Fractions. What fraction is this? 4 8 4 7 What is the sum of these fractions? + This is one whole.
CHAPTER 2 FRACTIONS - aplustestbank.euaplustestbank.eu/sample/Solution-Manual-for... · CHAPTER 2...
26
15 CHAPTER 2 FRACTIONS Preview 2 1. (a) 4 3 7 7 3 28 31 4 4 31 = = (b) 8 31 8 7 24 8 7 3 8 8 7 3 = + = + × = (c) 64 20 4 4 16 5 = × (d) 32 56 8 8 4 7 , 4 7 4 3 1 = × = (e) 32 5 32 64 10 5 = (f) 8 7 1 ; 24 40 3 5 , 24 45 8 15 8 7 1 = = = is larger 3. (a) 8 5 16 10 16 3 16 7 = = + (b) 16 15 1 16 31 16 12 16 19 4 3 16 3 1 = = + = + (c) 20 11 20 4 20 15 5 1 4 3 = − = − (d) 16 11 2 16 43 16 21 16 64 16 5 1 4 = = − = − Exercises 2-1 Working with Fractions A. 1. 3 7 3 1 2 = 3. 8 67 8 3 8 = 5. 8 23 8 7 2 = 7. 3 8 3 2 2 = 9. 6 29 6 5 4 = B. 1. 2 1 8 2 17 = 3. 8 3 1 8 11 = 5. 2 1 1 2 3 = 7. 3 2 16 6 4 16 6 100 = = 9. 2 1 2 22 16 2 32 80 = = C. 1. 4 3 16 12 = 3. 8 3 16 6 = 5. 5 2 10 4 = 7. 5 4 30 24 =
Transcript of CHAPTER 2 FRACTIONS - aplustestbank.euaplustestbank.eu/sample/Solution-Manual-for... · CHAPTER 2...
15
CHAPTER 2 FRACTIONS Preview 2
1. (a) 4
37
7
328314
4
31== (b)
8
31
8
724
8
738
8
73 =
+=
+×=
(c) 64
20
4
4
16
5=× (d)
32
56
8
8
4
7,
4
7
4
31 =×=
(e) 32
5
3264
105
= (f) 8
71;
24
40
3
5,
24
45
8
15
8
71 === is larger
3. (a) 8
5
16
10
16
3
16
7==+ (b)
16
151
16
31
16
12
16
19
4
3
16
31 ==+=+
(c) 20
11
20
4
20
15
5
1
4
3=−=− (d)
16
112
16
43
16
21
16
64
16
514 ==−=−
Exercises 2-1 Working with Fractions A.
1. 3
7
3
12 = 3.
8
67
8
38 = 5.
8
23
8
72 =
7. 3
8
3
22 = 9.
6
29
6
54 =
B.
1. 2
18
2
17= 3.
8
31
8
11= 5.
2
11
2
3=
7. 3
216
6
416
6
100== 9.
2
12
22
162
32
80==
C.
1. 4
3
16
12= 3.
8
3
16
6= 5.
5
2
10
4= 7.
5
4
30
24=
16
9. 4
14
12
34 = 11.
32
21
64
42= 13.
12
5
36
15= 15.
12
19
24
38=
D.
1. 16
14
8
7= 3.
64
8
8
1= 5.
16
20
4
5
4
11 ==
7. 10
36
5
18
5
33 == 9.
3
5
3
21
60
401 == 11.
16
42
8
21
8
52 ==
E.
1. 5
3;
35
20
7
4,
35
21
5
3== is larger
3. 2
11;
14
61
7
31,
14
71
2
11 == is larger
5. 8
7;
24
20
6
5,
,24
21
8
7== is larger
7. 4
6;
20
30
4
6,
20
28
5
7
5
21 === is larger
9. 5
13;
10
25
2
5,
10
26
5
13== is larger
11. 12
5;
24
10
12
5,
24
9
8
3== is larger
F.
1. 4
315
8
615 = in.
3. 920,10
125,34
8
25,
920,10
216,34
15
47,
920,10
580,34
6
19,
920,10
320,34
7
22====
6
19;
10,920
34,440
13
41= is largest approximation;
8
25 is smallest approximation.
5. in.; 32
28 in.
8
7= it is not possible to have an inner diameter of in.
