CHAPTER ONE
CRITICAL THINKING SKILLS
Exercise Set 1.1
1. Counting 2. Divisible
3. Hypothesis 4. Counterexample
5. Inductive 6. Deductive
7. Deductive 8. Inductive
9. Inductive reasoning, because a general conclusion was made from observation of specific cases.
10. Inductive reasoning, because a general conclusion was made from observation of specific cases.
11. 5×5 = 25 12. 12×14 = 168
13. 1 5 (= 1 + 4) 10 (= 4 + 6) 10 (= 6 + 4) 5(= 4 + 1) 1 14. 100,000 = 105
15. 16.
17. 18.
20. 19, 23, 27 (Add 4 to the previous number.)
19. 10, 12, 14 (Add 2 to previous number.)
21. 3, −3, 3 (Alternate 3 and −3.) 22. −3, −5, −7 (Subtract 2 from previous
number.)
1 1 1 24. 2500, −12,500, 62,500 (Multiply previous
23. , , (Increase the denominator value by 1.)
5 6 7 number by –5.)
25. 36, 49, 64 (The numbers in the sequence are 26. 21, 28, 36 (15 + 6 = 21, 21 + 7
the squares of the counting numbers.)
= 28, 28 + 8 = 36)
1
Copyright © 2013 Pearson Education, Inc.
,2 CHAPTER 1 Critical Thinking Skills
27. 34, 55, 89 (Each number in the sequence is (Multiply previous number
the sum of the previous two numbers.) 243 729 2187
28. ,− , 3
256 1024 4096 by − .)
4
29. There are three letters in the pattern. 30. a) Answers will vary.
39× 3 = 117 , so the 117th entry is the second b) The sum of the digits is 9.
R in the pattern. Therefore, the 118th entry is Y. c) When a one- or two-digit number is multiplied
by 9, repeated summing of the digits in the
product yields the number 9.
31. a) 36, 49, 64 32. a) 28 and 36
b) To find the 7th triangular number, add 7 to the 6th
b) Square the numbers 6, 7, 8, 9 and 10.
triangular number. To find the 8th triangular
c) 8×8 = 64 9 × 9 = 81 number, add 8 to the 7th triangular number. To find
the 9th triangular number, add 9 to the 8th triangular
72 is not a square number since it falls number. To find the 10th triangular number, add 10
between the two square numbers 64 and to the 9th triangular number. To find the 11th
81. triangular number, add 11 to the 10th triangular
number.
c)
36 + 9 = 45; 45 + 10 = 55; 55 + 11 = 66; 66 + 12 = 78
72 is not a triangular number since it falls
between the consecutive triangular numbers
66 and 78.
33. Blue: 1, 5, 7, 10, 12 Purple: 2, 4, 6, 9, 11 Yellow: 3, 8
34. a) 19 (Each new row has two additional triangles.)
b) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100
35. a) ≈ $200, 000 b) We are using observation of specific cases to make a prediction.
36. a) ≈ $3.7 trillion b) We are using observation of specific cases to make a prediction.
37. 38.
39. a) You should obtain the original number.
b) You should obtain the original number.
c) Conjecture: The result is always the original number.
4n + 12 4n 12
d) n, 4n, 4n + 12, = + = n + 3, n + 3 − 3 = n
4 4 4
40. a) You should obtain twice the original number.
b) You should obtain twice the original number.
c) Conjecture: The result is always twice the original number.
4n + 6 4n 6
d) n, 4n, 4n + 6, = + = 2n + 3, 2n + 3 − 3 = 2n
2 2 2
Copyright © 2013 Pearson Education, Inc.
, SECTION 1.2 3
41. a) You should obtain the number 5.
b) You should obtain the number 5.
c) Conjecture: No matter what number is chosen, the result is always the number 5.
2n + 10 2n 10
d) n, n + 1, n + ( n + 1) = 2n + 1, 2n + 1 + 9 = 2n + 10, = + = n + 5, n + 5 − n = 5
2 2 2
42. a) You should obtain the number 0.
b) You should obtain the number 0.
c) Conjecture: No matter what number is chosen, the result is always the number 0.
n + 10 ⎛⎜ n + 10 ⎞⎟
d) n, n + 10, = n + 10, n + 10 − 10 = n, n − n = 0
⎜⎝ 5 ⎠⎟⎟
, 5⎜
5
43. 7 − 5 = 2 is one counterexample.
