Test bank and solution of mathematics (1)

Chapter 2 Review of Fractions
Section Exercises
2-1, p. 49
1. proper
7.

13.

2. improper

157
7ͤ 12
7
5

8.

3. improper

1
1 20
20ͤ 21
20
1

9.

13
3
1,300
=

= 1 phones per person
1,000
10
10

4. proper

1
18ͤ 18
18

14.

10.

5. proper

2 37
7ͤ 17
14
3

11.

6. improper

2
8ͤ 16
16

12.

1,500
3
1
= = 1 phones per person
1,000
2
2

15. (4 * 6) + 1 = 25;

25
4

16. (5 * 27) + 2 = (135) + 2 = 137;

18. (5 * 3) + 4 = 19;

19
5

19. (8 * 1) + 5 = 13;

137
5

13
8

17. (3 * 2) + 1 = 7;

12 , 3
4
=
15 , 3
5

22.

12 , 4
3
=
20 , 4
5

23.

5
20 , 4
=
24 , 4
6

24.

1
18 , 18
=
36 , 18

2

25.

24 , 12
2
=
36 , 12
3

26.

13 , 13
1
=
39 , 13
3

27.

400 million
2
=
9,000 million
45

28.

4,000 million
1

=
24,000 million
6

30.

31.

32.

1 R15
21ͤ 36
21
15
1 R9
15ͤ 24
15
9

1 R6
15ͤ 21
15
6
1 R6
9ͤ 15
9
6

2 R3
6ͤ 15

12
3
1 R3
6ͤ 9
6
3

2 R0
3ͤ 6
6
0
2 R0
3ͤ 6
6
0

2
3ͤ 6
6
0

GCD = 3

GCD = 3

21
21 , 3
7
=
=

36
36 , 3
12

15
15 , 3
5
=
=
24
24 , 3
8

2 R12
18ͤ 48
36
12

1 R6
12ͤ 18
12
6

2 R0
6ͤ 12
12
0

GCD = 6

18
18 , 6
3
=
=
48
48 , 6
8

2 R10
15ͤ 40
30
10

1 R5
10ͤ 15
10
5

2 R0
5ͤ 10
10
0

GCD = 5

15
15 , 5
3
=

=
40
40 , 5
8

33.

2
8ͤ 16

3 * 2
6
=
8 * 2
16

34.

4
5ͤ 20

4 * 4
16
=
5 * 4
20

35.

4

8ͤ 32

3 * 4
12
=
8 * 4
32

36.

3
9ͤ 27

5 * 3
15
=
9 * 3
27

37.

5
3ͤ 15

1 * 5
5
=
3 * 5
15

38.

3
5ͤ 15

3 * 3
9
=
5 * 3
15

8

Chapter 2

7
3

20. (3 * 6) + 2 = 20;

21.

29.

24 163
16ͤ 387
32
67
64
3

Copyright © 2014 Pearson Education, Inc.

20
3


2-2, p. 57
1.

4.

7.

10.

13.

16.

19.

1
9
2
9
5
+
9
8

9
5
15
=
8
24
7
14
+
= +
12
24
29
5
= 1
24
24
5
20
= 51
18
72
9
27
+86
= +86
24
72
47
137

72
51

5
20
= 3
9
36
1
3
5
= 5
12
36
2
24
+2 = +2
3
36
47
11
10
= 11
36
36
3

21
3
=

4
28
5
20
- = 7
28
1
28
3
6
16
= 21
= 20
5
10
10
7
7
7
-12
= -12
= -12
10
10
10
9
8
10
21

81
3
-5
1
33

2.

7
8
5
+
8
12
4
1
= 1 = 1
8
8
2

5
10
= 4
6
12
1
6
+7 = +7
2

12
16
4
1
11
= 12
= 12
12
12
3
7
7
8. 5
= 5
12
12
1
3
3 = 3
4
12
2
8
+2 = +2
3
12
18
6
1
10

= 11
= 11
12
12
2

5. 4

11.

14.

7
8
3
8
4
1
=
8
2

2
4
= 9
3
6
1
3
-6 = -6

2
6
1
3
6
9

8
32
= 15
15
60
5
25
-7
= -7
12
60
7
8
60

17. 15

1
6
= 11
5
5
4

4
-7 = -7
5
5
2
4
5

20. 12

Copyright © 2014 Pearson Education, Inc.

3.

25
5
=
6
30
7
14
+
= +
15
30
39
9
3
= 1
= 1

30
30
10

5
20
= 23
12
48
7
21
+48
= +48
16
48
41
71
48
7
21
9.
=
8
24
3
3
2
= 2
24
24

1
4
+6
= +6
6
24
28
4
1
8
= 9
= 9
24
24
6
6.

