Preview Extract

Chapter 2
2.1
Fractions
Fractions
5 ( 8 ร 3) + 5 29
=
1. 3 =
8
8
8
4 ( 5 ร 2 ) + 4 14
2. 2 =
=
5
5
5
3. 4
1 ( 4 ร 4) + 1 17
=
=
4
4
4
2 ( 3 ร 3) + 2 11
4. 3 =
=
3
3
3
5. 12
6. 2
2 ( 3 ร 12 ) + 2 38
=
=
3
3
3
8 (11ร 2 ) + 8 30
=
=
11
11
11
7 ( 8 ร 22) + 7 183
7. 22 =
=
8
8
8
5 ( 8 ร 17 ) + 5 141
8. 17 =
=
8
8
8
9. 7
6 ( 7 ร 7 ) + 6 55
=
=
7
7
7
14 (15 ร 21) + 14 329
10. 21 =
=
15
15
15
11. 15
12. 7
19 ( 23 ร 15 ) + 19 364
=
=
23
23
23
9 (16 ร 7 ) + 9 121
=
=
16
16
16
3
13. 4 13
12
1
13
1
=3
4
4
1
14. 5 9
5
4
2
15. 3 8
6
2
2
16. 10 23
20
3
3
17. 10 38
30
8
7
18. 8 56
56
0
3
19. 11 40
33
7
6
20. 12 78
72
6
1
21. 63 125
63
62
4
22. 45 195
180
15
Copyright ยฉ 2015 Pearson Education, Inc.
9
4
=1
5
5
8
2
=2
3
3
23
3
=2
10
10
38
8
4
=3 =3
10
10
5
56
=7
8
40
7
=3
11
11
78
6
1
=6 =6
12
12
2
125
62
=1
63
63
195
15
1
=4 =4
45
45
3
21
22
Chapter 2 Fractions
7
23. 25 183
175
8
4
24. 149 720
596
124
183
8
=7
25
25
37.
720
124
=4
149
149
38.
14 14 รท 2 7
=
=
24 24 รท 2 12
7
14 Kt. gold is
gold.
12
10 10 รท 2 5
=
=
24 24 รท 2 12
5
10 Kt. gold is
gold.
12
25. Answers will vary.
39. Answers will vary.
26. Answers will vary.
40. Answers will vary.
27.
8
8รท8 1
=
=
16 16 รท 2 2
28.
15 15 รท 5 3
=
=
20 20 รท 5 4
29.
25 25 รท 5 5
=
=
40 40 รท 5 8
30.
36 36 รท 6 6
=
=
42 42 รท 6 7
31.
27 27 รท 9 3
=
=
45 45 รท 9 5
112 112 รท 16 7
32.
=
=
128 128 รท 16 8
33.
165 165 รท 15 11
=
=
180 180 รท 15 12
34.
12
12 รท 12
1
=
=
600 600 รท 12 50
35.
36.
24 24 รท 24
=
=1
24 24 รท 24
24 Kt. gold is pure gold.
18 18 รท 6 3
=
=
24 24 รท 6 4
3
18 Kt. gold is
gold.
4
41. 32 is divisible by 2 since the last digit is an
even number.
32 is not divisible by 3 since 3 + 2 = 5 is not
divisible by 3.
32 is divisible by 4 since 32 ยธ 4 = 8.
32 is not divisible by 5 since the last digit is
not 0 or 5.
32 is not divisible by 6 since 3 + 2 = 5 is not
divisible by 3.
32 is divisible by 8 since 32 ยธ 8 = 4.
32 is not divisible by 9 since 3 + 2 = 5 is not
divisible by 9.
32 is not divisible by 10 since the last digit is
not 0.
42. 45 is not divisible by 2 since the last digit is
not an even number.
45 is divisible by 3 since 4 + 5 = 9 is
divisible by 3.
45 is not divisible by 4 since
45 รท 4 โ integer.
45 is divisible by 5 since the last digit is 5.
45 is not divisible by 6 since it is not an
even number.
45 is not divisible by 8 since
45 รท 8 โ integer.
45 is divisible by 9 since 4 + 5 = 9 is
divisible by 9.
45 is not divisible by 10 since the last digit is
not 0.
Copyright ยฉ 2015 Pearson Education, Inc.
Chapter 2 Fractions
43. 60 is divisible by 2 since the last digit is an
even number.
60 is divisible by 3 since 6 + 0 = 6 is
divisible by 3.
60 is divisible by 4 since 60 ยธ 4 = 15.
60 is divisible by 5 since the last digit is 0.
60 is divisible by 6 since 60 is even and since
6 + 0 = 6 is divisible by 3.
60 is not divisible by 8 since
60 ยธ 8 ยน integer.
60 is not divisible by 9 since 6 + 0 = 6 is not
divisible by 9.
60 is divisible by 10 since the last digit is 0.
44. 72 is divisible by 2 since the last digit is an
even number.
