Chapter 2 Fractions And Mixed Numbers: Multiplication
Basic College Mathematics 2nd Edition Miller Solutions ManualFull Download: er 2Fractions and Mixed Numbers: Multiplicationand DivisionChapter Opener PuzzleSection 2.1Introduction to Fractions and Mixed NumbersSection 2.1 Practice Exercises1. Answers will vary.7. 6 1; 62. (a) A fraction is a part of a whole unit.(b) The numerator of a fraction denotesthe number of pieces of the wholebeing considered.(c) The denominator of a fractiondenotes the number of equal piecesinto which a whole unit is divided.(d) A fraction is a proper fraction if thenumerator is less than thedenominator.(e) An improper fraction is a fraction inwhich the numerator is greater than orequal to the denominator.(f) A mixed number is a sum of a wholenumber and a fractional part of awhole.8. 9 1; 99. 2 2; 110. 8 8; 111. 0 3; 012. 0 7; 013. 2 0; undefined14. 11 0; undefined3. Numerator: 2; denominator: 315.3416.1217.594. Numerator: 8; denominator: 95. Numerator: 12; denominator: 116. Numerator 1; denominator: 251Full download all chapters instantly please go to Solutions Manual, Test Bank site: testbanklive.com
Chapter 218.Fractions and Mixed Numbers: Multiplication and Division3537. Proper38. .3443.7 3;14 424.1444.13 1;34 425.1845.13 5;18 826.21or8446.5 1;22 227.411033 4 !1 3 747. 1 44428.431031 6 ! 3 1 1948. 6 33329.10212 4 ! 9 2 3849. 4 99930.10631 3 ! 5 1 1650. 3 55531. Proper3 3 ! 7 3 2451. 3 77732. Proper2 8 ! 3 2 2652. 8 33333. Improper34. Improper53. 735. Improper36. Improper521 7 ! 4 1 29 444
Section 2.13 10 ! 5 3 5354. 10 555267. 10 27!2075 11 ! 12 5 137 12121255. 11268. 18 43!3671 12 ! 6 1 7356. 12 6663 21 ! 8 3 17157. 21 888569. 9 52!4571 15 ! 2 1 3158. 15 222570. 12 67!6073 2 ! 8 3 1959. 2 88819 eighths3 2 ! 5 3 1360. 2 55513 fifths1271. 11 133!1123!2213 1! 4 3 761. 1 4447 fourths2 5 ! 3 2 1762. 5 33317 thirds463. 8 37!325164. 7 13!76765. 5 39!354466. 4 19!163Introduction to Fractions and Mixed Numbers72. 10551!501458373. 6 23!1851677451674. 7 115!745!42344475. 7 7
Chapter 2Fractions and Mixed Numbers: Multiplication and Division230492176.!812!121!01105677. 5 5281!52!028!2531!30190178. 8 7213!721!013!8581079. 11 8913!8811!113!0318580. 23 4257!23195!184117!11521281. 15 53483. Divide the distance between 0 and 1 into4 equal parts.84. Divide the distance between 0 and 1 into2 equal parts.5901885. Divide the distance between 0 and 1 into3 equal parts.81031186. Divide the distance between 0 and 1 into5 equal parts.87. Divide the distance between 0 and 1 into3 equal parts.18522388. Divide the distance between 0 and 1 into6 equal parts.54