32
29
7. 5
3
15
9,9615 ==− will remain
9. 5
1
60
12= fertilizer in final mixture
17
11. 3 24 11 22= =
4 32 16 32
Try 23
32 in.
Exercises 2-2 Multiplication of Fractions A.
1. 8
1
4
1
2
1=× 3.
15
2
36
1
5
42
=× 5. 3
22
3
813
39
8==×
7. 9
11
9
10
312
5
3
82
==× 9. 2
12
2
5
39
155
28
1241
==×
11. 3
13
21
12
93
3
2
2
14 =×=× 13.
4
13
4
13
2
31
26
13
2
11
6
12 ==×=×
15. 69315
15
2315
5
34 =×=× 17. 74
117
37
1
342
17
3234 =×=×
19. 8
310
8
83
8
71
17
83
8
7
7
611 ==×=× 21.
8
1
2
1
2
1
2
1=××
23. 15
1
5
21
3
21
124
1=×× 25. 22
12
31
13
21
=××
B.
1. 6
1
3
1
2
1=× 3.
2
1
24
31
13
21
=×
18
5. 4
3
2
3
2
1
2
11
2
1=×=× 7.
16
51
16
21
210
21
8
51
10
12
8
5==×=×
9. 1
14
31
13
41
=× 11. 20
11
20
21
5
63
48
7
5
11
8
7==×=×
13. 8
52
8
2136
816
7==× 15. 1
13
81
18
31
3
22
8
3=×=×
C.
1. in. 4
3137
4
551
48
291938
8
5338 ==×=× 3. ft
3
211
3
35728
312
5==×
5. in 21
1 ft 14 or in., 21
1692
33936
2
4113
641
28 ==×=× .
7. 21
3182
6371
14
7
2
491
1443
22 ==×=× mi
9. lb 21
3562
713
1
323
2
93
31
32
721
46 ==×=×
11. in.109
201
18 =× 13. in. 43
943913
26
4
83
==×
15. min 4
334845
4
3303
4
215,1
4
2745
4
3645 =+==×=×
17. hr3
210
3
323264
36
1==× 19.
5
25
5
27
5
4
1
1
4
27
5
4
4
36 ==×=× in.
19
21. 2
122
2
45
2
4
1536
4
336 ==×=× picas
23. 8
131
8
1427
8
33
14
9312
8
311
4
1212 =+=+×=×+× in.
25. 4
13
4
13
4
8
11326 ==× in. 27.
32
15
16
3
2
5
16
3
2
12 =×=× in.
29. pounds41
9437
1
2
1
4
837
285
4 ==×=×
31. in.8
73
8
31
4
1
2
31
4
1
2
115 ==×=×
Exercises 2-3 Division of Fractions A.
1. 3
21
3
5
1
21
36
5
2
1
6
5==×=÷ 3.
16
5
4
31
412
5
3
4
12
5=×=÷
5. 2
1
13
41
2416
621
4
3
16
6=×=÷ 7.
4
1
26
81
216
31
8
6
16
3=×=÷
9. 91
63
12
3
6
1
2
3
6
1
2
11 =×=÷=÷
11. 3
11
3
4
333
142
17
222
14
33
7
22
14
52
7
13 ==×=÷=÷
13. 5
11
5
6
116
3
5
322
3
16
5
32
3
15
5
26 ==×=÷=÷
20
15. 161
28
2
18 =×=÷ 17. 18
12
3612
3
212 =×=÷
19. 2
17
2
15
2
35
3
25 ==×=÷ 21.
6
5
3
81
216
5
8
3
16
5=×=÷
23. 8
1
17
41
832
71
4
7
32
7
4
31
23
7=×=÷=÷
B.
1. 81
24
2
14 =×=÷ ft 3.
137
86222
8
37222
8
54222 ×=÷=÷ = 48 boards
5. 1
242
2
14 ×=÷ = 84 pieces
7.
1
21
8
2
1
4
189
9
821
4189
85
241
47 ×=÷=÷ = 18 courses of brick
9. 5
26
5
32
525
4840
4
2540
4
1640 ==×=÷=÷ = 6 × 35 = 210 pieces
11. ;14
17
14
99
7
21
24
99
2
7
4
99
2
13
4
324 ==×=÷=÷ 7 full sheets can be cut
13. 1
189
12
5
18
1
2
12 ×=÷ = 45 threads
15. 1061
2 sq ft ÷
3
8 = ×
71 4
213 8
2 3
1 1
sq ft = 284 sq ft
21
17. 81
1
7
2
1
8
16
7
1
27
167
21
3167
=×=÷=÷ in. per year
19.