72 is divisible by 3 since 7 + 2 = 9 is
divisible by 3.
72 is divisible by 4 since 72 ยธ 4 = 18.
72 is not divisible by 5 since the last digit is
not 0 or 5.
72 is divisible by 6 since 72 is even and
7 + 2 = 9 is divisible by 3.
72 is divisible by 8 since 72 ยธ 8 = 9.
72 is divisible by 9 since 7 + 2 = 9 is
divisible by 9.
72 is not divisible by 10 since the last digit is
not 0.
45. 90 is divisible by 2 since the last digit is an
even number.
90 is divisible by 3 since 9 + 0 = 9 is
divisible by 3.
90 is not divisible by 4 since
90 ยธ 4 ยน integer.
90 is divisible by 5 since the last digit is 0.
90 is divisible by 6 since 90 is even and since
9 + 0 = 9 is divisible by 3.
90 is not divisible by 8 since
90 ยธ 8 ยน integer.
90 is divisible by 9 since 9 + 0 = 9 is
divisible by 9.
90 is divisible by 10 since the last digit is 0.
23
46. 105 is not divisible by 2 since the last digit is
not an even number.
105 is divisible by 3 since 1 + 0 + 5 = 6 is
divisible by 3.
105 is not divisible by 4 since 5 is not
divisible by 4.
105 is divisible by 5 since the last digit is 5.
105 is not divisible by 6 since it is not an
even number.
105 is not divisible by 8 since
105 ยธ 8 ยน integer.
105 is not divisible by 9 since 1 + 0 + 5 = 6 is
not divisible by 9.
105 is not divisible by 10 since the last digit
is not 0.
47. 4172 is divisible by 2 since the last digit is an
even number.
4172 is not divisible by 3 since
4 + 1 + 7 + 2 = 14 is not divisible by 3.
4172 is divisible by 4 since 72 is divisible by
4.
4172 is not divisible by 5 since the last digit
is not 0 or 5.
4172 is not divisible by 6 since
4 + 1 + 7 + 2 = 14 is not divisible by 3.
4172 is not divisible by 8 since
172 ยธ 8 ยน integer.
4172 is not divisible by 9 since
4 + 1 + 7 + 2 = 14 is not divisible by 9.
4172 is not divisible by 10 since the last digit
is not 0.
48. 5688 is divisible by 2 since the last digit is an
even number.
5688 is divisible by 3 since 5 + 6 + 8 + 8 = 27
is divisible by 3.
5688 is divisible by 4 since 88 ยธ 4 = 22.
5688 is not divisible by 5 since the last digit
is not 0 or 5.
5688 is divisible by 6 since 5688 is even and
5 + 6 + 8 + 8 = 27 is divisible by 3.
5688 is divisible by 8 since 688 ยธ 8 = 86.
5688 is divisible by 9 since 5 + 6 + 8 + 8 = 27
is divisible by 9.
5688 is not divisible by 10 since the last digit
is not 0.
Copyright ยฉ 2015 Pearson Education, Inc.
24
Chapter 2 Fractions
2.2
Addition and Subtraction
of Fractions
1.
2.
4
=
5 20
20 ยธ 5 = 4
4ยด 4 = 16
4 16
=
5 20
3
=
4 16
16 ยธ 4 = 4
4ยด3 = 12
3 12
=
4 16
3.
4.
9
=
10 40
40 ยธ 10 = 4
4ยด9 = 36
9
36
=
10 40
7
=
8 56
56 ยธ 8 = 7
7 ยด 7 = 49
7 49
=
8 56
5.
6
=
5 40
40 ยธ 5 = 8
8ยด 6 = 48
6 48
=
5 40
6.
7
=
8 64
64 ยธ 8 = 8
7.
6
=
7 49
49 ยธ 7 = 7
7 ยด 6 = 42
6 42
=
7 49
8.
11
=
15 120
120 ยธ 15 = 8
8ยด11 = 88
11 88
=
15 120
9. 3, 8, ___
1 1
3 3 1
2 3 2
2 3 4
2 3 8
2ยด 2ยด 2ยด3 = 24
10. 18, 24, ___
1 1
3 3 1
3 9
3
2 9
6
2 9 12
2 18 24
2ยด 2ยด 2ยด3ยด3 = 72
11. 12, 18, 20, ___
1 1 1
5 1 1 5
3 1 3 5
3 3 9
5
2 6 9 10
2 12 18 20
2ยด 2ยด3ยด3ยด5 = 180
8ยด 7 = 56
7 56
=
8 64
Copyright ยฉ 2015 Pearson Education, Inc.
