Beginning Algebra, Tobey - Solutions, summaries, and outlines. 2022 updated

Chapter 0
0.1 Exercises 5 ? 5 × 6 30
26. = ⇒ =
9 54 9 × 6 54
13
2. : 17 is the denominator
17 5 ? 5 × 5 25
28. = ⇒ =
9 45 9 × 5 45
3 17
4. 1: or
3 17 13 ? 13 × 3 39
30. = ⇒ =
17 51 17 × 3 51
3
6. 3
4 20 1 × 20 1
32. = =
440 22 × 20 22
20 4 × 5 4
8. = = 14, 664 4 × 3666 4
35 7 × 5 7 34. = =
18,330 5 × 3666 5
12 12 × 1 1
10. = = 3 3
48 12 × 4 4 36. = is raisins
1+ 3 +1 5
45 15 × 3
12. = =3 1+ 3 4
15 15 × 1 38. = does not contain nuts
1+ 3 +1 5
3
19 4 16 16
14. = 5 19 = 3 40. =
5 15 5 16 + 15 31
4 16
of the visitors when to Magic Kingdom.
31
15
124 4 1
16. = 8 124 = 15 = 15 5
8 8 2 42. of the fish caught in 2000 was used as food
8 6
44 for humans.
40
Classroom Quiz 0.1
4
56 7 × 8 7
6 1. = =
41 5 88 11× 8 11
18. = 6 41 = 6
6 36 6
11 (5 × 14) + 11 70 + 11 81
5 2. 5 ⇒ = =
14 14 14 14

2 (4 × 5) + 2 20 + 2 22 109 1
20. 4 = = = 3. =9
5 5 5 5 12 12
9
1 (5 × 12) + 1 60 + 1 61 12 109
22. 5 = = =
12 12 12 12 108
1
78 13 × 6
24. = = 13
6 6



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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

,Chapter 0: A Brief Review of Arithmetic Skills ISM: Beginning Algebra


0.2 Exercises 1 1 25 13 75 52 127 7
28. 3 + 2 = + = + = =5
8 6 8 6 24 24 24 24
2. You must change the fractions to equivalent
fractions with a common denominator.
2 3 20 3 80 9 89 5
30. 6 + = + = + = =7
21 8 3 4 3 4 12 12 12 12
4. and
25 15
2 3 37 15 148 75 73 13
25 = 5 ⋅ 5 32. 7 − 3 = − = − = =3
15 = 3 ⋅ 5 5 4 5 4 20 20 20 20
LCD = 3 ⋅ 5 ⋅ 5 = 75
8 3 113 13 113 39 74 14
34. 7 −2 = − = − = =4
4 15 5 15 5 15 15 15 15
6. 16 = 2
24 = 23 ⋅ 3 1 1 22 13 66 91 157 10
LCD = 24 ⋅ 3 = 48 36. 3 + 4 = + = + = =7
7 3 7 3 21 21 21 21

8. 24 = 23 ⋅ 3 1 3 86 53 33 3
4
38. 17 − 10 = − = =6
48 = 2 ⋅ 3 5 5 5 5 5 5
LCD = 24 ⋅ 3 = 48
13 3 45 35 80
40. 2 +2 = + = =5
5 3 11 16 16 16 16 16
10. , and
8 14 16
19 3 19 9 28 14
8=2⋅2⋅2 42. + = + = =
14 = 2 ⋅ 7 30 10 30 30 30 15
16 = 2 ⋅ 2 ⋅ 2 ⋅ 2
LCD = 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 7 = 112 2 2 17 37 85 111 196 1
44. 5 + 7 = + = + = = 13
3 5 3 5 15 15 15 15
2 5 2+5 7
12. + = = 15 3 15 9 6 1
9 9 9 9 46. − = − = =
24 8 24 24 24 4
9 3 9−3 6 3
14. − = = = 1 1 19 17 76 51 25 1
20 20 20 20 10 48. 6 − 4 = − = − = =2
3 4 3 4 12 12 12 12
7 8 21 16 37 7
16. + = + = or 1 1 1 2 21 21 56
10 15 30 30 30 30 50. 10 + 5 + 18 = + +
2 4 3 2 4 3
7 2 7 × 3 2 × 8 21 16 5 =
126 63 224
+ +
18. − = − = − =
8 3 8 × 3 3 × 8 24 24 24 12 12 12
413
=
2 1 2 × 3 1× 7 6 7 13 12
20. + = + = + = 5
7 3 7 × 3 3 × 7 21 21 21 = 34
12
11 1 11 × 2 1 × 3 22 3 25 5 5
22. + = + = + = = They ran a total of 34 miles.
15 10 15 × 2 10 × 3 30 30 30 6 12

4 7 1 36 49 21 106 43
24. + + = + + = =1
7 9 3 63 63 63 63 63

5 3 1 5 9 8 6 1
26. + − = + − = =
24 8 3 24 24 24 24 4

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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