1
3
16
2
1
8
9
3
163
81
1 ×=÷ = 6 washers
Exercises 2-4 Addition and Subtraction of Fractions A.
1. 4
1
16
4
16
3
16
1==+ 3.
4
3
16
12
16
7
16
5==+
5. 2
1
4
2
4
1
4
3==− 7.
5
2
5
1
5
3=−
9. 16
15
16
7
16
3
16
5=++ 11.
2
11
8
41
8
12
8
3
8
15
8
3
8
71 ===−=−
13. 4
3
4
2
4
1
2
1
4
1=+=+ 15.
24
17
24
2
24
15
12
1
8
5=+=+
17. 8
1
8
3
8
4
8
3
2
1=−=− 19.
16
7
16
8
16
15
2
1
16
15=−=−
21. 40
29
40
5
40
24
8
1
5
3=+=+ 23.
40
19
40
16
40
35
5
2
8
7=−=−
25. 8
5
8
1
8
6
8
1
8
2
8
4
8
1
4
1
2
1=−=−+=−+
27. 4
31
4
7
4
1
4
6
4
1
2
3
4
1
2
11 ==+=+=+
29. 8
14
8
33
8
13
8
20
8
13
2
5
8
51
2
12 ==+=+=+
31. 15
83
15
53
15
18
15
35
5
6
3
7
5
1
3
12 ==+=+=+
33. 8
32
8
19
8
14
8
33
4
7
8
33
4
31
8
14 ==−=−=−
35. 60
71
60
67
60
125
60
192
12
25
5
16
12
12
5
13 ==−=−=−
22
B.
1. 8
15
8
41
8
23
8
64
8
72
1
8==−=−
3. 16
132
16
45
16
13
16
58
16
13
8
29
16
13
8
53 ==−=−=−
5. 8
7
8
1
8
2
8
4
8
1
4
1
2
1=++=++
7. 81
2817
810
827
810
820
87
45
25
87
==−=−+=−+
9. 16
112
16
43
16
35
16
78
16
35
8
39
16
32
8
74 ==−=−=−
11. 10
93
10
39
10
26
10
65
5
13
2
13
5
32
2
16 ==−=−=−
C.
1. 1 5 3 1 1 5+ + 5 + + 1 + in.
4 8 4 2 4 8
= 2 5 46 4 10 5 72+ + + + + in. =
8 8 8 8 8 8 8 in. = 9 in.
3. = =3 3 11 6 5
46 - 34 in. 45 - 34 in. 11 in.8 4 8 8 8
5. 16
91
16
25
16
4
16
21
8
2
16
51 ==+=+ in.
7. 4
125
4
9235
4
34
4
13
4
35
4
265
4
34
4
13
4
35
2
16 =+=++++=++++ ci
9. 8
11
16
21
16
18
16
6
16
24
16
6
2
3
16
6
2
11 ===−=−=− in.
11. 16
3721
16
8
16
102
16
96
16
48
16
65
2
1
8
52
16
96
4
18
8
35 =++++=++++
= 21 + 2165
165
23= in.
13. 16
1315
16
1018
16
2
16
76
16
49
16
1018
16
2
16
76
4
19
8
518 −=
++−=
++−
1645
16253
16298
=−= in. remain
23
15. in.83
in.8807
in.8810
in.8807
in.4405
in.87
10041
101 =−=−=−
17. 4
37
4
31
4
2
4
33
2
1
4
18 ==−=− in.;
2
16
4
1
4
36 =− in.
Finished size is 4
37 in. ×
2
16 in.
19. 16
9
16
62
16
152
8
32
16
152 =−=− in.
21. − = − =5 7 40 7 33
4 in. in. 4 in. in. 48 64 64 64 64
in.
23. 1 1 21 9 21 18 3
5 qt - 4 qt = - = - = qt4 2 4 2 4 4 4
25. 313
327
31
49 −=−
= 314
= 32
4 cu yd remaining in the truck
Problem Set 2 A.