12.

15.

23

8
9
2
9
6
2
=

9
3

9
9
7
7
-12 = -12
9
9
2
2
9
15

=

14

1
3
27
= 23
= 22
8
24
24
7
14
14

= =12
24
24
13
22
24

18. 23

3
3
5
+ 11 + 18 =
4
4
8
6
6
5
17
11 + 11 + 18 = 40
=
8
8
8
8
1
42 yards
8

21. 11

Chapter 2

9


5
3
3
3
+ 37 + 12 + 23 =
8
8
8
4
3
5
3
6
42 + 37 + 12 + 23 =
8
8
8
8
17
1
114
= 116 feet
8

8

23.

22. 42

4
4
4
3
3
+ 4 + 4 + 7 + 7 =
5
5
5
8
8
32
32
32
15
15
4
+ 4
+ 4
+ 7
+ 7
=
40
40

40
40
40
126
3
26
= 29
inches
40
20

3
5
5
5
+ 12 + 12 + 12
4
8
8
8
1
1
+ 8 + 8 =
2
2
6
5
5
5
+ 10 + 12 + 12 + 12

8
8
8
8
4
4
40
+ 8 + 8 = 84
= 89 feet
8
8
8
+ 10

25. 45 - 42

24. 4

26. 12 - 10

3
4
5
+12
8
6
10
8
5
+12

8
10

2

3
4
3
1
= 11 - 10 = 1 feet
4
4
4
4

1
8
1
= 44 - 42 =
8
8
8

7
yards; she can use the fabric.
8

5
15
10

5
15
- 12 = 13
- 12
= 1 feet
16
8
16
16
16
1
5
9
5
4
1
14 - 12 = 13 - 12 = 1 = 1 feet
8
8
8
8
8
2
5
8
5
3
14 - 12 = 13 - 12 = 1 feet
8
8

8
8
13
5
13
10
3
13
- 12 = 13
- 12
= 1 feet
16
8
16
16
16

27. 13

3
6
2
1
3
+ 8 = 16 = 17 = 17
4
4
4
4
2

1
2
1
1
36 - 17 = 35 - 17 = 18 inches
2
2
2
2

28. 8

2-3, p. 64
1

1.

3
4
3
* =
8
5
10

2.

12
7

6.

2

5.

4
39 7
;
9. 5 =
7
7 39

1
5
5
* =
7
6
42

3.

5
3

7.

3

35
805
13
23
*
=
= 22
4
9
36
36

4.

1
9

8.

1

1

2

3

2
1
12

8
12
7
21
1
, =
* =
= 2
13. 2 , 1 =
5
7
5
7
5
8
10
10
2

14. 5

1
12

25

75
9
75
8

200
1
, =
* =
16. 75 , 1 =
8
1
8
1
9
3
3
2
= 66 , or 67 sheets
3

3
39
200
4
800
17. 200 , 9 = 200 ,
=
*
=
4
4
1
39
39

20
= 20 rooms
39

3
35
40
4
32
18. 40 , 8 = 40 ,
=
*
=
4
4
1
35
7
7
4
= 4 ; 4 boxes
7

8

1

3

5

4
149
149
1
20. 4 * 18 = *
=
= 74 feet
8
1
8
2
2
2

1

Theoretically, 6 cabinets will exactly fit on the wall.

10

Chapter 2

2

1

3

1
2

21
8
21
3
63
31
, 2 =
, =
* =
= 1
4
3
4
3
4
8
32
32

3
3
5
3
1
3
15.
, 5 = , = * =
4
4
1

4
5
20

1
21
7
21
2
19. 21 , 3 =
, =
* = 6
2
1
2
1
7

1

10
2
9
3
3
=
,
= *
12.
5

10
5
9
3

5
3
5
4
5
11.
, = * =
8
4
8
3
6

3
27 8
10. 3 =
;
8
8 27

24
3
*
= 9
8

1

Copyright © 2014 Pearson Education, Inc.


1

1
13
2
13
1
* 2 =
* =
= 6 inches long
4
4
1
2
2
28 , 2 = 14 inches wide
6 12 inches long * 14 inches wide

1
4
33
33
1
21. 4 * 4 = *
=

= 16 feet
8
1
8
2
2

22. 3

2

Yes, if no more than a total of 18 inch is needed for
spacing between the desks.

