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1. 7 20 7 24
Solutions Manual for Business Math 10th Edition by Cleaves
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Chapter 2 Review of Fractions
Section Exercises
2-1, p. 49
1. proper 2. improper 3. improper 4. proper 5. proper 6. improper
7. 15
7 12
7
5
1,300 13
8. 1 1
20 21
20
1
3
9. 1
18 18
18
1,500
10. 23
7 17
14
3
3 1
11. 2
8 16
16
12. 3
16
16 387
32
67
64
3
13.
1,000
=
10
= 1
10
phones per person
25
14.
1,000
=
2
= 1
2
phones per person
137 7
15. (4 * 6) + 1 = 25;
4
19
16. (5 * 27) + 2 = (135) + 2 = 137;
13
17. (3 * 2) + 1 = 7;
5 3
20
18. (5 * 3) + 4 = 19; 19. (8 * 1) + 5 = 13;
5 8
20. (3 * 6) + 2 = 20;
3
21.
12 , 3 4
15 , 3
=
5
18 , 18 1
22.
12 , 4 3
20 , 4
=
5
24 , 12 2
23.
20 , 4 5
24 , 4
=
6
13 , 13 1
24.
36 , 18
=
2
25.
36 , 12
=
3
26.
39 , 13
=
3
27.
400 million
9,000 million
2
=
45
28.
4,000 million 1
24,000 million
=
6
29. 1 R15 1 R6 2 R3 2 R0 2
21
GCD = 3
21 , 3 7
36
=
36 , 3
=
12

2. 21 36 15 21 6 15 3 6 3 6
21 15 12 6 6
15 6 3 0 0
30. 1 R9 1 R6 1 R3 2 R0
15 24 9 15 6 9 3 6
GCD
15 9 6 6
9 6 3 0
15 15 , 3 5
= 3
24
=
24 , 3
=
8
31. 2 R12
18 48
1 R6
12 18
2 R0
6 12 18
GCD = 6
18 , 6 3
36 12 12
12 6 0
48
=
48 , 6
=
8
32. 2 R10
15 40
1 R5
10 15
2 R0
5 10 15
GCD = 5
15 , 5 3
30 10 10
10 5 0
40
=
40 , 5
=
8
33.
2 3 * 2 6 4 4 * 4 16 4 3 * 4 12
8 16 8 * 2
=
16
34.
5 20 5 * 4
=
20
35.
8 32 8 * 4
=
32
36.
3 5 * 3 15 5 1 * 5 5 3 3 * 3 9
9 27 9 * 3
=
27
37.
3 15 3 * 5
=
15
38.
5 15 5 * 3
=
15

3. 2-2, p. 57
1 7
1. 2.
9 8
2 5
5 25
3.
6
=
30
7 14
9
+
8
5 12 4 1
+
15
= +
30
39 9 3
+
9
8
9
8
= 1
8
= 1
2 30
= 1
30
= 1
10
5 15
4.
8
=
24
7 14
5. 4
5 10
6
= 4
12
1 6
5
6. 23
12
7
20
= 23
48
21
+
12
= +
24
29 5
+7
2
= +7
12
16 4 1
+48
16
= +48
48
41
5
7. 51
18
9
24
= 1
24
20
= 51
72
27
7
8. 5
12
1
11 = 12 = 12
12 12 3
7
= 5
12
3
71
48
7 21
9.
8
=
24
3 3
+86
24
= +86
72
3 = 3
4 12
2 = 2
24 24
47
137
2
+2 = +2
8 1
+6 = +6
4
5
10. 3
9
1
5
72
20
= 3
36
3
= 5
3
7
11.
8
3
-
12
18
10
12
6
= 11
12
1
= 11
2
12.
6
8
9
2
-
24
28
8
24
4
= 9
24
1
= 9
6
12 36 8 9
2 24 4 1 6 2+2
3
= +2
36
47
10
36
11
= 11
36
8
=
2 9
=
3
13.
3 21
4
=
28
5 20
2
14. 9
3
1
4
= 9
6
3
9
15. 15 = 14
9
7 7
-
7
= -
28
1
28
-6
2
= -6
6
1
3
6
-12
9
= -12
9
2
2
9
3
16. 21
5
6
= 21
10
16
= 20
10
8
17. 15
15
32
= 15
60
1
18. 23
8
3
= 23
24
27
= 22
24
7 7 7 5 25 7 14 14