Section 2.289.90.71 166Divide the distance between 1 and 2 into6 equal parts.92.72 155Divide the distance between 1 and 2 into5 equal parts.Prime Numbers and Factorization31 122Divide the distance between 1 and 2 into2 equal parts.93. False; whole numbers cannot be written asproper fractions.94. True95. True96. True91.52 133Divide the distance between 1 and 2 into3 equal parts.Section 2.2Prime Numbers and FactorizationSection 2.2 Practice Exercises1. Answers will vary.2. (a) A factor of a number n is a nonzerowhole number that divides evenly inton.(b) A factorization of a number n is aproduct of factors that equals n.(c) A prime number is a whole numbergreater than 1 that has only twofactors (itself and 1).(d) A composite number is a wholenumber greater than 1 that is notprime.(e) The prime factorization of a numberis the factorization in which everyfactor is a prime number.3.8 4;12 124.5 1;2 25.5 3;4 46.6; improper57.7; proper128.6; improper649. 5 23!2034352 6 ! 7 2 4410. 6 77711. For example: 2 4 and 1 855
Chapter 2Fractions and Mixed Numbers: Multiplication and Division12. For example: 2 10 and 4 524. 241(a) No; 241 is not even.(b) No; 2 4 1 7 is not divisible by 3.(c) No; the ones-place digit is not 0 or 5.(d) No; the ones-place digit is not 0.13. For example: 4 6 and 2 2 2 314. For example: 1 14 and 2 4525. 108(a) Yes; 108 is even.(b) Yes; 1 0 8 9 is divisible by 3.(c) No; the ones-place digit is not 0 or 5.(d) No; the ones-place digit is not 0.26. 1040(a) Yes; 1040 is even.(b) No; 1 0 4 0 5 is not divisibleby 3.(c) Yes; the ones-place digit is 0.(d) Yes; the ones-place digit is 0.27. 3140(a) Yes; 3140 is even.(b) No; 3 1 4 0 8 is not divisibleby 3.(c) Yes; the ones-place digit is 0.(d) Yes; the ones-place digit is 0.17. A whole number is divisible by 2 if it is aneven number.18. A whole number is divisible by 10 if itsones-place digit is 0.28. 2115(a) No; 2115 is not even.(b) Yes; 2 1 1 5 9 is divisible by3.(c) Yes; the ones-place digit is 5.(d) No; the ones-place digit is not 0.19. A whole number is divisible by 3 if thesum of its digits is divisible by 3.20. A whole number is divisible by 5 if itsones-place digit is 5 or 0.21. 45(a)(b)(c)(d)329. 28 84!840Yes, 84 is divisible by 28.No; 45 is not even.Yes; 4 5 9 is divisible by 3.Yes; the ones-place digit is 5.No; the ones-place digit is not 0.22. 100(a) Yes; 100 is even.(b) No; 1 0 0 1 is not divisible by 3.(c) Yes; the ones-place digit is 0.(d) Yes; the ones-place digit is 0.530. 22 110!1100Yes, 110 is divisible by 22.23. 137(a) No; 137 is not even.(b) No; 1 3 7 11 is not divisible by3.(c) No; the ones-place digit is not 0 or 5.(d) No; the ones-place digit is not 0.31. Prime32. Prime5633. Composite2 5 1034. Composite3 7 21
Section 2.235. Composite3 17 5136. Composite3 19 57Prime Numbers and Factorization1155558.3 1653 49537. Prime38. Prime1359. 5 652 1302 26039. Neither40. Neither41. Composite11 11 12142. Composite3 23 6943. Prime44. Prime45. Composite3 13 3946. Composite7 7 4947. There are two whole numbers that areneither prime nor composite, 0 and 1.48. False; the square of any prime number isdivisible by that prime number.49. False; 9 is not prime.50. False; 2 is not composite.51. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,41, 43, 4752. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,41, 43, 47, 53, 59, 61, 67, 71, 73, 7954. No, 8 is not a prime number.2 ! 2 ! 5 ! 13 22 ! 5 ! 13 260760. 5 355 1755 ! 5 ! 7 52 ! 7 175761. 7 493 1473 ! 7 ! 7 3 ! 7 2 1471735162.2 1022 3 17 512363. 3 692 1382 3 23 1381164. 7 773 2313 7 11 23165. 722253. No, 9 is not a prime number.3 ! 3 ! 5 ! 11 32 ! 5 ! 11 49511771543086162 ! 2 ! 2 ! 7 ! 11 23 ! 7 ! 11 61655. Yes1379166.2 1822 36456. Yes757. 5 352 702 5 7 7067. 47 is prime.68. 41 is prime.572 ! 2 ! 7 ! 13 22 ! 7 ! 13 364
Chapter 2Fractions and Mixed Numbers: Multiplication and Division69. 1, 2, 3, 4, 6, 1282. Yes; 520 is divisible by 8.70. 1, 2, 3, 6, 9, 1883. No; 126 is not divisible by 8.71. 1, 2, 4, 8, 16, 3284. No; 58 is not divisible by 8.72. 1, 5, 11, 5585. Yes; 3 9 6 18 is divisible by 9.73. 1, 3, 9, 27, 8186. Yes; 4 1 4 9 is divisible by 9.74. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 6087. No; 8 4 5 3 20 is not divisible by9.75. 1, 2, 3, 4, 6, 8, 12, 16, 24, 4888. No; 1 5 8 7 21 is not divisible by9.76. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 7277. No; 30 is not divisible by 4.89. Yes; 522 is even and 5 2 2 9 isdivisible by 3.78. No; 46 is not divisible by 4.79. Yes; 16 is divisible by 4.90. Yes; 546 is even and 5 4 6 15 isdivisible by 3.80. Yes; 64 is divisible by 4.91. No; 5917 is not even.81. Yes; 32 is divisible by 8.92. No; 6 3 9 4 22 is not divisible by3.Section 2.3Simplifying Fractions to Lowest TermsSection 2.3 Practice Exercises1. Answers will vary.2. (a) A fraction is said to be in lowestterms if the numerator anddenominator share no common factorother than 1.(b) The largest number that dividesevenly into the numerator anddenominator is call their greatestcommon factor.293. 5 145194. 3 572 114235. 2 462 922 ! 2 ! 23 22 ! 23 92176. 3 513 1533 ! 3 ! 17 32 ! 17 153177. 5 855 29 1458. 32222 3 19 1145851530601205 17 852 ! 2 ! 2 ! 3 ! 5 23 ! 3 ! 5 120
Section 2.3135659.3 195531510.Simplifying Fractions to Lowest Terms19. 1! 6 ! 2 ! 36 61 3 2 63 5 13 19520. 6 ! 8 ! 16 ! 348 486 3 16 82 ! 2 ! 3! 3!5 22 ! 32 !5 1803 452 902 18021. 12 ! 4 ! 16 ! 348 4812 3 6 411.22. 4 ! 15 ! 5 ! 1260 604 12 5 1512.23. 8 ! 27 ! 9 ! 20216 " 1808 20!9 2713.24. 5 ! 18 ! 6 ! 1290 " 725 12!6 1814.25.122!2!31 24 2 ! 2 ! 2 ! 3 226.153 !55 18 2 ! 3 ! 3 627.62!31 18 2 ! 3 ! 3 328.213 !77 24 2 ! 2 ! 2 ! 3 829.36 2 ! 2 ! 3 ! 3 9 202 ! 2 !5530.497 !77 42 2 ! 3 ! 7 615. False; 5 5 4 416. Two fractions are equivalent if they bothrepresent the same part of a whole.17. 2 ! 5 ! 3 ! 310 " 92 3!3 518. 1! 9 ! 4 ! 29"81 2!4 959