1. 8
9
8
11 = 3.
3
5
3
21 = 5.
32
99
32
33 =
7. 8
13
8
51 = 9.
2
12
4
22
4
10== 11.
3
18
3
25=
13. 16
91
16
25= 15.
4
38
4
35= 17.
16
3
1632
63
=
19. 8
3
832
123
= 21. 6
1
630
51
= 23. 5
41
20
161 =
25. 12
9
4
3= 27.
16
44
4
11
4
32 == 29.
12
68
3
17
3
25 ==
31. 12
15
4
5
4
11 == 33.
16
7;
240
32
15
2,
240
105
16
7== is larger
24
35. 8
7;
16
14
8
7,
16
13= is larger 37.
5
3;
160
96
5
3,
160
65
32
13== is larger
39. 4
7;
16
121
4
31,
16
71 = is larger
B.
1. 32
3
16
3
2
1=× 3.
12
7
3
41
416
7=×
5. 4
11
4
5
26
5
2
31
6
5
2
11 ==×=× 7.
64
5
412
5
16
31
=×
9. 2
17
2
15510
24
3==× 11. 27
1
23
9
118
21
118 =×=×
13. 3
211
3
35
18
35
3
81
8
34
3
22 ==×=× 15. 2
1
42
12
1
4
1
2
1=×=÷
17. 3218
14
81
4 =×=÷ 19. 6
1
24
1
3
21
43
2=×=÷
21. 10
7
5
1
2
75
2
13 =×=÷
23. 9
42
9
22
9
82
14
11
8
9
4
11
8
11
4
32 ==×=÷=÷
C.
1. 4
11
8
21
8
10
8
7
8
3===+ 3.
32
7
32
4
32
3
8
1
32
3=+=+
25
5. 30
131
30
43
30
25
30
18
6
5
5
3==+=+ 7.
8
3
16
6
16
3
16
9==−
9. 16
7
16
4
16
11
4
1
16
11=−=− 11.
40
23
40
12
40
35
10
3
8
7=−=−
13. 8
33
8
27
8
10
8
17
4
5
8
17
4
11
8
12 ==+=+=+
15. 2
14
2
9
2
3
2
12
2
3
1
6
2
116 ==−=−=−
17. 24
191
24
43
24
45
24
88
8
15
3
11
8
71
3
23 ==−=−=−
19. 30
11
30
31
30
6
30
10
30
15
5
1
3
1
2
1==++=++
21. 6
11
6
7
6
14
6
21
3
7
2
7
3
12
2
13 ==−=−=−
23. 5
2
5
8
5
10
5
82
5
312 =−=−=−
D.
1. 8
137
8
297
8
182
8
68
8
47
4
91
2
17
8
47
4
322
2
18
8
75 ==++=++=++ in.
3. Shortest: −3 1
22 in.8
16
= − =5
22 2216
6 116 16
in.
Longest: 3 1
22 + in.8
16
= + =22 in. 226 1 716 16 16
in.
5. 32
25
32
31
32
281
32
31
8
71 =−=− in. difference
7. 5
34
15
94
15
69
15
2
2
69
2
15
2
69
2
17
2
134 ===×=÷=÷ cu ft
9. 8
731
2
125
16
139
8
317
4
18 ++++
16
1431
16
825
16
139
16
617
16
48 ++++=
1613
921613
2901645
90 =+== in.
11. 16
15
16
3
16
12
16
3
4
3=+=+ in.
26
13. Radius #1 = 3235
1635
21
163
221
=×=×
Radius #2 = 32
18
16
9
8
9
2
1
8
11
2
1==×=×
32
34
32
131
32
53
32
184
32
35
32
18
4
23==−=−− in.
15. 2
1244
2
113231
2
113
14
33728
2
127
4
1828 =+=+×=×+× in.
17. 16
17
2
1
8
172
8
12
8
12
8
24
8
12
4
14 =×=÷=−=−
16
11= in. margin on each side width−wise
21
811
283
181
484
581
421
5 ×=÷=−=−
= 16
11 in. margin on each side length-wise
19. 16
35
16
83
8
1
2
838 in.
2
141
2
1446
4
12246 ==×=÷=−=×− in.
