #5-16, 19-22
5. B because you get 33.75 mpg compared to 30 mpg
6. A because you get 18 mpg compared to 15 mpg
7. A because it costs $3/refill compared to $4/refill
8. B because it costs $0.75/can compared to $0.83/can
9. B because it costs $1.75/pound compared to $1.90/pound
10. B because it costs $0.32/slice compared to $0.36/slice
11. The first recipe because in two cups of water there will be 1.5 teaspoons of salt compared to the 1 teaspoon in the second recipe.
12. I can’t draw the graphs, but the graph for the water tank is steeper, so the water tank leaks faster than the swimming pool.
13. I can’t draw the graphs, but the graph for the museum is steeper, so the cost to attend the museum is greater than the cost to attend the zoo.
14. Whole milk has more milk fat because 2% has 8 parts out of 400 is milk fat compared to 13 parts out of 400 in whole milk.
15. I can’t draw the double number line, but the cow has the greater heart rate because 1950 beats in 30 minutes is greater than 1320 beats in 30 minutes.
16. a. Sample answer: Solution 2 has the greater concentration of acid.
b. I can’t draw the graphs, but the graph for solution 2 is steeper, so solution 2 has a greater concentration of acid.
c. Sample answer: A graph is preferable because the rates are visible more quickly.
19. 16
20. 18 R26
21. 34 R109
22. B
5.3 Exercises #6-22 (even), 23, 25, 28-32
6. 150 gallons for every 25 seconds (other answers are also acceptable)
8. 6 necklaces per hour
10. 19 students per class
12. 110 calories per serving
14. $2.50 per ounce
16. 60 beats per minute
18. 30 minutes
20. equivalent
22. equivalent
23. a. 6 minutes b. 10 minutes
25. about 3.88 items per student
28-31. Many answers are acceptable
32. B
5.2 Exercises #1-3, 10-24 (even), 35-38
1. Two ratios are equivalent if they can be written as the same ratio.
2. No; You can only create an equivalent ratio by adding or subtracting corresponding parts, or by multiplying or dividing each part of the ratio by the same number.
3. 12 : 15; all other ratios are equivalent
10. 14 : 8, 7 : 4, 28 : 16
12. $68
14. 16 printers
Printers 2 4 8 16
Computers 5 10 20 40
16. 18 girls
Girls 81 9 18
Boys 72 8 16
18. Each part of the original ratio was not multiplied by the same number.
20. 32 rock songs
22. Add the corresponding quantities of Recipes C and D to create Recipe F.
24. Subtract the corresponding quantities of Recipe C from Recipe F to create Recipe D.
35. 27(2 + 1)
36. 12(5x - 7)
37. 14(3x + 2y)
38. D
5.1 Exercises #8-20, 25-29
8. 2 : 6; For every 2 calculators, there are 6 pencils.
9. 3 : 7; For every 3 shirts, there are 7 pants.
10. 3 : 15; 3 out of every 15 movies are dramas.
11. 8 : 15; 8 out of 15 movies are comedies.
12. 15 : 4; Out of 15 movies, 4 are action.
13. 15 : 3; Out of 15 movies, 3 are dramas.
14. 14 out of 35 stamps have celebrities on them.
15. 9 h
16. 4 h
17. 12 : 16
18. 21 states
19. 6 black pieces; The ratio of black to red is 3 : 5, so each part is 16/8=2. So, there are 3 • 2 = 6 black pieces and 5 • 2 = 10 red pieces.
20. 8; The ratio of boys to girls is 5 : 7, so each part is 48/12 = 4. So, there are 5 • 4 = 20 boys and 7 • 4 = 28 girls.
25. 4.6
26. 3.29
27. 2.53
28. 1.478
29. B
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 #39-53 (odd)
39. 6x + 25
41. 68 + 28k
43. 19y + 5
45. 3d + 1
47. 5v
49. 2.7w - 14.04
51. 11/4z + 3/10
53. 7x + 12y
3.4 Exercises #5-33 (odd), 66-70
5. 63
7. 516
9. 936
11. 504
13. 4/7
15. 2 ½
17. 3x + 2
19. 6s - 54
21. 96 + 8a
23. 72 - 12k
25. 63 + 9c
27. 40g + 24
29. 4x + 4y
31. 7p + 7q + 63
33. The 6 was not distributed to the 8 inside the parentheses. 6(y + 8) = 6y + 48
66. 10.641
67. 34.006
68. 135.213
69. 0.387
70. B
3.3 Exercises #12-34 (even), 35-43
12. 11 + x
14. 12b
16. 8.3 + x
18. 36c
20. 3k + 12 ⅘
22. 24s
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. 8 • (y • 9) = 72y
30. 13.2 • (1 • x)
32. 2 + c
34. a. x + 37
b. In the expression, 37(14) + 10x; 14 represents the cost of the hats you sold and 10 represents the cost of the hats your friend sold. Therefore, she was selling them at a discounted price.
c. x < or = 51
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 #4-20 (even), 29, 32, 36-40
4. 3 • 12 or 12 • 3
6. 6 + 10 or 10 + 6
8. 15 + 17 or 17 + 15
10. 5d or d • 5
12. s - 6
14. b2
16. 12 - x
18. t3
20. The expression is not written in the correct order; 16 - x
29. 8x + 6; 46
32. a. 5a - 8 b. 2f + 25 c. Florida has 67 counties. Georgia has 159 counties.