Chapter 2 Fractions
12. 18, 20, 24, ___
1 1 1
5 1 5 1
16. 5, 18, 25, 30, 36, ___
1 1 1 1 1
5 1 1 5 1 1
3 3 5 1
5 5
1 25 5 1
3 9 5
3
3 5
3 25 5 3
2 9 5
6
3 5
9 25 15 9
2 9 10 12
2 5
9 25 15 18
2 18 20 24
2 5 18 25 30 36
2ยด 2ยด 2ยด3ยด3ยด5 = 360
2ยด 2ยด3ยด3ยด5ยด5 = 900
13. 15, 24, 32, ___
1 1 1
5 5 1 1
17. Answers will vary.
18. Answers will vary.
3 15 3 1
2 15 3
2
2 15 3
4
2 15 6
8
2 15 12 16
19.
2 1 2 +1 3
+ =
=
5 5
5
5
20.
2 4 2+4 6 2
+ =
= =
9 9
9
9 3
21.
3
5
3+ 5 8
4
+ =
= =
10 10
10
10 5
22.
5 7 5 + 7 12
4
1
+ =
= =1 =1
8 8
8
8
8
2
23.
11 5 11- 5 6 1
– =
= =
12 12
12
12 2
24.
5 1 5 -1 4
– =
=
7 7
7
7
25.
5
1
20 3
20 – 3 17
– = – =
=
12 16 48 48
48
48
26.
2 3 16 9 16 – 9
7
– = – =
=
3 8 24 24
24
24
2 15 24 32
2ยด 2ยด 2ยด 2ยด 2ยด3ยด5 = 480
14. 6, 8, 10, 12, ___
1 1 1 1
5 1 1 5 1
3 3 1 5
3
2 3 2
5 3
2 3 4
5 6
2 6 8 10 12
2ยด 2ยด 2ยด3ยด5 = 120
15. 10, 35, 50, 60, ___
1 1 1 1
7 1 7 1 1
5
1 7 5 1
5 5 35 25 5
3 5 35 25 15
27.
2 5 35 25 30
2 10 35 50 60
2ยด 2ยด3ยด5ยด5ยด 7 = 2100
28.
3 5 1 27 20 12
+ + =
+ +
4 9 3 36 36 36
27 + 20 + 12 59
23
=
=
=1
36
36
36
1 1 1
6
3
2
+ + =
+ +
4 8 12 24 24 24
6 + 3 + 2 11
=
=
24
24
Copyright ยฉ 2015 Pearson Education, Inc.
25
26
29.
30.
Chapter 2 Fractions
3 2 1
30 28 7
+ + = + +
7 5 10 70 70 70
30 + 28 + 7 65 13
=
=
=
70
70 14
36.
5 3 5 20 18 15
+ + =
+ +
6 4 8 24 24 24
20 + 18 + 15 53
5
=
=
=2
24
24
24
7
8 5 21 16 25
31.
+ + = + +
10 15 6 30 30 30
21 + 16 + 25 62
2
1
=
=
=2 =2
30
30
30
15
32.
33.
34.
35.
3 2 3
6
8
3
+ + = + +
10 5 20 20 20 20
6 + 8 + 3 17
=
=
20
20
3
27
=
4
36
2
24
=
3
36
8
32
+ =
9
36
83
11
=2
36
36
7
14
=
12 24
5 15
=
8 24
7 28
+ =
6 24
57
9
3
=2 =2
24
24
8
8
16
=
15 30
3
9
=
10 30
3
18
+ =
5
30
43
13
=1
30
30
37.
38.
39.
40.
1
3
=
6 18
5 10
=
9 18
13 13
+
=
18 18
26
8
4
=1 =1
18
18
9
7
14
=
10 20
1
5
– =
4
20
9
20
4 12
=
5 15
2 10
– =
3 15
2
15
5 15
=
8 24
1
8
– =
3 24
7
24
19 38
=
24 48
5
15
=
16 48
23
48
41. Answers will vary.
42. Answers will vary.
43.
1 3 1
6
9
8
23
+ + = + + =
4 8 3 24 24 24 24
23
Zalia ordered
cubic yards.
24
Copyright ยฉ 2015 Pearson Education, Inc.
Chapter 2 Fractions
44.
45.
1 1 1
1 15 10 6
5
+ + + = + + +
4 6 10 12 50 60 60 60
36 3
=
=
60 5
3
Chuck has spent of his total savings.
5
1 1 1 12 20 15 47
+ + = + + =
5 3 4 60 60 60 60
47
The total length of the bolt is
inch.
60
1 1 2
5 10 16 31
46. + + = + + =
8 4 5 40 40 40 40
31
The total length of the screw is
inch.
40
47.
48.
49.
50.
51.
52.
7 1 1 21 6
8
7
– – = – – =
8 4 3 24 24 24 24
7
of the contents remain.
24
7 1 1 21 4
8
9
3
– – = – – =
=
8 6 3 24 24 24 24 8
3
gallon of fluid remaining.
There is
8
53.
54.
1 1
4
3
7
+ = + =
6 8 24 24 24
7
of the day was spent in class and study.
24
1 1
4
1
5
+ = + =
3 12 12 12 12
5
of the day was spent in work and travel,
12
and other.
55. The greatest amount of time (the largest
segment of the graph) was spent in work and
travel.