21. ÷ ×
1 118 rev in.7 in. min rev162
÷ × = =
15 9 in. 15 8 min 60 2 in. = in. min = 6 min
2 8 min 2 9 in. 9 3
23. in.21
2in.25
in.85
4 ==×
25. in.329
163
23
in.163
21
1 =×=×
27. tablets225415
60in.43
360 =×=×
29. in.81
189
86
83
43
83
==+=+
The 1-in. screw is the longest one less than this.
27
31. (a)
+++
31
15232
2221
841
10
346
12
128
22126
8123
10 ×+++=
392
12272
12102
12123
+++=
12368
12272
12102
12123
+++=
ft121
7212865
==
(b) ftsq86512865
112
=×
(c) 865 × $6 = $5190
209
CHAPTER 2 FRACTIONS
Preview 2
2. (a) 256
35
32
5
8
7=× (b) 3
1
3
13
21
12
93
3
2
2
14 ==×=×
(c) 5
3 of
10
9
2
3
5
3
2
11 =×= (d)
2
11
2
3
1
21
24
3
2
1
4
3==×=÷
(e) 10
32
10
23
5
41
28
23
4
5
8
23
4
11
8
72 ==×=÷=÷
(f) 4 ÷ 1
8
1
2
1
4
2
1=×= = 8
4. + + = + + = = =3 5 5 12 5 5 22 11 3
1 in.4 16 16 16 16 16 16 8 8
Exercises 2-1 Working with Fractions A.
2. 2
15
2
17 = 4.
16
17
16
11 = 6. 2 =
1
2
8. 64
259
64
34 = 10.
16
29
16
131 =
B.
2. 53
158
= 4. 2
12
16
82
16
40== 6.
3
23
3
11=
8. 3
11
3
4= 10.
2
12
2
5=
210
C.
2. 3
2
6
4= 4.
2
9
4
18= 6.
6
7
30
35= 8.
2
5
4
10=
10. 16
17
32
34= 12.
72
3510
= 14. 2
5
18
45=
D.
2. 16
12
4
3= 4.
64
24
8
3= 6.
3292
823
87
2 ==
8. 32
34
16
11 = 10. 4 =
6
24 12.
1234
617
65
2 ==
E.
2. 8
13;
8
13,
8
12
2
3= is larger 4.
16
13;
16
13,
16
12
4
3= is larger
6. 2
12;
8
32
8
111,
8
42
2
12 == is larger
8. 60
25;
240
100
60
25,
240
45
16
3== is larger
10. 4
72;
4
33
4
72,
4
23
2
13 == is larger
12. 5
11;
35
40
7
8,
35
42
5
6
5
11 === is larger
F.
2. 10 × 150 + 6 × 100 = 1,500 + 600 = 2,100 4
3
2800
2100= of the old load
4. 64
13;
64
13,
64
12
16
3= in. fastener is thickest
6. 3
22
3
8
9
24== in. between rivets 8.
2
11
2
3
40
60== times faster
10. pitch = 12
3
672
618
run
rise=
÷÷
=
211
12. (a) 165
4815
= (b) 103
4012
= (c) Girls: 8025
165
=
Boys: 8024
103
=
The fraction of overweight Girls is higher.
Exercises 2-2 Multiplication of Fractions A.
2. 15
4
3
2
5
2=× 4.
12
136 × = 3 6.
45
11
15
41
312
11=×
8. 16
13
214
13
8
71
=× 10.
12
497
17
42
× = 14 12. 8
13
426
3
116 =×=×
14. 21
11
21
22
315
22
7
51
15
71
7
5==×=×
16. 4
335
4
143
210
3311
26
6513
10
33
6
510 ==×=×
18. 8
79
8
79
4
51
210
79
4
11
10
97 ==×=× 20. 18 ×
3
121
3
64
327
32
1
182
27
51 ==×=
22. 10
3
24
1
13
21
5
93
4
1
3
2
5
41 =××=××
24. 3
11
3
4
39
84
15
31
12
51
9
8
5
3
2
12 ==××=××
B.
2. 32
3
8
3
4
1=× 4.
16
7
2
1
8
7=×
212
6. 16
15
4
5
4
3
4
11
4
3=×=× 8.
9
72
9
25
3
5
3
5
3
21
3
5==×=×
10. 10
7
26
7
5
31
6
11
5
3=×=× 12.