4. 3
-12
10
= -12
10
= -12
10
9
8
10
19. 8 1
-7
12
= -7
60
7
8
60
1 6
20. 12 = 11
-
12
= -
24
= -
24
13
22
24
3 3 5
21. 11 + 11 + 18 =
3
-5
5 5 4 4 8
4 4 6 6 5 17
1 -7
5
= -7
5
3
2
11 + 11 + 18 = 40 =
8 8 8 8
1
4 42
5 8
yards

5. 3
22. 42
8
3
5
+ 37
8
5
3
+ 12
8
3
3
+ 23
4
=
6
3
23. 10
4
5
3
+ 10
4
1
5
+ 12
8
1
5
+ 12
8
5
+ 12
8
42
8
+ 37
8
17
+ 12
8
1
+ 23
8
= +12
8
6
+ 8
2
+ 8
2
=
6 5 5 5
114
8
= 116
8
feet 10
8
+ 10
8
+ 12
8
+ 12
8
+ 12
8
5 4 4 40
+12
8
+ 8
8
+ 8
8
= 84
8
= 89 feet
4
24. 4
5
4
+ 4
5
4
+ 4
5
3
+ 7
8
3
+ 7
8
=
1
25. 45 - 42
8
8
= 44
8
1
- 42
8
=
32 32
4
40
+ 4
40
32
+ 4
40
15
+ 7
40
15
+ 7
40
=
7
2 yards; she can use the fabric.
8
126
26
40
3
= 29
20
3
inches
4 3 1 15 5 15 10 5
26. 12 - 10
4
= 11
4
- 10
4
= 1
4
feet 27. 13
16
- 12
8
= 13
16
- 12
16
= 1
16
feet
1 5
14
8
- 12
8
5
9
= 13
8
8
5
- 12
8
5
4
= 1
8
3
1
= 1
2
feet
14 - 12
8
= 13
8
- 12
8
= 1
8
feet
3
28. 8
4
3
+ 8
4
1
6
= 16
4
2
2
= 17
4
1
1
= 17
2
1
13 5
13
16
- 12
8
13
= 13
16
10
- 12
16
3
= 1
16
feet
36 - 17
2
= 35
2
- 17
2
= 18
2
inches
2-3, p. 64
1 3
3 4
1.
8
*
5
2
12
5.
7
3
=
10
5
2.
7
*
5
6.
3
1 5
6
=
42
23 35
3.
4
*
9
1
7.
9
805
=
36
13
= 22
36
3 24
4.
8
*
1
= 9
1
1
8.
12
4
9. 5
7
39 7
=
7
;
39
3
10. 3
8
27 8
=
8
;
27
11.
5 3 5
8
,
4
=
8
2
1
4 5
*
3
=
6
12.
3 9
5
,
10
1 2
3 10 2
=
5
*
9
=
3
1 3
2
13. 2
5
1 12
, 1
7
=
5
3
8 12
,
7
=
5
7 21
*
8
=
10
2
1
= 2
10
1
14. 5
4
2 21
, 2
3
=
4
8 21
,
3
=
4
25
3 63
*
8
=
32
31
= 1
32
3 3 5 3 1 3 1 75 9 75 8 200
15.
4
, 5 =
4
,
1
=
4
*
5
=
20
16. 75 , 1
8
=
1
,
8
=
2
1
*
9
=
3
3

6. = 66
3
, or 67 sheets
3 39 200 4 800
8
3 35 40 4 32
17. 200 , 9
4
= 200 ,
4
=
20
1
*
39
=
39
18. 40 , 8
4
= 40 ,
4
4
=
1
*
35
=
7
7
= 20
39
rooms = 4
7
; 4 boxes
1 21 7
3
21 2
1
5 4 149 149 1
19. 21 , 3
2
=
1
,
2
=
1
*
7
= 6
1
20. 4 * 18
8
=
1
*
8
2
=
2
= 74
2
feet
Theoretically, 6 cabinets will exactly fit on the wall.

