Chapter 2 Review of Fractions Section Exercises 2-1, p. 49 1. proper 7.
13.
2. improper
157 7冄 12 7 5
8.
3. improper
1 1 20 20冄 21 20 1
9.
13 3 1,300 = = 1 phones per person 1,000 10 10
4. proper
1 18冄 18 18
14.
10.
5. proper
2 37 7冄 17 14 3
11.
6. improper
2 8冄 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 21冄 36 21 15 1 R9 15冄 24 15 9
1 R6 15冄 21 15 6 1 R6 9冄 15 9 6
2 R3 6冄 15 12 3 1 R3 6冄 9 6 3
2 R0 3冄 6 6 0 2 R0 3冄 6 6 0
2 3冄 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 18冄 48 36 12
1 R6 12冄 18 12 6
2 R0 6冄 12 12 0
GCD = 6
18 18 , 6 3 = = 48 48 , 6 8
2 R10 15冄 40 30 10
1 R5 10冄 15 10 5
2 R0 5冄 10 10 0
GCD = 5
15 15 , 5 3 = = 40 40 , 5 8
33.
2 8冄 16
3 * 2 6 = 8 * 2 16
34.
4 5冄 20
4 * 4 16 = 5 * 4 20
35.
4 8冄 32
3 * 4 12 = 8 * 4 32
36.
3 9冄 27
5 * 3 15 = 9 * 3 27
37.
5 3冄 15
1 * 5 5 = 3 * 5 15
38.
3 5冄 15
3 * 3 9 = 5 * 3 15
8
Chapter 2
7 3
20. (3 * 6) + 2 = 20;
21.
29.
24 163 16冄 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 Š 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 Š 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 15冄 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 冄 77
3
20 4 4冄 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 10冄 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 9冄 21 18 3
Chapter 2
13
10.
4 4 13 13冄 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
Copyright Š 2014 Pearson Education, Inc.
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
Copyright Š 2014 Pearson Education, Inc.
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
Copyright © 2014 Pearson Education, Inc.