1 1 2 1 3 1
+ = + = =
3 6 6 6 6 2
1
of the day was spent in work and travel,
2
and class time.
56. The least amount of time (the smallest
segment of the graph) was spent in other.
1 1
2
3
5
+ = + =
12 8 24 24 24
5
of the day was spent in other and study.
24
1 1 1 1+1+1 3
+ + =
=
4 4 4
4
4
3
cup of butter is needed.
4
57.
2 1 1
48
15
20
83
+ + =
+
+
=
5 8 6 120 120 120 120
83
Joan has saved
of the start-up costs.
120
58.
15 3 3 15 6
6
3
– – = – – =
16 8 8 16 16 16 16
3
The diameter of the hole is
inch.
16
59.
3 1 2 1
– = =
4 4 4 2
The difference in the width is
1 1 1 1 2 2 5
+ + = + + =
8 4 4 8 8 8 8
5
Martin has run
mile.
8
3 5 6 5 1
– = – =
4 8 8 8 8
1
inch.
2
1 1 2 1 1
– = – =
2 4 4 4 4
The difference in the width is
60.
Martin must run an additional
27
1
inch.
4
7 1 1 3 21 6
4
9
– – – = – – 8 4 6 8 24 24 24 24
2
1
=
=
24 12
1
The length of the fourth side is
mile.
12
7 3
3 14 3
3
8
1
– – = – – = =
8 16 16 16 16 16 16 2
1
The diameter of the hole is
inch.
2
1
mile.
8
Copyright ยฉ 2015 Pearson Education, Inc.
28
Chapter 2 Fractions
2.3
Addition and Subtraction
of Mixed Numbers
1.
3
5
1
+ 15
5
4
97
5
82
8.
2
25
2.
7
3
+ 14
7
5
39
7
3.
4.
5.
7.
1
2
41 = 41
2
4
1
1
+ 39 = 39
4
4
3
80
4
9.
1
5
= 28
4
20
3
12
+ 23 = 23
5
20
17
51
20
28
10.
3
30
46 = 46
4
40
5
25
12 = 12
8
40
4
32
+ 37 = 37
5
40
87
7
7
95 = 95 + 2 = 97
40
40
40
5
35
26 = 26
6.
8
56
3
12
17 = 17
14
56
2
16
+ 32 = 32
7
56
63
7
1
75 = 75 + 1 = 76
56
56
8
11.
12.
3
18
= 32
4
24
1
8
6 = 6
3
24
5
15
+ 14 = 14
8
24
41
17
17
52 = 52 + 1 = 53
24
24
24
32
7
28
= 16
10
40
1
8
26 = 26
5
40
3
15
+8 = 8
8
40
51
11
11
50 = 50 + 1 = 51
40
40
40
16
3
6
= 16
4
8
3
3
– 12 = 12
8
8
3
4
8
16
13
13
= 25
24
24
5
10
– 18 = 18
12
24
3
1
7 =7
24
8
25
7
21
=9
8
24
5
10
-6 =6
12
24
11
3
24
9
6
6
5
5
– 211 = 211
6
6
1
162
6
374 = 373
Copyright ยฉ 2015 Pearson Education, Inc.
Chapter 2 Fractions
13.
14.
15.
16.
1
3
1
3
21. 34 + 23 + 34 + 23
2
4
2
4
2
3
2
3
= 34 + 23 + 34 + 23
4
4
4
4
10
2
1
= 114 = 116 = 116
4
4
2
1
116 inches of lead stripping are needed.
2
4
4
3
3
– 12 = 12
4
4
1
6
4
19
29
= 18
3
9
71 = 71
8
24
1
8
– 62 = 62
3
24
1
9
24
7
1
7
1
16
22. 9 + 5 + 9 + 5 = 28 = 30
8
8
8
8
8
30 inches of brass trim are needed.
2
3
5
23. 107 + 150 + 138
3
4
8
16
18
15
49
1
= 107 + 150 + 138 = 395 = 397
24
24
24
24
24
1
feet.
Lengths of the three sides total 397
24
1
1
527 – 397 = 130
24
24
The length of the fourth side is 130 feet.
1
4
16
= 6 =5
3
12
12
5
5
5
-2 =2 =2
12
12
12
11
3
12
6
3
9
39
= 72
= 71
10
30
30
8
16
16
– 25 = 25
= 25
15
30
30
23
46
30
72
17. Answers will vary.
18. Answers will vary.
3
1
3
1
19. 3 + 5 + 4 + 3 + 6
8
2
4
4
3
4
6
2
= 3 +5 +4 +3 +6
8
8
8
8
15
7
= 21 = 22
8
8
7
Loren worked 22 hours altogether.
8
5
1
5
1
3
20. 2 + 6 + 1 + 3 + 7
8
2
6
4
8
15
12
20
6
9
= 2 + 6 +1 + 3 + 7
24
24
24
24
24
62
14
7
= 19 = 21 = 21
24
24
12
7
The total weight is 21
tons.