7. 20 , 10 2
10. =
30 , 10 3
5 * 4 20
13. =
30 , 6 5
11. =
48 , 6 8
9 * 13 117
14. =
8 * 4 32 11 * 13 143
of the employees 16. 2)4 12 16 17. 2)56 24 12 42
2)2 6 8 2)28 12 6 21
2)1 3 4 2)14 6 3 21
2)1 3 2 3) 7 3 3 21
3)1 3 1 7) 7 1 1 7
1 1 1 1 1 1 1
8
2
= =
=
3
5
1
1 4 33 33 1 1 13 2 13 1
21. 4 * 4
8
=
1
*
8
2
=
2
= 16
2
feet 22. 3 * 2 =
4 4
*
1
=
2
= 6
2
inches long
Yes, if no more than a total of 1
inch is needed for
spacing between the desks.
28 , 2 = 14 inches wide
61
inches long * 14 inches wide
Exercises Set A, p. 71
1. Examples will vary.
3 7 5
, , ,
5 9 8
100
,
301
41
; proper fractions
53
2. Examples will vary.
4 8 12
, , ,
4 5 4
132
,
89
7
; improper fractions
1
2
3. 20
3
1
4. 7 5. 8
2
6.
(6 * 5) + 5 35
6 6
7.
(3 * 4) + 1 13
3 3
8.
(3 * 33) + 1
3
100
=
3
9.
15 , 3 5
18 , 3 6
12.
15.
5 * 2
6 * 2
15
=
10
=
12
3 1
=
105 21 7
2 * 2 * 2 * 2 * 3 = 48
2 * 2 * 2 * 3 * 7 = 168
18. 2)1 5 10 6
3 4 7 2
19. + = = 1
2 2 6 10 16
20. + = + =
1
= 1
3)1 5 5 3
5)1 5 5 1
1 1 1 1
2 * 3 * 5 = 30
5 5 5 5 5 3 15 15 15 15
1
21. 7
2
3
+ 4
8
4
= 7
8
3
+ 4
8
7
= 11
8
5
22. 11
6
2
+ 8
3
5
= 11
6
4
+ 8
6
9
= 19
6
3
= 20
6
1
= 20
2
3
23. 12
8
4
5
+ 16
8
8
= 28
8
8
= 29 yards 24.
5
5 3
12
-
12
2 1
=
12
=
6
5 5
25. 7
5
1
= 7
10
5
26. 5 = 4
5
27. 4
6
1
= 4
6
2
-4
2
= -4
10 -3
2 2 -3 =-3
5
= -3
5
3 3
10 1
3 6
3 1
1
6
= 1
2

8. 28. 6 = 5
8
8
5 5
5
29.
18 30.
5 2 10
1
*
3
=
3
1
= 3
3
-3
8
= -3
8
3
2 feet
8
31.
28 1
56 9
9
*
2
1 1
8
= 28 32.
5
33. 4