,ISM: Beginning Algebra Chapter 0: A Brief Review of Arithmetic Skills


3 1 2 71 5 8 21 11 3 ⋅ 7 11 7 3
52. 17 + 1 − 2 = + − 6. × = × = =1
4 4 3 4 4 3 22 6 2 ⋅ 11 2 ⋅ 3 4 4
213 15 32
= + −
12 12 12 5 7 35
8. × =
196 6 11 66
=
12
= 16
4 15 8 3 ⋅ 5 8 5
10. × = × =
12 24 9 3 ⋅ 8 3 ⋅ 3 9
1
= 16
3 8 8 3 24 2
12. ×3 = × = =2
1 11 11 1 11 11
There are now 16 gallons.
3
13 13 13 7 7
14. ÷ = × =
5 9 37 73 74 73 1 9 7 9 13 9
54. 4 − 4 = − = − = inch
8 16 8 16 16 16 16
It is smaller so it will slide in and out easily. 7 7 1 7
16. ÷4 = × =
8 8 4 32
Cumulative Review
2 18 9 9 9
36 9 × 4 9 18. 18 ÷ = × = × = 81
55. = = 9 1 2 1 1
44 1 × 4 11
5
3 26 × 5 + 3 133 6 5 10 5 13 5 × 13 13 1
56. 26 = = 20. = ÷ = × = = =1
5 5 5
10 6 13 6 10 6 × 2 × 5 12 12
13

Classroom Quiz 0.2 3
4 3 11 3 12 3 × 3 × 4 9
22. = ÷ = × = =
1 2 3 4 16 9 29 5 11 4 12 4 11 4 × 11 11
1. + + = + + = or 1 12
6 3 8 24 24 24 24 24
1 3 9 27 9 8 4 1
17 5 53 41 24. 4 ÷ 3 = ÷ = × = =1
2. 2 + 4 = + 2 8 2 8 2 27 3 3
18 9 18 9
53 82 1 3 11 15
= + 26. 5 ÷ 3 = ÷
18 18 2 4 2 4
135 11 4
= = ×
18 2 15
9 11 2 × 2
=7 = ×
18 2 15
1 22
=7 =
2 15
7
2 2 37 11 111 55 56 11 =1
3. 7 − 3 = − = − = =3 15
5 3 5 3 15 15 15 15
18 1 18 9 18 2 9 ⋅ 2 2
0.3 Exercises 28. = 18 ÷ 4 = ÷ = × = × =4
4 12 2 1 2 1 9 1 9
2. Invert the second fraction. Multiply the result by
the first fraction. 5
6 5 1 5 5 5 2 5 2 1
30. = ÷2 = ÷ = × = × =
3 24 3 3 ⋅ 8 9 4 2 12 6 2 6 2 6 5 3⋅2 5 3
4. × = × = =1
8 5 8 5 5 5

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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

, Chapter 0: A Brief Review of Arithmetic Skills ISM: Beginning Algebra


12 9 6 ⋅ 2 3 ⋅ 3 Classroom Quiz 0.3
32. × = × =3
18 2 6 ⋅ 3 2
4 26 4 13 ⋅ 2 8
1. × = × =
5 11 5 18 5 3 ⋅ 6 15 4 13 29 13 29 29
34. ÷ = × = × = =1
6 18 6 11 6 11 11 11
1 5 11 17 187 7
2. 5 × 2 = × = = 15
2 1 92 7 2 6 2 6 12 12
36. 10 ÷ 2 = ÷
9 3 9 3
92 3 3 1 10 29 10 14 10 7 ⋅ 2 20
= × 3. 1 ÷ 2 = ÷ = × = × =
9 7 7 14 7 14 7 29 7 29 29
92 1
= × 0.4 Exercises
3 7
92
= 2. We write 0.42 in words as forty-two hundredths.
21
8 4. When dividing 96.3 by 10,000 we move the
=4
21 decimal point 4 places to the left.

1 8 4 8 3 4⋅2 3 0.24
38. 8 ÷ 1 = ÷ = × = × =6 6.
6
= 25 6.00 = 0.24
3 1 3 1 4 1 4 25 50
1 11 2 ⋅ 5 100
40. 5 × 10 = × = 55
2 2 1 100
0
1 1 2 10 1 2 2 ⋅ 5 1 2 4
42. 3 × × = × × = × × =
3 5 3 3 5 3 3 5 3 9 0.8
12
8. = 15 12.0 = 0.8
1 26 13 15 12 0
44. 26 ÷ 2 = ÷
6 1 6 0
26 6
= ×
1 13 0.66
13 ⋅ 2 6 2
= × 10. = 3 2.00 = 0.6
1 13 3 18
= 12
20
You can make 12 pairs of jeans.
18
1 1 1 31 31 11 2
46. ⋅6 = ⋅ = =1
4 5 4 5 20 20
15 3
The course has 1
11
km that are uphill. 12. 0.15 = =
20 100 20

Cumulative Review 8 2
14. 0.08 = =
100 25
11 11 × 5 55
47. = =
15 15 × 5 75 625 25 × 25 25 1
16. 6.25 = = = or 6
1000 4 × 25 4 4
7 7 × 7 49
48. = = 18. 3.42
9 9 × 7 63
+ 0.38
3.80 or 3.8


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