Exercises Set A, p. 71
3 7 5 100 41
1. Examples will vary. , , ,
, ; proper fractions
5 9 8 301 53
3. 20

2
3

4 8 12 132 7
2. Examples will vary. , , ,
, ; improper fractions
4 5 4 89 1

4. 7

5. 8

(3 * 4) + 1
13
=
3
3

1
2

(3 * 33) + 1
100
=
3
3

6.

(6 * 5) + 5
35
=
6
6

9.

15 , 3
5

=
18 , 3
6

10.

20 , 10
2
=
30 , 10
3

11.

5
30 , 6
=
48 , 6
8

12.

10
5 * 2
=
6 * 2
12

13.

5 * 4
20
=
8 * 4
32

14.

9 * 13
117
=
11 * 13
143

15.

3
1
15
=
= of the employees
105
21
7

16.

7.

8.

2)4 12 16
8
2)2 6
2)1 3
4
2)1 3
2
3)1 3
1
1 1
1
2 * 2 * 2 * 2 * 3 = 48

18. 2)1 5 10 6
3)1 5 5 3
5)1 5 5 1
1 1 1 1
2 * 3 * 5 = 30
1
3
4
3
7
21. 7 + 4 = 7 + 4 = 11
2
8
8
8
8

23. 12
25.

4
8
= 7
5
10
1
5
-4 = -4
2
10
3
3
10

28. 6
-3

5

=

8
8

20.

22. 11

24.
26. 5
-3

=

4

24 12 42
12 6 21
6 3 21
3 3 21
1 1
7
1 1
1
* 2 * 3 * 7 = 168

2
2
6
10
16
1
+ =
+
=
= 1
5
3

15
15
15
15

2
5
4
9
3
1
5
+ 8 = 11 + 8 = 19 = 20 = 20
6
3
6
6
6
6
2

5
3
2
1
=
=
12
12
12

6

5
5

27.

2
2
= -3
5
5
3
1
5

5
5
= 4
6
6
1
2
-3 = -3
3
6
3
1
1 = 1
6

2
4

29.

5
18

30.

32.

8
5

33. 4

5
2
10
1
* =
= 3
1
3
3
3

5
5

= -3
8
8
3
2 feet
8
1

9
56
* = 28
31.
9
2
1

3
4
7
2
+ = = 1
5
5
5
5

3
5
8
+ 16 = 28 = 29 yards

8
8
8

7

28

19.

17. 2)56
2)28
2)14
3) 7
7) 7
1
2 * 2

1

Copyright © 2014 Pearson Education, Inc.

Chapter 2

11


1

3

1
3
4
35.
, = * = 3
4
4
4
1

1
13 4
34. 3 =
;
4
4 13

1

2

1
15
2
15
1
15
3
, =
* =

= 3
36. 7 , 2 =
2
2
1
2
2
4
4

22
1
1
22 11
2
4
37. 3 , 5 =
,
=
*
=
7
2
7
2
7
11
7
1

4

38. 244 , 7

5
244
61
244
8
= 32 pieces
=
,
=
*
8
1
8
1
61

39.

1

6

3
1
5
6

1
10
5
1
5
+ - = + - =
= = 1 inches
8
4
8
8
8
8
8
4
4
96

18
2
*
= 12 hours
40.
3
1

1
3
1
2 2

$288
41. 1 - = - = ; *
= +192
3
3
3
3 3
1

1

1

Exercises Set B, p. 73
1.

3
15ͤ 52
45
7

7
15

5.

(8 * 7) + 3
59
=
8

8

9.

18 , 9
2
=
63 , 9
7

13.

2.

6.
10.

7
3. 11 77
ͤ
77

3

20 4
4ͤ 83
8
3
0
3

(5 * 10) + 1
51
=
5
5
78 , 6
13
=
96 , 6
16

8
4
=
of the class
30
15

9
110
10ͤ 19
10
9

7.

18 , 2
9
=
20 , 2

10

8.

27 , 9
3
=
36 , 9
4

11.

7 * 9
63
=
9 * 9
81

12.

28
4 * 7
=
7 * 7
49

14. 2)8 20 16
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
7
1
8
17.
+ = = 1
8
8
8

16. 2)12 15
2) 6 15
3) 3 15
5) 1 5
1 1

4.

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
11 1 1
2 * 2 * 2 * 3 * 3 = 72
1
11
7

18.
+
+
=
4
12
16
12
44
21
77
29
+
+
=
= 1
48
48
48
48
48

2 * 2 * 3 * 5 = 60
1
5
1
+ 2
+ 3 =
4
3

6
3
4
10
3
+ 2
+ 3
=
12
12
12
17
5
8
= 9
12
12

20. 5

19. 3

21.