9. 1. 3 15 2. 20
3
1
= = =
=
1
34. 3
4
13 4
=
4
;
13
35.
3 1 3
4
,
4
=
4
1
1
4
*
1
= 3
1
36. 7
2
15
, 2 =
2
2 15
,
1
=
2
1 15
*
2
=
4
4
3
= 3
4
1
37. 3
7
1 22
, 5
2
=
7
2
11 22
,
2
=
7
*
2 4
11
=
7
1
5 244 61 244 8 5 3 1 5 6 1 10 5 1
38. 244 , 7
8
=
1
,
8
=
1
*
61
= 32 pieces 39.
1
8
+
4
-
8
=
8
+
8
-
8
=
8
=
4
= 1
4
inches
40.
6
2 18
3
*
1
1
= 12 hours 41. 1 -
1 3
3
=
3
1 2 2
-
3
=
3
;
3
1
96
$288
*
1
= +192
Exercises Set B, p. 73
7
4
7
3. 11 77
9
4. 10
15 52
45
7
4 83
8
3
0
3
77
10 19
10
9
5.
(8 * 7) + 3 59
8 8
6.
(5 * 10) + 1 51
5 5
7.
18 , 2
20 , 2
9
=
10
8.
27 , 9 3
36 , 9 4
9.
18 , 9 2
63 , 9 7
10.
78 , 6
96 , 6
13
=
16
11.
7 * 9
9 * 9
63
=
81
12.
4 * 7
7 * 7
28
=
49
13.
8
30
=
4
of the class 14. 2)8 20 16
15 2)4 10 8
2)2 5 4
2)1 5 2
5)1 5 1
1 1 1
2 * 2 * 2 * 2 * 5 = 80
15. 2)8 9 12 24
2)4 9 6 12
2)2 9 3 6
3)1 9 3 3
3)1 3 1 1
1 1 1 1
2 * 2 * 2 * 3 * 3 = 72
16. 2)12 15
2) 6 15
3) 3 15
17.
7 1
8
+
8
8
=
8
= 1 18.
1 11
4
+
12
+
12 44
7
16
=
21 77 29
5) 1 5
1 1
2 * 2 * 3 * 5 = 60
48
+
48
+
48
=
48
= 1
48
1
19. 3
4
1
+ 2
3
5
+ 3
6
=
3
20. 5
8
1
+ 7
2
3
+ 9
4
3
= 5
8
4
+ 7
8
6
+ 9
8
3 4
3
12
+ 2
12
17 5
10
+ 3
12
=
13
= 21
8
5
= 22
8

10. 8
12
= 9
12
6 5 12 5 1 7 21
21.
7
-
14
=
14
7 1
-
14
= 22. 4
2
6
= 4
14
12
= 3
14
12
14
=
2
-3
7
= -3
14
= -3
14
9
14

11. 21
8 1 2 12
23. 12 = 11
8
24. 4 = 4 = 3
5 10 10
1 1 3 3 3
-4
8
= -4
8
7
7
8
-2 = -2 = -2
10 10 10
9
1
10
3
25. 7
4
1
3
= 7
4
2
2
40 = 39
2
1 1
27
26.
40
5
2
= 5
4
1 1
6
4
= 6
4
1 1
9
4
= 9
4
3 3
8 = 8
-37
2
= -37
2
1
2
2 hours
4 4
10
35
4
2
= 37
4
1
= 37
2
hours Maxine Ford worked
2 hours more than
George Mackie.
27.
7
*
1
=
7
= 3
7
28.
1 1 1
10
*
5
*
9
5 1 1
*
7
=
35
29. 10
2
3 6
* 1
7
=
2
*
7
1 1
= 18
2
30. 10
3
4
3 32
*
8
=
3
1
1
3 3
*
8
= 4 cakes 31.
2
1
8 1
32. 8 =
1
;
8
4
3
33. 2
8
19 8
=
8
;
19
5
3 15 4
1
34. 5
12
61 12
=
12
;
61
1 2 15
5
35. ,
6
5
1 5
8
=
6
3
8 20
*
1
=
3
2
= 6
3
36. 15 ,
4
=
1
*
3
= 20 37. 7
2
, 1
3
=
1
2
,
3
3
15 3 9 1
7
5 91 13 91 8
=
2
*
5
=
2
= 4
2
1
38. 91 , 1
8
=
1
,
8
=
1
*
13
= 56 pieces
1
1
39. 1
5
3
+ 2
4
1
+ 1
2
4
= 1
20
15
+ 2
20
10
+ 1
20
29
= 4
20
9
= 5
20
feet
1
3 16 3 13 5 8 13
40. 8 - 2
16
= 7
16
- 2
16
= 5
16
feet 41. 8 * 1
8
=
1
*
8
1
Practice Test, p. 75
= 13 feet
1 5 3 8 5
1. 2.
5 3
3. 1
5
=
5
;
8