12
1
3
1
24. 108 + 162 + 143
4
8
2
2
3
4
9
1
= 108 + 162 + 143 = 413 = 414
8
8
8
8
8
1
Lengths of the three sides total 414 feet.
8
3
1
6
1
5
518 – 414 = 518 – 414 = 104
4
8
8
8
8
5
The length of the fourth side is 104 feet.
8
1
3
2
3
5
1
25. 2 + 3 + 1 = 2 + 3 + 1 = 6 = 7
2
4
4
4
4
4
1
7 cubic yards have been unloaded.
4
7
1
7
2
5
8 -7 = 8 -7 =1
8
4
8
8
8
5
1 cubic yards of concrete remain.
8
3
1
7
6
1
7
14
3
26. 3 + 4 + 3 = 3 + 4 + 3 = 10 = 11
4
8
8
8
8
8
8
4
3
11 yards of material have been used.
4
3
4
3
1
15 -11 = 14 -11 = 3
4
4
4
4
1
3 yards of material remain.
4
Copyright ยฉ 2015 Pearson Education, Inc.
30
Chapter 2 Fractions
2.4
Multiplication and Division
of Fractions
1
5
11.
1
2 1 1 20 1
ยด6 ยด = ยด
ยด
4
3 5 4
3
5
1
1
3 2
3ยด1
3
1.
ยด =
=
4 5 2ยด5 10
2
1
1ยด1ยด1 1
=
=
1ยด3ยด1 3
1
1
2.
2 5 1ยด5
5
=
ยด =
3 8 3ยด 4 12
1
4
3.
9 11
9ยด11
99
ยด =
=
10 16 10ยด16 160
1
=
4
1ยด3ยด13 39
7
=
=2
1ยด 4ยด 4 16
16
1
1
5
1
2 5 9 11
13. ยด 2 ยด3 = ยด ยด
9
4
3 9 4 3
4
5ยด1ยด11 55
7
=
= =4
1ยด 4ยด3 12
12
2 3 1ยด1 1
ยด =
=
4.
3 8 1ยด 4 4
1
3
2 9
1
2 9 13
12. ยด ยด3 = ยด ยด
3 8
4
3 8 4
1
1
9 11
9ยด1
9
ยด
=
=
5.
22 16 2ยด16 32
2
1
1
1
6.
5
7
1ยด 7
7
ยด
=
=
12 10 12ยด 2 24
=
4
1
1
9
2
1
1 3 1 4
16. ยธ = ยด
4 4 4 3
1
1ยด9 9
1
=
= =4
1ยด 2 2
2
=
1ยด1 1
=
1ยด3 3
1
1
1
28 3
9. 3 ยด 3 = ยด
9
9 1
3 5 3 8
17. ยธ = ยด
8 8 8 5
3
28ยด1 28
1
=
=9
3ยด1
3
3
1
1
3ยด1 3
=
=
1ยด5 5
2
3 8
1
3 8 5
10. ยด ยด 2 = ยด ยด
4 9
2
4 9 2
1
2
7
4ยด 2ยด 2 16
7
=
= =1
1ยด9ยด1
9
9
2
7
5 27
8. 1 ยด 2 = ยด
3
10 3 10
=
2
3 5 10
28 14 10
ยด ยด
15. 5 ยด1 ยด =
5 9 49
9
5
49
1
1 5 7
7. 1 ยด3 = ยด
4
2 4 2
5ยด7 35
3
=
=
=4
4ยด 2
8
8
1
1
3ยด1ยด 4 12
= = 12
1ยด1ยด1
1
2
1
4
1
2 3 3 8
14. 3ยด1 ยด 2 = ยด ยด
2
3 1 2 3
3
1ยด 2 ยด5 10
4
2
=
= =1 =1
1ยด3ยด 2
6
6
3
1
3
13 26 13 30
ยธ =
ยด
18.
20 30 20 26
2
=
1ยด3 3
=
2ยด 2 4
Copyright ยฉ 2015 Pearson Education, Inc.
2
Chapter 2 Fractions
3
1
9 3
9
5
19.