44. 5 ÷ 2 = 2 12 , which is not a counting number.
5
45. Two is a counting number. The sum of 2 and 3 is 5. Five divided by two is , which is not an even number.
2
46. 900 is a three-digit number. The product of 900 and 900 is 810,000, which is not a five-digit number.
47. One and two are counting numbers. The difference of 1 and 2 is 1− 2 = −1 , which is not a counting
number.
48. The sum of the odd numbers 1 and 5 is 6, which is not divisible by 4.
49. a) The sum of the measures of the interior angles should be 180° .
b) Yes, the sum of the measures of the interior angles should be 180° .
c) Conjecture: The sum of the measures of the interior angles of a triangle is 180° .
50. a) The sum of the measures of the interior angles should be 360° .
b) Yes, the sum of the measures of the interior angles should be 360° .
c) Conjecture: The sum of the measures of the interior angles of a quadrilateral is 360° .
a b
51. 129, the numbers in positions are found as follows:
c a +b+ c
52. 1881, 8008, 8118 (They look the same when looked at in a mirror.)
53. c
Exercise Set 1.2
(Note: Answers in this section will vary depending on how you round your numbers. The answers may differ
from the answers in the back of the textbook. However, your answers should be something near the answers
given. All answers
are approximate.)
1. Estimation
2. Equal
261 + 127.4 + 273.9 + 16.2 + 81.5 4. 2.57 + 212.6 +176.2 + 83
3.
≈ 260 + 127 + 274 + 16 + 82 = 759 ≈ 0 + 210 +180 + 80 = 470
5. 198, 600×3.072 ≈ 200, 000×3.000 = 600, 000 6. 1854 ×0.0096 ≈ 1900×0.01 = 19
405 400
7. ≈ = 8000
0.049 0.05 8. 0.63×1523 ≈ 0.6×1500 = 900
Copyright © 2013 Pearson Education, Inc.
, 4 CHAPTER 1 Critical Thinking Skills
9. 10.
51, 608× 6981 ≈ 50, 000× 7000 = 350, 000,000 11% of 8221 ≈ 10% of 8000 = 0.10×8000 = 800
11. 18% ×1576 ≈ 20%×1600 = 0.20×1600 = 320 12. 296.3 ÷ 0.0096 ≈ 300 ÷ 0.01 = 30, 000
$10.49 $10 $37.80 $40
13. ≈ = $2 14. ≈ = $2
5 5 20 20
15. 12 months ×$120.80 ≈12×$120 = $1440 16. 8% of $11, 250 ≈ 0.08 × $11, 000 = $880
17. One third of an annual profit of $8795 $1.29 + $6.86 + $12.43 + $25.62 + $8.99
18.
1 ≈ $1+ $7 + $12 + $26 + $9 = $55
≈ × $9, 000 = $3000
3
19. 95lb +127 lb + 210 lb ≈100 +100 + 200 = 400 lb 3.25 lb 3.00 lb
20. ≈ = 0.5 lb
6 6
21. $400 $400
22. ≈ = 16
$23 $25
15% of $26.32 ≈ 15% of $26 = 0.15×$26 = $3.9
23. 24.
($65.99 + $49.99 + $49.95) − $114.99
≈ ($66 + $50 + $50) − $115 = $166 − $115 = $5 Team A: 189 + 172 + 191 ≈ 190 + 170 + 190 = 550
Team B: 183 + 229 + 167 ≈ 180 + 230 + 170 = 580
580 − 550 = 30 lb
25. 11 × 8 × $1.50 ≈ 10 × 8 × $1.50 26.
= 10 × $12 = $120 6 min, 25 sec×26.2 mi
≈ 6.5 min × 26 mi =169 min
169 min
≈ 3hours
60 min
27. 100 Mexican pesos = 100× 0.083 U.S. dollars 28. $973 + 6 ($61) + 6 ($97) + 6 ($200)
≈ 100× 0.08 U.S. dollars = 8 U.S. dollars ≈ $970 + 6 ($60) + 6 ($100) + 6 ($200)
$50 − $8 = $42
= $970 + $360 + $600 + $1200 = $3130
29. ≈ 60 miles 30. ≈ 55 miles
Copyright © 2013 Pearson Education, Inc.