5
22
5
124
5
3==×
14. 14
5
7
81
216
5
7
11
16
5=×=× 16.
2
11
2
3
15
81
216
153
5
31
16
15==×=×
C.
2. 4
399
4
399714
48
5714
8
17 ==×=× in.
4. 16
54
16
69
4
3
4
23
4
3
4
35 ==×=× in.
6. 12 × 4
1110
4
441
416
147312
16
39 ==×= in.
8. 4
336
4
14736
48
496
8
16 ==×=× in.
10. 28
14
598
4
314 ×=× = 118 in. 12. 48 ×
18
35648
8
34 ×= = 210 in.
14. 64
41431
64
27625
4
17
8
65
2
25
4
14
8
18
2
112 ==××=×× cu in.
16. 77231
13
13231
3
14 ×=× = 1001 cu in. 18. 36 ×
12
71836
2
13 ×= = 126 in.
20. 1020
312
128
132012
8
51 ××=×× = 390 lb 22.
832
14
3× = 24 MGD
24. 6
1,72360
5
1,45360
8
1°=×°=× × 360 = 60°
213
26. 2
12
2
5
216
518 ==× in.
28. × = ×1201 7
3 240 2402 2
1
= 840 mg
30. hours11292
1
43
1
12
3
243
12 =+=+×=+×
32. 648
324
162
81
===
The only choice smaller than this is 645in.
Exercises 2-3 Division of Fractions A.
2. 6 ÷
1
233
632
×= = 9 4. 8 ÷ 14
841
×= = 32
6. 1
21
12
1
2
1
2
1×=÷ = 1 8.
52
2512
5
16
4
1
43
165
43
==×=÷
10. 6 ÷ 4
13
226
2
36
2
11 =×=÷= 12.
4
31
4
7
2
1
2
72
2
72
2
13 ==×=÷=÷
14. 10 ÷ 3
18
3
25
36
5510
5
610
5
11 ==×=÷=
16. 9
1
36
1
3
21
63
2=×=÷ 18.
7
6
7
82
14
3
8
7
4
3=×=÷
214
20. 5
3
5
21
12
3
2
5
2
3
2
12
2
11 =×=÷=÷ 22.
8
7
2
31
412
7
3
2
12
7=×=÷
24. 3
11
3
4
15
4
3
51
4
5
3
5
4
11
3
21 ==×=÷=÷
B.
2. 1
41
12
7
4
1
2
7
4
1
2
13 ×=÷=÷ = 14 ft
4. 8
37
24
97
24
177
12
1
2
17712
2
17712
2
188 ===×=÷=÷ ft long per column
22 ÷ 59
582
59
176
59
822
8
5922
8
37 ==×=÷= , not enough for 3 columns
Each piece gives 2 supporting columns. Six pieces give 12 supporting columns.
6. 2
140
1
41
28
81
4
1
8
81
4
1
8
110 =×=÷=÷ ft
8.
121
8121
8
2121
8
5221 ×=÷=÷ = 8 lengths of pipe
10. 1
81
18
29
8
1
8
53 ×=÷ = 29 ft
1
82
14
17
8
1
4
17
8
1
4
14 ×=÷=÷ = 34 ft
Dimensions are 29 ft × 34 ft.
12. 1
324
18
27
32
1
8
33 ×=× = 108 rev
215
14. 1
4
2
1
27
41
27
41
21
3 ×=÷=÷ = 14 ft
ft 21
181
4
1
2
837
41
837
41
85
4 =×=÷=÷
Dimensions are 14 ft × 2
118 ft.
16.
532
8 ÷ 3 =
131
8261
87
× = 887
= 7
108 in.
18. turns41
1or45
1
8
1
4
325
81
325
=×=÷
20. 57 in. - 3621 in. = 20
21 in.
yearperin.185
21841
91
241
19
241
921
20 ==×=÷=÷
Exercises 2-4 Addition and Subtraction of Fractions A.
2. 31
1124
11216
1211
125
===+ 4. 6
5
6
3
6
2=+
6. 8
5
16
10
16
3
16
13==− 8.
4
1
12
3
12
2
12
5==−
10. 8
31
8
11
8
7
8
3
8
1==++ 12.
4
12
16
42
16
51
16
93 ==−
14. 16
13
16
6
16
7
8
3
16
7=+=+ 16.