ยธ =
ยด
10 5 10 3
2
=
1
3ยด1 3
1
= =1
2ยด1 2
2
1
7 3 7 4
20. ยธ = ยด
8 4 8 3
2
7ยด1 7
1
=
= =1
2ยด3 6
6
1
3 5 15
21. 2 ยธ 3 = ยธ
2
4 2 4
1
=
2
5
4
1ยด 2 2
ยด
=
=
2 15 1ยด3 3
1
3
=
1
3
2
5
5 5
21 5
27. 2 ยธ = ยธ
8 16
8 16
2
21 16 21ยด 2 42
2
= ยด
=
=
=8
5
1ยด5
5
5
8
1
2
17 6
28. 5 ยธ 6 = ยธ
3
3 1
17 1 17 ยด1 17
= ยด =
=
3 6 3ยด6 18
29. Answers will vary.
30. Answers will vary.
4
1 $8 3
ยด
31. $8ยด1 =
2
1
2
=
1
1 5 25
22. 1 ยธ 4 = ยธ
4
6 4 6
5
6
1ยด3
3
ยด
=
=
4 25 2ยด5 10
7
15
23. 5 ยธ 1 = 5 ยธ
8
8
1
5 8
1ยด8 8
2
= ยด
=
= =2
1 15 1ยด3 3
3
3
1
5
24. 3 ยธ 1 = 3 ยธ
4
4
3 4 3ยด 4 12
2
= ยด =
= =2
1 5
5
5
5
3
1 3 5
25. ยธ 2 = ยธ
8
2 8 2
4
1 $17 3
ยด
32. $17ยด1 =
2
1 2
$17 ยด3 $51
1
=
=
= $25 = $25.50
1ยด 2
2
2
1 $25 3
ยด
33. $12.50ยด1 =
2
2 2
$25ยด 3 $75
3
=
=
= $18 = $18.75
2ยด2
4
4
1 $19 3
ยด
34. $9.50ยด1 =
2
2 2
$19 ยด3 $57
1
=
=
= $14 = $14.25
2ยด 2
4
4
35. Answers will vary.
36. Answers will vary.
1
15
4
3ยด1
3
=
ยด
=
=
8
25 2ยด5 10
2
3
3
30
3
3ยด3
ยด
=
=9
37. 30ยด =
10
1 10 1ยด1
1
7
1 15 25
26. 1 ยธ 6 = ยธ
8
4
8
4
3
1
$4ยด3
= $12
1ยด1
1
3 2
3ยด1
3
= ยด =
=
8 5 4ยด5 20
31
The cost of operating the hair dryer for 30
minutes is 9 cents.
18
2 90 2 18ยด 2
ยด =
= 36
38. 90ยด =
5
1
1ยด1
5
5
1
The cost of brewing coffee for 90 minutes is
36 cents.
Copyright ยฉ 2015 Pearson Education, Inc.
32
Chapter 2 Fractions
4
1 16 9
4ยด9
ยด =
= 36
39. 16ยด 2 =
4
1
1ยด1
4
1
Matthew needs 36 yards of ribbon.
1
125
46. 6750 ยธ 62 = 6750 ยธ
2
2
54
6750
2
54ยด 2
=
= 108
=
ยด
1ยด1
1
125
1
5
1 10 153 5ยด153
1
ยด
=
= 382
40. 10ยด 38 =
4
1
1ยด 2
2
4
2
Jack made $382.50.
108 units can be carpeted.
7
3 28 51 7ยด51
ยด =
= 357
47. 28ยด12 =
4
1
1ยด1
4
1
2
1 1314 219
ยธ
41. 1314 ยธ 109 =
2
1
2
1 16 57 2 ยด57
16ยด 7 =
ยด =
= 114
8
1
1ยด1
8
6
1
1314
2
6ยด 2
ยด
=
= 12
=
1
1ยด1
219
357 + 114 = 471
1
12 homes can be fitted with cabinet trim.
471 gallons of fuel are used.
18
1 36 13 18ยด13
= 234
48. 36ยด 6 =
ยด =
2
1
1ยด1
2
1 1200 15
42. 1200 ยธ 7 =
ยธ
2
1
2
1
80
1200
2
80ยด 2
=
=
= 160
ยด
1
1ยด1
15
1
11
1 22 25 11ยด 25 275
3
22ยด3 =
=
= 68
ยด =
8
1
1ยด 4
4
4
8
4
160 acres can be fertilized.
1 135 39
43. 135ยด19 =
ยด
2
1
2
135ยด39 5265
1
=
=
= 2632
1ยด 2
2
2
1
2632 inches of steel tubing are needed.
2
3
3
234 + 68 = 302
4
4
It takes a total of 302
3
minutes.
4
1 11 8 11ยด8
= 88
49. 11 ยธ = ยด =
8 1 1
1ยด1
88 dispensers can be filled.
91
1 182 123
ยด
44. 182ยด 61 =
2
1
2
2
1
91ยด123 11,193
=
=
= 11,193
1ยด1
1
11,193 inches of wood are needed.
1
5
45. 40 ยธ 1 = 40 ยธ
4
4
8
40 4 8ยด 4
= 32
=
ยด =
1
1ยด1
5
5
10 16 2ยด16
= 32
50. 10 ยธ =
ยด =
16
1
1ยด1
5
1
32 footings can be constructed.
1
17
51. 40 ยธ 8 = 40 ยธ
2
2
40 2
40ยด 2 80
12
= ยด =
= =4 ยป5
1 17 1ยด17 17
17
Approximately 5 round trips are required.
1
32 strawberry cheesecakes can be made.
40
5 200 8 40ยด8
= 320
52. 200 ยธ =
ยด =
8
1
1ยด1
5
1
320 pieces of weather stripping may be cut
from the roll.