CRITICAL THINKING SKILLS
Exercise Set 1.1
1. Counting 2. Divisible
3. Hypothesis 4. Counterexample
5. Inductive 6. Deductive
7. Deductive 8. Inductive
9. Inductive reasoning, because a general conclusion was made from observation of specific cases.
10. Inductive reasoning, because a general conclusion was made from observation of specific cases.
11. 5×5 = 25 12. 12×14 = 168
13. 1 5 (= 1 + 4) 10 (= 4 + 6) 10 (= 6 + 4) 5(= 4 + 1) 1 14. 100,000 = 105
15. 16.
17. 18.
20. 19, 23, 27 (Add 4 to the previous number.)
19. 10, 12, 14 (Add 2 to previous number.)
21. 3, −3, 3 (Alternate 3 and −3.) 22. −3, −5, −7 (Subtract 2 from previous
number.)
1 1 1 24. 2500, −12,500, 62,500 (Multiply previous
23. , , (Increase the denominator value by 1.)
5 6 7 number by –5.)
25. 36, 49, 64 (The numbers in the sequence are 26. 21, 28, 36 (15 + 6 = 21, 21 + 7
the squares of the counting numbers.)
= 28, 28 + 8 = 36)
1
Copyright © 2013 Pearson Education, Inc.
,2 CHAPTER 1 Critical Thinking Skills
27. 34, 55, 89 (Each number in the sequence is (Multiply previous number
the sum of the previous two numbers.) 243 729 2187
28. ,− , 3
256 1024 4096 by − .)
4
29. There are three letters in the pattern. 30. a) Answers will vary.
39× 3 = 117 , so the 117th entry is the second b) The sum of the digits is 9.
R in the pattern. Therefore, the 118th entry is Y. c) When a one- or two-digit number is multiplied
by 9, repeated summing of the digits in the
product yields the number 9.
31. a) 36, 49, 64 32. a) 28 and 36
b) To find the 7th triangular number, add 7 to the 6th
b) Square the numbers 6, 7, 8, 9 and 10.
triangular number. To find the 8th triangular
c) 8×8 = 64 9 × 9 = 81 number, add 8 to the 7th triangular number. To find
the 9th triangular number, add 9 to the 8th triangular
72 is not a square number since it falls number. To find the 10th triangular number, add 10
between the two square numbers 64 and to the 9th triangular number. To find the 11th
81. triangular number, add 11 to the 10th triangular
number.
c)
36 + 9 = 45; 45 + 10 = 55; 55 + 11 = 66; 66 + 12 = 78
72 is not a triangular number since it falls
between the consecutive triangular numbers
66 and 78.
33. Blue: 1, 5, 7, 10, 12 Purple: 2, 4, 6, 9, 11 Yellow: 3, 8
34. a) 19 (Each new row has two additional triangles.)
b) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100
35. a) ≈ $200, 000 b) We are using observation of specific cases to make a prediction.
36. a) ≈ $3.7 trillion b) We are using observation of specific cases to make a prediction.
37. 38.
39. a) You should obtain the original number.
b) You should obtain the original number.
c) Conjecture: The result is always the original number.
4n + 12 4n 12
d) n, 4n, 4n + 12, = + = n + 3, n + 3 − 3 = n
4 4 4
40. a) You should obtain twice the original number.
b) You should obtain twice the original number.
c) Conjecture: The result is always twice the original number.
4n + 6 4n 6
d) n, 4n, 4n + 6, = + = 2n + 3, 2n + 3 − 3 = 2n
2 2 2
Copyright © 2013 Pearson Education, Inc.
, SECTION 1.2 3
41. a) You should obtain the number 5.
b) You should obtain the number 5.
c) Conjecture: No matter what number is chosen, the result is always the number 5.
2n + 10 2n 10
d) n, n + 1, n + ( n + 1) = 2n + 1, 2n + 1 + 9 = 2n + 10, = + = n + 5, n + 5 − n = 5
2 2 2
42. a) You should obtain the number 0.
b) You should obtain the number 0.
c) Conjecture: No matter what number is chosen, the result is always the number 0.
n + 10 ⎛⎜ n + 10 ⎞⎟
d) n, n + 10, = n + 10, n + 10 − 10 = n, n − n = 0
⎜⎝ 5 ⎠⎟⎟
, 5⎜
5
43. 7 − 5 = 2 is one counterexample.