48
29
48
9
48
20
16
3
12
5=+=+
18. 32
7
32
3
32
10
32
3
16
5=−=− 20.
32
13
32
1
32
14
32
1
16
7=−=−
22. 15
71
15
22
15
12
15
10
5
4
3
2==+=+ 24.
36
7
36
9
36
16
4
1
9
4=−=−
216
26. 4811
4816
4827
4816
486
4833
31
81
1611
=−=−−=−−
28. 163
31651
1612
1639
1612
167
243
167
2 ==+=+=+
30. 20
73
160
563
160
161
160
402
10
11
32
82 ==+=+
32. 8
12
8
17
8
2
8
15
4
1
8
71 ==+=+
34. 3
23
12
83
12
44
12
25
12
69
12
25
4
23
12
12
4
35 ===−=−=−
36. 15
142
15
44
15
36
15
80
5
12
3
16
5
22
3
15 ==−=−=−
B.
2. 1613
11629
1619
1648
163
113
==−=−
4. 60
171
60
77
60
12
60
15
60
20
60
30
5
1
4
1
3
1
2
1==+++=+++
6. 8
320
8
163
8
65
8
46
8
52
8
65
4
23
2
13
8
18
4
35
2
16 ==++=++=++
8. 83
3827
811
838
811
419
83
143
4 ==−=−=−
10. 12
55
12
65
12
15
12
80
4
5
3
20
4
11
3
26 ==−=−=−
12. 56
15
56
105
56
120
8
15
7
15
8
71
7
81 =−=−=−
C.
2. 16
13
16
3
16
10
16
3
8
5=+=+ in. 4.
16
3
16
6
16
9
8
3
16
9=−=− in.
32
3
16
3
2
1=⋅ in.
6. 16
15
16
4
16
1
16
10
4
1
16
1
8
5=++=++ in.
217
8. 14 ft − +
3 1 1 12 ft 4 ft + 3 ft + 1 ft4 8 2 4
= 14 ft − +
12 ft 4 ft + 3 ft + 1 ft
8
6 4 28 8 8
= 14 ft − 5
118 ft =
8112
ft − 893
ft = 819
ft
= 3
28 ft
10. 32
40
32
78
32
37
32
100
4
5
16
39
32
37
8
25
4
11
16
72
32
51
8
13 +++=+++=+++
32
317
32
255== in.
12. 8
51
8
13
8
39
8
52
8
39
2
13
8
74
2
16 ==−=−=− in.
14. 87
2823
86
812
85
43
23
85
43
21
185
==++=++=++ rolls
He does not have enough.
16. 4
323
4
95
4
7
4
18
4
120
4
31
2
1430 ==−−=−− in. for drawers
18. 420
415
43
42
43
343
21
=++=++ = 5 in.
20. 1 3 1 5 1 1" + " + " + " + + "
8 8 8 16 16 8 =
2 6 2 5 1 2" + " + " + " + " + "
16 16 16 16 16 16
= "1618
= "89
= 1
1 "8
22. 17 in. − 3
74 in. =
468
in. − 431
in. = 437
in. = 1
94 in.
24. 2 in. - 41
1 in. = 43 in. penetration into the second piece.
Problem Set 2 A.
2. 5
21
5
14 = 4.
16
35
16
32 = 6.
16
33
16
12 = 8.
16
55
16
73 =
10. =192
2
19 12.
8
11
8
9= 14.
16
51
16
21= 16.
3
12
3
7=
218
18. 4
1
32
8= 20.
4
3
24
18= 22.
7
41
21
121 = 24.
5
23
25
103 =
26. 64
28
16
7= 28.
3244
811
83
1 == 30. 1018
514
54
1 == 32. 1026
513
53
2 ==
34. 3
2;
21
12
7
4,
21
14
3
2== is larger 36.
4
11;
12
14
6
7,
12
15
4
11 == is larger
38. 10
2;
80
15
16
3,
80
16
10
2== is larger
40. 9
1;
288
32
9
1,
288
27
32
3== is larger
B.
2. 2
1
13
21
24
31
=× 4. 256
5
412
1
64
155
=×
6. 80
49
5
1
16
49
5
1
16
13 =×=× 8.