Copyright ยฉ 2015 Pearson Education, Inc.
Chapter 2 Fractions
2.5
Converting Decimals to Fractions
and Fractions to Decimals
17. .096 =
96
12
=
1000 125
12
3
=
1000 250
1. .75 =
75
3
=
100 4
18. .012 =
2. .55 =
55
11
=
100 20
19. .0375 =
375
3
=
10, 000 80
3. .24 =
24
6
=
100 25
20. .0875 =
875
7
=
10,000 80
4. .64 =
64 16
=
100 25
21. .1875 =
1875
3
=
10, 000 16
5. .73 =
73
100
22. .9845 =
9845
1969
=
10,000 2000
6. .33 =
33
100
23. .0016 =
16
1
=
10, 000 625
7. .85 =
85 17
=
100 20
24. .0085 =
85
17
=
10,000 2000
8. .68 =
68 17
=
100 25
25. Answers will vary.
9. .34 =
34 17
=
100 50
10. .288 =
288
36
=
1000 125
11. .444 =
444
111
=
1000 250
12. .125 =
125
1
=
1000 8
13. .625 =
625
5
=
1000 8
14. .875 =
875
7
=
1000 8
15. .805 =
805
161
=
1000 200
16. .791 =
791
1000
26. Answers will vary.
27.
1
= .25
4
28.
7
= .875
8
29.
3
= .375
8
Copyright ยฉ 2015 Pearson Education, Inc.
.25
4 1.00
8
20
20
0
.875
8 7.000
64
60
56
40
40
0
.375
8 3.000
24
60
56
40
40
0
33
34
Chapter 2 Fractions
30.
5
= .625
8
31.
2
= .667 (rounded)
3
32.
33.
34.
5
= .833 (rounded)
6
7
= .778 (rounded)
9
1
= .111 (rounded)
9
.625
8 5.000
48
20
16
40
40
0
.6666
3 2.0000
18
20
18
20
18
20
18
2
.8333
6 5.0000
48
20
18
20
18
20
18
2
.7777
9 7.0000
63
70
63
70
63
70
63
7
.1111
9 1.0000
9
10
9
10
9
10
9
1
35.
7
= .636 (rounded)
11
36.
8
= .32
25
37.
22
= .88
25
38.
14
= .56
25
39.
181
= .883 (rounded)
205
40.
1
= .010 (rounded)
99
Copyright ยฉ 2015 Pearson Education, Inc.
.6363
11 7.0000
66
40
33
70
66
40
33
7
.32
25 8.00
7 50
50
50
0
.88
25 22.00
200
2 00
2 00
0
.56
25 14.00
12 5
150
150
0
.8829
205 181.0000
1640
1700
1640
600
410
1900
1845
55
.0101
99 1.0000
99
10
0
100
99
1
Chapter 2 Fractions
41. (a) 1 out of 8, or
1
quit taking their
8
medicine.
(b)
(c)
42. (a)
.125
8 1.000
8
20
16
40
40
0
1
= .125
8
1
1 1521 1ยด1521
ยด1521 = ยด
=
8
8
1
8ยด1
1521
1
=
= 190 ยป 190
8
8
190 patients in the study quit taking
their medicine.
2. Divide each annual amount by the total
annual operating expenses.
$120,000
5
=
Salaries:
$288,000 12
$72,000
1
=
Rent:
$288,000 4
$24,000
1
=
Utilities:
$288,000 12
$18,000
1
Insurance:
=
$288,000 16
$18,000
1
=
Advertising:
$288,000 16
$36,000
1
Miscellaneous:
=
$288,000 8
3.
.2
5 1.0
10
0
1
= .2
5
1600
1
1 8000
(b) ยด8000 = ยด
1
5
5
1
1ยด1600
=
= 1600
1ยด1
1600 smokers are expected to develop
lung cancer.
Case Study
1. Multiply each monthly amount by 12.
Salaries: $10,000ยด12 = $120,000
Rent: $6000ยด12 = $72,000
Utilities: $2000ยด12 = $24,000
Insurance: $1500ยด12 = $18,000
Advertising: $1500ยด12 = $18,000
Miscellaneous: $3000ยด12 = $36,000
$120,000 + $72,000 + $24,000
+$18,000 + $18,000 + $36,000 = $288,000
The total annual operating expenses are
$288,000.
4. Multiply each fraction by 360๏ฏ.
5
Salaries:
ยด360๏ฏ = 150๏ฏ
12
1
Rent: ยด360๏ฏ = 90๏ฏ
4
1
Utilities: ยด360๏ฏ = 30๏ฏ
12
1
ยด360๏ฏ = 22.5๏ฏ
Insurance:
16
1
Advertising: ยด360๏ฏ = 22.5๏ฏ
16
1
Miscellaneous: ยด360๏ฏ = 45๏ฏ
8
Copyright ยฉ 2015 Pearson Education, Inc.