44. 5 ÷ 2 = 2 12 , which is not a counting number.
5
45. Two is a counting number. The sum of 2 and 3 is 5. Five divided by two is , which is not an even number.
2
46. 900 is a three-digit number. The product of 900 and 900 is 810,000, which is not a five-digit number.
47. One and two are counting numbers. The difference of 1 and 2 is 1− 2 = −1 , which is not a counting
number.
48. The sum of the odd numbers 1 and 5 is 6, which is not divisible by 4.
49. a) The sum of the measures of the interior angles should be 180° .
b) Yes, the sum of the measures of the interior angles should be 180° .
c) Conjecture: The sum of the measures of the interior angles of a triangle is 180° .
50. a) The sum of the measures of the interior angles should be 360° .
b) Yes, the sum of the measures of the interior angles should be 360° .
c) Conjecture: The sum of the measures of the interior angles of a quadrilateral is 360° .
a b
51. 129, the numbers in positions are found as follows:
c a +b+ c
52. 1881, 8008, 8118 (They look the same when looked at in a mirror.)
53. c
Exercise Set 1.2
(Note: Answers in this section will vary depending on how you round your numbers. The answers may differ
from the answers in the back of the textbook. However, your answers should be something near the answers
given. All answers
are approximate.)
1. Estimation
2. Equal
261 + 127.4 + 273.9 + 16.2 + 81.5 4. 2.57 + 212.6 +176.2 + 83
3.
≈ 260 + 127 + 274 + 16 + 82 = 759 ≈ 0 + 210 +180 + 80 = 470
5. 198, 600×3.072 ≈ 200, 000×3.000 = 600, 000 6. 1854 ×0.0096 ≈ 1900×0.01 = 19
405 400
7. ≈ = 8000
0.049 0.05 8. 0.63×1523 ≈ 0.6×1500 = 900
Copyright © 2013 Pearson Education, Inc.
, 4 CHAPTER 1 Critical Thinking Skills
9. 10.
51, 608× 6981 ≈ 50, 000× 7000 = 350, 000,000 11% of 8221 ≈ 10% of 8000 = 0.10×8000 = 800
11. 18% ×1576 ≈ 20%×1600 = 0.20×1600 = 320 12. 296.3 ÷ 0.0096 ≈ 300 ÷ 0.01 = 30, 000
$10.49 $10 $37.80 $40
13. ≈ = $2 14. ≈ = $2
5 5 20 20
15. 12 months ×$120.80 ≈12×$120 = $1440 16. 8% of $11, 250 ≈ 0.08 × $11, 000 = $880
17. One third of an annual profit of $8795 $1.29 + $6.86 + $12.43 + $25.62 + $8.99
18.
1 ≈ $1+ $7 + $12 + $26 + $9 = $55
≈ × $9, 000 = $3000
3
19. 95lb +127 lb + 210 lb ≈100 +100 + 200 = 400 lb 3.25 lb 3.00 lb
20. ≈ = 0.5 lb
6 6
21. $400 $400
22. ≈ = 16
$23 $25
15% of $26.32 ≈ 15% of $26 = 0.15×$26 = $3.9
23. 24.
($65.99 + $49.99 + $49.95) − $114.99
≈ ($66 + $50 + $50) − $115 = $166 − $115 = $5 Team A: 189 + 172 + 191 ≈ 190 + 170 + 190 = 550
Team B: 183 + 229 + 167 ≈ 180 + 230 + 170 = 580
580 − 550 = 30 lb
25. 11 × 8 × $1.50 ≈ 10 × 8 × $1.50 26.
= 10 × $12 = $120 6 min, 25 sec×26.2 mi
≈ 6.5 min × 26 mi =169 min
169 min
≈ 3hours
60 min
27. 100 Mexican pesos = 100× 0.083 U.S. dollars 28. $973 + 6 ($61) + 6 ($97) + 6 ($200)
≈ 100× 0.08 U.S. dollars = 8 U.S. dollars ≈ $970 + 6 ($60) + 6 ($100) + 6 ($200)
$50 − $8 = $42
= $970 + $360 + $600 + $1200 = $3130
29. ≈ 60 miles 30. ≈ 55 miles
Copyright © 2013 Pearson Education, Inc.