36. 45
37. 59
38. 390
39. 140
40. D
3.1 Exercises #3, 14-20 (even), 43-50, 53. 56-60
3. Decrease; When you subtract greater and greater values from 20, you will have less and less left
14. There is only one term, not 3. Term: 2x2y, Coefficient: 2, Constant: none
16. b3
18. 8w4
20. a2c2
43. 23
44. 8.2
45. 2 ⅚
46. 10 ⅔
47. 22
48. 82
49. 46
50. 48.3
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), 40-46 (even), 54, 55, 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
44. 9.6
46. About 6.04
54. >
55. <
61. 1 ⅙
62. 1 3/20
63. 1/20
64. 1/24
65. B
2.5 Exercises #17-27 (odd), 36-42 (even), 54-56, 70-74
17. 21.45
19. 13.888
21. 2.4
23. 0.0342
25. The decimal is in the wrong place. 0.0045 • 9 = 0.0405
27. 30.06 lb
36. 0.0000032
38. 2.48
40. 5.6952
42. 117.96438
54. 4.355
55. 23.112
56. 2.016
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 #1-6, 27, 32-54 (even), 56
1. Many answers possible. Ex: ⅖ and 5/2
2. 2/9 does not belong because its reciprocal is not a whole number.
3. B
4. D
5. A
6. C
32. Yes
34. No; Both fractions are equal to ⅚. The reciprocal of ⅚ is 6/5.
36. 12/5
38. ⅛
40. =; When you divide a fraction by 1, the quotient is a fraction.
42. >; When you divide a fraction by a fraction less than 1, the quotient is greater than the fraction.
44. 1/144
46. 4
48. ⅚
50. 1/10
52. 3
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.
56a. I can make about 10 plates.
56b. 2 plates; ½ pint left over
56c. 3 bowls and 6 plates
2.2 Exercises #11-26, 58-62
11. ½
12. 2 11/12
13. 16
14. 20
15. 1/14
16. 3/25
17. ⅓
18. ⅔
19. 3
20. 1 13/15
21. 2/27
22. 1/24
23. 27/28
24. 26/75
25. 20 ¼
26. 24
58. 8
59. 6
60. 16
61. 5
62. D
2.1 Exercises #4-20 (even), 26-42 (even), 48, 51
4. 2/21
6. 1/10
8. 8/21
10. 1/24
12. 4 ⅙
14. ⅖
16. 9/49
18. 13/21
26. 8/9
28. 2
30. 5
32. 1
34. 3 ½
36. 23 ⅖
38. 7 ⅞
40. 17 6/7
42. You must first rewrite the mixed number as an improper fraction and then multiply.
48. 2 1/12
51. 9/25
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. 2 7/40 lb
Page 44 #1-17 (odd)
1. 1, 48; 2, 24; 3, 16; 4, 12; 6, 8
3. 22 • 3 • 5
5. 6
7. 2
9. 56
11. 90
13. 1415
15. 6 baskets
17. 12 days
1.6 Exercises #12-18, 22-32 (even), 37-40
12. 63
13. 108
14. 90
15. 66
16. 180
17. 350
18. The product of 2 numbers is not necessarily the LCM. Use the ladder method to find that the LCM is 18.
22. 42
24. 36
26. 126
28. Prime factorization because it is tedious to list all of the multiples of two numbers.
30. Sometimes
32. 60 minutes
37. 32
38. 54
39. 175
40. B
1.5 Exercises #13-19, 22-30 (even), 35-39
13. 15
14. 9
15. 9
16. 12
17. 1
18. 1
19. 7 is the greatest common prime factor. The GCF is 2 • 7 = 14.
22. 8 arrangements
24. 6
26. There are many different answers to this. Share your answers with me!
28. Sometimes
30. Never
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 #3, 14-32 (even), 39-44
3. 6, 9 do not belong because it is a factor pair of 54 and the others are factor pairs of 56
14. 1, 59
16. 24
18. 2 • 3 • 5
20. 22 • 3 • 7
22. 5 • 13
24. 9 is not prime. It is equal to 3 • 3. 72 = 23 • 32
26.180
28. 12,584
30. 25
32. 1
39. 6 prisms; There are 6 unique arrangements of length, width, and height using the factors of 40.
40. 145
41. 357
42. 2395
43. 1248
44. B
1.3 Exercises #6-14 (evens), 15-27 (odds), 34-38
6. 8
8. 60
10.6
12. 41
14. 24
15. Addition was performed before multiplication. 9 + 2 • 3 = 9 + 6 = 15
17. 8 pages
19. 25
21. 47
23. 8
25. 22 people
26. 12
27. 1
34. 5.7
35. 6.1
36. 9.6
37. 0.9
38. D
1.2 Exercises #5-13 (odds), 14-24 (evens), 25-39 (odds), 40-44
5. 132
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
40. 84
41. 165
42. 8
43. 7
44. C
1.1 Exercises #1-7, 28-46 (evens), 47-51
1. addition
2. multiplication
3. division
4. subtraction
5. addition
6. subtraction
7. a. dividend b. quotient c. divisor
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
40. 399/129; The first quotient 3999/129 has a greater dividend and a lesser divisor than the second quotient 3834/124. So, the first quotient will be greater than the second quotient.
42. 64 cups
44. a. You need to borrow 9 bookcases. b. There are 19 books on the third shelf.
46. 36,000/900=40
47-50. I cannot draw the graphs on here. Please check with a partner.
51. A