35
36
Chapter 2 Fractions
Case in Point Summary Exercise
3
1 6 129
1. 6ยด32 = ยด
4 1
4
Chapter 2 Test
1.
25 25 รท 5 5
=
=
30 30 รท 5 6
2.
875
875 รท 125 7
=
=
1000 1000 รท 125 8
3.
84
84 รท 12
7
=
=
132 132 รท 12 11
2
3ยด129 387
1
=
=
= 193
1ยด 2
2
2
1
193 inches of cherry wood are needed.
2
1
1 129 29
ยด
2. 32 ยด14 =
4
2
4
2
129ยด 29 3741
5
=
=
= 467
4ยด 2
8
8
The area of each panel is 467
5
square
8
inches.
3
5
3741 6
ยด
3. 467 ยด 6 =
8
1
8
4
3741ยด3 11, 223
3
=
=
= 2805
4ยด1
4
4
3
A total area of 2805 square inches of
4
cherry wood is needed.
5 2250 3741
4. 2250 ยธ 467 =
ยธ
8
1
8
750
2250
8
750ยด8 6000
ยด
=
=
=
1
3741 1ยด1247 1247
1247
=4
1012
, which must be rounded down
1247
to 4.
4 side panels can be made.
8
4. 8 65
64
1
65
1
=8
8
8
4
5. 12 56
48
8
56
8
2
=4 =4
12
12
3
2
6. 45 120
90
30
7. 7
120
30
2
=2 =2
45
45
3
3 ( 4 ร 7 ) + 3 31
=
=
4
4
4
4 ( 5 ร 18 ) + 4 94
=
8. 18 =
5
5
5
3 ( 8 ร 18 ) + 3 147
=
9. 18 =
8
8
8
10. 2, 6, 5, ___
1 1 1
5 1 1 5
31 3
5
2 2 6
5
2ยด3ยด5 = 30
Copyright ยฉ 2015 Pearson Education, Inc.
Chapter 2 Fractions
11. 6, 8, 15, ___
1 1 1
51 1 5
1 200 100 20
17. 33 ยธ
=
ยธ
3
9
3
9
1
3 3 1 15
2 3 2 15
1
2 3 4 15
2ยด 2ยด 2ยด3ยด5 = 120
12. 6, 9, 12, 24, ___
1 1 1 1
3 1 3 1 1
3 3 9 3
3
2 3 9 3
6
2 3 9 6 12
2 6 9 12 24
2ยด 2ยด 2ยด3ยด3 = 72
14.
1
19. $1275ยด = $425 rent
3
$1275 – $425 = $850
3
$850ยด = $510
5
Rhonda paid $510 for food, utilities, and
transportation.
1
8
=
5
40
3
12
=
10
40
3 15
+ =
8 40
35 7
=
40 8
$1275 – $425 – $510 = $340
Rhonda has $340 left.
5
5
= 32
16
16
1
4
– 17 = 17
4
16
1
15
16
32
3
3
19
= 126 = 125
16
16
16
7
14
14
– 89 = 89 = 89
8
16
16
5
36
16
15. 126
9
4
1 8
135
8
9ยด 4
=
= 36
ยด
16. 67 ยด =
2 15
1ยด1
2
15
1
2
1
3
5
4
6
5
18. 23 + 34 + 17 = 23 + 34 + 17
2
4
8
8
8
8
15
7
= 74 = 75
8
8
7
Becky used 75 pounds of sugar.
8
7
7
(2ยด50) – 75 = 100 – 75
8
8
8
7
1
= 99 – 75 = 24
8
8
8
1
24 pounds of sugar remain.
8
2 6 8 15
13.
3
9
1ยด3 3
1
100
ยด
=
= =1
=
2
3
200 1ยด 2 2
1
3
3
4
3
6
20. 68 + 37 + 5 = 68 + 37 + 5
2
8
4
8
8
8
13
5
= 110 = 111
8
8
5
111 gallons of paint were used.
8
1
4
12
147 = 147 = 146
2
8
8
5
5
5
– 111 = 111 = 111
8
8
8
7
35
8
7
There are 35 gallons of paint remaining.
8
1
Copyright ยฉ 2015 Pearson Education, Inc.
37
38
Chapter 2 Fractions
1 1000 17
ยธ
21. 1000 ยธ 8 =
2
1
2
1000 2 1000ยด 2 2000
11
=
ยด =
=
= 117
1
17
1ยด17
17
17
117 pizzas can be made.
1 117 17
117 ยด8 =
ยด
2
1
2
117ยด17 1989
1
=
=
= 994
1ยด 2
2
2
1
994 ounces of mozzarella will be used.
2
1
1
1000 – 994 = 5
2
2
1
5 ounces of mozzarella will remain.
2
22. .625 =
23. .82 =
625 5
=
100 8
82
41
=
100 50
.25
24. 4 1.00
8
20
20
0
.875
25. 8 7.000
64
60
56
40
40
0
.25 inch
.875 inch
Copyright ยฉ 2015 Pearson Education, Inc.

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