12

6
5
12
5

=
=
7
14
14
14
1
7
=
14
2

22.

Chapter 2

1
3
3
4
6
3
+ 7 + 9 = 5 + 7 + 9
8
2
4
8
8
8
13

5
= 21
= 22
8
8

1
7
21
= 4
= 3
2
14
14
6
12
12
-3 = -3
= -3
7
14
14
9
14
4

Copyright © 2014 Pearson Education, Inc.


8

8
1
1
-4 = -4
8
8
7
7
8

23. 12

3
4
1
5
2
1
6
4
1
9
4
3
8
4

25. 7

24.

= 11

1
2
12
= 4
= 3
5
10
10
3
3
3
-2
= -2
= -2
10
10
10
9
1
10
4

2
3
27
40 = 39
26.

2
4
40
1
1
2
-37 = -37
5
2
2
4
1
1
2 hours
6
2
4
1
9
4
3
8
4
10
2
1
35
= 37 = 37 hours Maxine Ford worked
4
4

2
2 1 hours more than

= 7
=
=
=
=

2

George Mackie.
3
8
24
3
27.
* =
= 3
7
1
7
7
4

1

2
3
32

3
* = 4 cakes
30. 10 * =
3
8
3
8
1

33. 2

1

1

1

5

1

1

9
2
5
3
3
28.
* * * =

10
5
9
7
35

31.

1

3
19 8
=
;
8
8 19

3
2

34. 5

32. 8 =

15
4
3
=
* = 20
4

1
3

6

1

1

8 1
;
1 8
4

1
61 12
=
;
12
12 61

35.

1
5
8
20
2
5
, = * =

= 6
6
8
6
1
3
3
3

5

36. 15 ,

3

21
12
1
5
29. 10 * 1 =
*
= 18
2
7
2
7

37. 7

1

1
2
15
5
, 1 =
,
2
3
2
3
3

15
3
9
1
=
* = = 4
2
5
2
2
1

7

38. 91 , 1

5

91
13
91
8
=
,
=
*
= 56 pieces
8
1
8
1
13
1

39. 1

1
3
1
4
15
10
29
9
+ 2 + 1 = 1
+ 2
+ 1
= 4

= 5
feet
5
4
2
20
20
20
20
20
1

8
13
5
= 13 feet
41. 8 * 1 = *
8
1
8

3
16
3
13
= 7
- 2
= 5
feet
40. 8 - 2

16
16
16
16

1

Practice Test, p. 75
1.

1
5

2.

5
3

3. 1

4.

4
12 , 3
=
15 , 3
5

5.

3
15 , 5
=
35 , 5
7

6.

7.

(8 * 2) + 5
16 + 5
21
=
=
8
8
8

8.

(12 * 3) + 1
36 + 1
37
=
=
12
12
12

9.

Copyright © 2014 Pearson Education, Inc.

3
8 5
= ;
5
5 8

21 , 3
7
=
51 , 3
17
2 39 = 213
9ͤ 21
18
3

Chapter 2

13


10.

4
4 13
13ͤ 56

52
4

11.

5
4
1
- =
6
6
6

12.

14.

3
5
, =
6
4

15. 10

1

5
7
7

13.
*
=
8
10
16
2

5
9
25
36
61
21
+
=
+
=
= 1
8
10
40
40
40
40

1
3
, 5 =
2

4
21
23
,
=
2
4

2

5
4
10
1
* =
= 1
6
3
9
9

2

3

21
4
*
=
2

23
1

42
19
= 1
23
23
16. 56 * 32

1
1
+ 3 =
2
3
3
2
5
2 + 3 = 5
6
6
6

6
=
7

4
=
5

5
4
1
136 - 89 = 47
5
5
5

18. 137 - 89

17. 2

8

56
230
= 1,840
*
1
7
1

19.

3
= entire load
3
3
1
2

3
- =
Part of the truckload to be unloaded
3
3
3
4
1

1

1

2

20.