12. 9 3
= =4.
12 , 3 4
15 , 3 5
5.
15 , 5 3
35 , 5 7
6.
21 , 3
51 , 3
7
=
17
7.
(8 * 2) + 5
8
16 + 5 21
=
8
=
8
8.
(12 * 3) + 1
12
36 + 1
=
12
37
=
12
2 3
9.
9 21
18
3
= 21

13. 1310. 4 4
5 4 1
11. - =
5 9 25
12. + =
36 61 21
+ = = 1
13 56
52
4
6 6 6 8 10 40 40 40 40
1
13.
5
*
7
=
7
14.
5
,
3
=
1 3
15. 10 , 5 =
8 10 16 6 4 2 4
2
2
5 4 10 1 21 23
, =
6
*
3
=
3
9
= 1
9 2 4
2
21 4
2
*
23
=
1
42 19
6 1 1
23
= 1
23
4
16. 56 * 32
7
= 17. 2 + 3 =
2 3
18. 137 - 89
5
=
8
56 230
3 2 5
2 + 3 = 5 5 4 1
136 - 89 = 47
1
*
7
1
= 1,840 6 6 6 5 5 5
19.
3
3
= entire load 20.
87
580
3
=
20
3 1 2 3
3
-
3
=
3
Part of the
4
truckload to be unloaded
1 1
2 3 1
3
*
4
=
2
of the truckload remains to be unloaded
1 2
1
21. 62
2
5
,
8
= 22. 5
1 1
2
% + 2
4
% =
125 5 2 1 3
2
,
8
= 5 % + 2 % = 7 %
4 4 4
25
125
2
1
4
8
*
5
= 100 sheets
1
23.
$80
$200
2
=
5
The main course cost was
2 1
of the total budget. 24. 1 *
5 4
900
36
5
=
4
*
1
225
900
36
1,125
=
36
9
= 31
36
1
1
= 31
4
The recipe for 900 cupcakes requires 31
4
cups of sugar.
Critical Thinking, p. 77
1. The two operations that require a common denominator
are addition and subtraction.
2. The number 1 can be written as any fraction that has a
21
3. The product of any number and its reciprocal is 1. Exam-
3 5
ples will vary. * = 1

14. denominator and numerator that are the same. = 1
21
4. Division requires the use of the reciprocal of a
fraction. Answers will vary. One example is:
5 3
3 8 3 15 45
7
,
15
=
7
*
8
=
56

15. 2
2
5. The parts that are known must be added. The sum of the
known parts is then subtracted from the total to give the
one unknown part. Examples will vary. The deductions
for a paycheck are: Withholding tax, $261; Credit Union,
$100; Insurance, $217; and Dues, $15. The Social Secu-
rity tax is not known. Find the Social Security tax if the
deductions total $680.
6. To find the reciprocal of a mixed number, first change
the mixed number to an improper fraction by multiply-
ing the denominator by the whole number and adding the
numerator to get the numerator of the improper fraction.
The denominator of the mixed number is the denomi-
nator of the improper fraction. Then, interchange the
numerator and denominator of the improper fraction to
make its reciprocal. 31
= 10
; reciprocal = 3
7. Two fractions are equal if the lowest terms of both fractions
are the same.
3 3 10
8. Answers will vary.
1
3 2 6 3 12 , = 12 * 2 = 24
4
7
*
2
=
14
=
7 3 12 4 16
3 3 9 6 9 3 12 ,
4
=
1
*
3
=
1
= 16
7
*
3
=
21
;
14
=
21
=
7
1
2 15 3 45 1
Therefore,
6
14
and
9
21
are equivalent or equal fractions.
15 ,
3
=
1
*
2
=
2
= 22
2
9. A whole number, like 5, divided by a proper fraction,
like 1
, means the wholes are being broken up into halves,
so you have more parts (pieces) than you started with.
5 , 1
=
5
* 2
= 10.
10. A proper fraction has a value that is less than 1 and an
improper fraction has a value that is greater than or equal
to 1.
2 1 1
11. The fraction in the minuend cannot be subtracted from
the fraction in the subtractend. The minuend must be
The division should be written as a multiplication by the
reciprocal of the divisor (second number).
rewritten so the fraction has a larger numerator. 4 1
1 4
12 = 11 +
1 5
+ = 11 9
, 2
4
=
4 4 4 4 4 9
3 3 9
,
4
=
- 7
4
- 7
4 4 4 16
2 1
4
4
= 4
2
9
*
9
=
81
Challenge Problem p. 77
1 3 51
25
2
* 32
4
=
2
131
*
4
6,681
72
19
= 92
24
6,681 1
=
8
= 835
8
square feet
Because a portion of the 93rd square yard is needed, we will
buy 93 yards and 4 additional yards for matching.
6,681 6,681 1 6,681 93 + 4 = 97
8
, 9 =
8
*
9
= square yards
72 97 * 12 = +1,164
Case Studies
2-1, p. 78
1. 21
= 5