4
15
4
21
48
3714 ==×
10. 3
2
3
42
12
1
3
11
2
1=×=× 12. 34
18
17216
8
1216 ==×
14. 2
17
2
15
15
123
28
255
5
22
8
13 ==×=× 16.
5
4
1
2
5
2
2
1
5
2=×=÷
18. 3
210
3
32
3
4
1
8
4
38 ==×=÷ 20.
4
3
2
1
2
32
2
11 =×=÷
22. 6
5
3
21
24
5
2
3
4
5
2
11
4
11 =×=÷=÷
24. 15
131
15
28
312
7
5
164
7
12
5
16
7
51
5
13 ==×=÷=÷
219
C.
2. 4
11
4
5
4
3
4
2
4
3
2
1==+=+ 4.
8
51
8
13
8
10
8
3
4
5
8
3
4
11
8
3==+=+=+
6. 40
29
40
4
40
25
10
1
8
5=+=+ 8.
8
3
8
4
8
7
2
1
8
7=−=−
10. 30
19
30
6
30
25
5
1
6
5=−=−
12. 32
131
32
45
32
3
32
48
32
3
2
3
32
3
2
11 ==−=−=−
14. 16
72
16
39
16
13
16
26
16
13
8
13
16
13
8
51 ==+=+=+
16. 3 − 8
11
8
9
8
15
8
24
8
15
1
3
8
71 ==−=−=
18. 12
51
12
17
12
10
12
27
6
5
4
9
6
5
4
12 ==−=−=−
20. 20
193
20
79
20
24
20
25
20
30
5
6
4
5
2
3
5
11
4
11
2
11 ==++=++=++
22. 3
11
15
51
15
20
15
19
15
39
15
19
5
13
15
41
5
32 ===−=−=−
24. 3
13
6
23
6
20
6
9
6
29
2
3
6
29
2
11
6
54 ===−=−=−
D.
2. 2
110
16
3
16
510 =+ in. are needed for each piece
21480
212
240221
1240
=×=÷ = 2276 or 22 pieces
4. − = −1 7 2 7
64 in. 62 in. 64 in. 62 in.4 8 8 8
=
in. 83
1 in. 811 in.
8503
-in. 8514
==
220
6. 32
1314
32
3
32
1014
32
3
16
514 =+=+
in.3227
1032347
32461
32808
32461
4101
3213
1441
25 ==−=−=−
Yes, a bar 8
310 in. can be cut from the remainder.
8. 16
1515
16
67
16
53
16
45
8
37
16
53
4
15 =++=++ in.
10. 432
18
3932
8
74 ×=× = 156 in. = 13 ft
12. A = 16
112
16
43
16
23
16
66
16
23
8
33
16
71
8
14 ==−=−=− in.
B =
++−=
++−
32
62
32
52
32
44
8
510
16
32
32
52
8
14
8
510
= 32
52
32
158
32
2010
32
158
8
510 =−=− in.
C = 32
96
32
52
32
44
32
52
8
14 =+=+ in.
D = 16
78
16
32
16
1010
16
32
8
510 =−=− in.
14. 8
321
8
171
8
16
8
15525
8
314
2
15
8
73 ==+=+×=
×+
× in.
16. 7 pieces 8
4368
2
1092712
2
13==×× in.
4 pieces 8
11121394
4
139==× in.
9 pieces 8
13959
8
155=× in.
Total 83
7 ft 71 or in. 83
8598
68758
13958
11128
4368==++ in.
18. Total margin = 11 − 2
11
2
19 =
Top margin = 10
6
2
3
5
2=× in. =
5
3 in.
Bottom margin = 10
9
2
3
5
3=× in.
221
20. Longest = + = + = =3 1 195 2 197 5
24 248 4 8 8 8 8
in.
Shortest = − = − = =3 1 195 2 193 1
24 248 4 8 8 8 8
in.
22. Total allowance = 3 × 16
15
16
5= in.
Each seam = 32
15
16
15
2
1=× in. allowance
24. + + = + +
= + + =
7 1 1 7 5 11
8 4 2 8 4 27 10 4 21 5
or 2 in.8 8 8 8 8
26. × = × = =1 1 1 13 13 5
3 1 in.2 4 2 4 8 8
28. in.241
18
41
8 =×=×
30. in.21
3216
3210
326
165
323
323
==+=++