87
3
=
580
20

2
3
1
* = of the truckload remains to be unloaded
3
4
2

1
1
22. 5 % + 2 % =
2
4
2
1
3
5 % + 2 % = 7 %
4
4
4

1
5
, =
2
8
125
5
, =
2
8

21. 62

25

4

1

1

125
8
* = 100 sheets
2
5
2
2
$80
= The main course cost was of the total budget.
23.
$200
5
5

225

1
900
5
900
1,125
9
1
24. 1 *
= *
=

= 31
= 31
4
36
4
36
36
36
4
1
1
The recipe for 900 cupcakes requires 31 cups of sugar.
4

Critical Thinking, p. 77
1. The two operations that require a common denominator
are addition and subtraction.
3. The product of any number and its reciprocal is 1. Exam3
5
ples will vary. * = 1
5
3

14

Chapter 2

2. The number 1 can be written as any fraction that has a
21
= 1

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

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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 Security 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 multiplying 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 denominator of the improper fraction. Then, interchange the
numerator and denominator of the improper fraction to
3
make its reciprocal. 3 13 = 10
3 ; reciprocal = 10

7. Two fractions are equal if the lowest terms of both fractions
are the same.
2
6
3
3
* =
=
7
2
14
7
3
3
9 6
9
3
* =
;
=
=
7
3

21 14
21
7
6
9
Therefore,
and
are equivalent or equal fractions.
14
21

8. Answers will vary.
1
12 , = 12 * 2 = 24
2
4
3
12
4
16
12 , =
* =
= 16
4
1
3
1

9. A whole number, like 5, divided by a proper fraction,
like 12, means the wholes are being broken up into halves,

so you have more parts (pieces) than you started with.
5 , 12 = 51 * 21 = 10.
11. The fraction in the minuend cannot be subtracted from
the fraction in the subtractend. The minuend must be
rewritten so the fraction has a larger numerator.
1
4
1
5
12 = 11 + + = 11
4
4
4
4
3
3
-7
-7
4
4
2
1
4 = 4
4
2

1

2
15

3
45
1
15 , =
* =
= 22
3
1
2
2
2
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.
The division should be written as a multiplication by the
reciprocal of the divisor (second number).
4
1
, 2 =
9
4
4
9
, =
9
4
4
4
16
* =

9
9
81

Challenge Problem p. 77
19
6,681
= 92
72
24
Because a portion of the 93rd square yard is needed, we will
buy 93 yards and 4 additional yards for matching.
93 + 4 = 97
97 * 12 = +1,164

1
3
51
131
* 32 =
*
2
4
2
4
6,681
1
=
= 835 square feet
8

8
6,681
6,681
1
6,681
, 9 =
* =
square yards
8
8
9
72

25

Case Studies
2-1, p. 78
1. 2 12 =

5
2

1 2 = 202 = 10 cups apples
5 1
5
1
2 1 2 2 cup = 4 = 1 4 cups brown sugar
5 1
5
1

2 1 2 2 tsp = 4 = 14 tsp cinnamon
5 1
5
2 1 4 2 tsp = 8 tsp each nutmeg/cloves
5 2
10
2 1 1 2 tsp = 2 = 5 tsp lemon juice
5 4
2 1

1 23 cup 2 = 106 = 123 cups sugar
5 1
5
2 1 8 tsp 2 = 16 tsp salt
5 3
15
7
2 1 4 cup 2 = 8 = 1 8 cups flour
5 1
5
2 1 3 cup 2 = 6 cup butter
5 1
5
2 1 4 cup 2 = 8 cup walnuts
5
2

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Chapter 2

15


2. 4 cups + 4 cups = 8 cups apples
1
2
1
2
1
4

cup +

1
2

cup = 1 cup brown sugar

tsp +

1
2

tsp = 1 tsp cinnamon

tsp +

1
4

tsp =

1
2

tsp each nutmeg/cloves

1
2

cup 1 12 2 =

1
4

2
3

cup 1

2
6

1
2

2

=

cup brown sugar; 14 1 31 2 =
=

1
3

cup granulated sugar;

cup +

1
8

tsp +

3
4
1
3
1
4

2 tsp + 2 tsp = 4 tsp lemon juice
3.

2
3

2

3
1
8

cup = 113 cup sugar

tsp =

2
8

=

cup +

3
4

cup =

6
4

cup +

1
3

cup =

2
3

cup +

1
4

cup =

2
4

3
4

cup for all 3 batches

1
3

1 31 2

1
4

tsp salt

= 112 cups flour
cup butter

=

1
2

cup walnuts

= 1 cup for 3 batches

2-2, p. 79
1
+240,000
1
+240,000
=
* =
= +120,000 materials
2
1
2
2
1
+240,000
1
+240,000
+240,000 * =
* =
= +80,000 labor
3
1

3
3
+240,000 - (+120,000 + +80,000) = +40,000 profit
40,000
1
or
= fraction of cost
240,000
6

1. +240,000 *

2. 400 ft * 400 ft = 160,000 square feet.
1 5,000
1 10,000
1 80,000
1
40,000
= ;
=
;
=
;
=
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
=
is the portion that remains for a water garden
160,000
32

16

Chapter 2

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