16. 2 2
5 4 20 5 2 10 2
211 2 = 2 = 10 cups apples 2 13 cup2 = 6 = 13 cups sugar
5 1 5 1 5 1 5
2 12 2 cup = 4 = 14 cups brown sugar 2 18 tsp2 = 16 tsp salt
5 1 5 1 5 3 15 7
2 12 2 tsp = 4 = 14 tsp cinnamon 2 14 cup2 = 8 = 18 cups flour
5 1 5 5 1 5
2 14 2 tsp = 8 tsp each nutmeg/cloves 2 13 cup2 = 6 cup butter
5 2 10 5 1 5
2 11 2 tsp = 2 = 5 tsp lemon juice 2 14 cup2 = 8 cup walnuts

17. 2. 4 cups + 4 cups = 8 cups apples 2
cup + 2
cup = 11
cup sugar3
1 1 1
3 3
1 2 1
2 cup + 2 cup = 1 cup brown sugar 8 tsp + 8 tsp = 8 = 4 tsp salt
1 1 3 3 6 1
2 tsp + 2 tsp = 1 tsp cinnamon 4 cup + 4 cup = 4 = 12 cups flour
1 1 1 1 1 2
4 tsp + 4 tsp = 2 tsp each nutmeg/cloves 3 cup + 3 cup = 3 cup butter
2 tsp + 2 tsp = 4 tsp lemon juice 1
cup + 1
cup = 2
= 1
cup walnuts4 4 4 2
3. 1
cup 11
2 = 1
cup brown sugar; 1
13
2 =
3
cup for all 3 batches2 2 4
2 1 2 1
4 1 4
1 3
3 cup 12 2 = 6 = 3 cup granulated sugar; 3 11 2 = 1 cup for 3 batches
2-2, p. 79
1
1. +240,000 *
2
=
+240,000 1
1
*
2
=
+240,000
2
= +120,000 materials
1 +240,000 1 +240,000
+240,000 *
3
=
1
*
3
=
3
= +80,000 labor
+240,000 - (+120,000 + +80,000) = +40,000 profit
40,000
or
240,000
1
=
6
fraction of cost
2. 400 ft * 400 ft = 160,000 square feet.
40,000 1 5,000 1 10,000 1 80,000 1
160,000
=
4
;
160,000
=
32
;
160,000
=
16
;
160,000
=
2
3. 160,000 - (40,000 + 5,000 + 10,000 + 80,000) = 25,000 square feet
25,000 5
160,000
=
32
is the portion that remains for a water garden
Solutions Manual for Business Math 10th Edition by Cleaves
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http://downloadlink.org/p/solutions-manual-for-business-math-10th-edition-
by-cleaves/
Test Bank for Business Math 10th Edition by Cleaves
Full clear download(no error formatting) at:
http://downloadlink.org/p/test-bank-for-business-math-10th-edition-by-cleaves/
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