Chapter 2Fractions and Mixed Numbers: Multiplication and Division31.153 !55 12 2 ! 2 ! 3 447.1302 ! 5 ! 13 13 150 2 ! 3 ! 5 ! 5 1532.30 2 ! 3 ! 5 6 255 !5548.702 ! 5 !77 120 2 ! 2 ! 2 ! 3 ! 5 1233.20 2 ! 2 ! 5 4 255 !5549.385 5 ! 7 ! 11 77 195 3 ! 5 ! 13 3934.881 16 2 ! 8 250.393 ! 133 130 2 ! 5 ! 13 1035.14 11451.34 2 ! 17 2 85 5 ! 17 536.8 1852.693 ! 233 92 2 ! 2 ! 23 437.50 2 ! 25 2252553.6!24 2 "2 2 10 4 14 2 " 7 738.24 4 ! 6 46654.9 !18 2 "2"2 4 15 3 18 2 " 3" 3 939.9 1955.5!5 0 07!2 540.2 1256.41.1053! 5 ! 73 140 2 ! 2 ! 5 ! 7 411 ! 11 0 04 7 1157.7!2 5 undefined5!5 042.84 2 ! 2 ! 3 ! 7 2 126 2 ! 3 ! 3 ! 7 358.4 7 11 undefined11 ! 11 043.33 3 ! 11 3111159.8!2 62 "3 3 8 2 10 2 " 5 544.65 5 ! 13 135560.15 3 18 6 " 3 3 15 ! 3 12 6 " 2 245.777 ! 117 110 10 ! 11 1061.120 122 ! 2 !33 160 16 2 ! 2 ! 2 ! 2 446.855 ! 175 153 3 ! 3 ! 17 962.720 72 8 ! 99 800 80 8 ! 10 1060
Section 2.363.3000 30 2 ! 3 ! 5 5 1800 18 2 ! 3 ! 3 364.2000 20 2 ! 2 ! 5 4 1500 153! 5365.42, 000 42 2 ! 21 21 22, 000 22 2 ! 11 1166.50, 000 50 2 ! 5 ! 5 10 65, 000 655 ! 13 1367.5100513 ! 1717 30,000 300 3 ! 100 10068.9800982 ! 7 !77 28,000 280 2 ! 2 ! 2 ! 5 ! 7 20(b) Jared sold the greater fractional part6 5because .7 7153 !55 24 2 ! 2 ! 2 ! 3 8142 !77 Lisa:16 2 ! 2 ! 2 ! 2 874. (a) Lynette:(b) Lisa has completed more of her course7 5because .8 875. (a) Raymond:720 2 ! 2 ! 2 ! 2 ! 3 ! 3 ! 5 10 7922 ! 2 ! 2 ! 3 ! 3 ! 11 11540 2 ! 2 ! 3 ! 3 ! 3 ! 5 9 Travis:6602 ! 2 ! 3 ! 5 ! 11 11202 ! 2 !55 48 2 ! 2 ! 2 ! 2 ! 3 12Tails: 48 20 28282 ! 2 !77 48 2 ! 2 ! 2 ! 2 ! 3 1269. Heads:70.(b) Raymond read the greater fractional10 9part because .11 1176. (a)70 2 ! 5 ! 7 2 105 3 ! 5 ! 7 371. (a)(b)62 !33 26 2 ! 13 13122 ! 2 !33 88 2 ! 2 ! 2 ! 11 22(b)36 2 ! 2 ! 3 ! 39 88 2 ! 2 ! 2 ! 11 22153 !55 27 3 ! 3 ! 3 916 2 ! 2 ! 2 ! 2 4 36 2 ! 2 ! 3 ! 3 977. (a) 300,000,000(b) 26 6 2020 2 ! 2 ! 5 10 262 ! 13 1372. (a)Simplifying Fractions to Lowest Terms(b) 36,000,000(c)36, 000 , 00036 300, 000 , 000 3002 ! 3 ! 2 !33 2 ! 2 ! 3 ! 5 ! 5 2578. (a) 300,000,000(b) 75,000,00025 5 ! 5 5 35 5 ! 7 724 2 ! 2 ! 2 ! 3 6 Jared:282 ! 2 !7773. (a) Jonathan:(c)300, 000 , 000 300 75, 000 , 000752!2! 3 ! 5 ! 5 4 3!5 !51(d) 4 times greater61
Chapter 2Fractions and Mixed Numbers: Multiplication and Division79. For example,6 9 12, ,8 12 1685.779 41 969 5180. For example,2 3 4, ,6 9 1286.462 21 220 1081. For example,6 4 2, ,9 6 387.493 29 510 3082. For example,40 8 4, ,50 10 588.871 13 469 783.792 8 891 989.969 3 646 284.728 13 784 1490.713 31 437 19Section 2.4Multiplication of Fractions and ApplicationsSection 2.4 Practice Exercises8.1. Pages 152 156; answers will vary.2. A power of one-tenth is1raised to a109.whole-number power.3. Numerator: 10; denominator: 1410 2 ! 5 5 14 2 ! 7 710.4. Numerator: 32; denominator: 3632 2 ! 2 ! 2 ! 2 ! 2 8 362 ! 2 !3!395. Numerator: 25; denominator: 1525 5 ! 5 5 15 3 ! 5 36. Numerator: 2100; denominator: 70002100 213! 73 7000 70 2 ! 5 ! 7 107.6211.1 1 1 !1 1! 2 4 2!4 812.2 1 2 !1 2! 3 5 3 ! 5 1513.33 8 24!8 ! 644 1 414.22 20 40! 20 ! 855 15
Section 2.4Multiplication of Fractions and Applications15.1 3 1! 3 3! 2 8 2 ! 8 1631.21 25 3 ! 7 5 ! 535! ! 5 125 2!2! 3 416.2 1 2 !1 2! 3 3 3! 3 932.16 15 16 3 ! 53! ! 25 32 5 ! 5 2 ! 16 1017.14 1 14 ! 1 14! 9 9 9 ! 9 8133.24 5 2 ! 2 ! 2 ! 3 5 8! ! 15 33!53 318.1 9 1! 9 9! 8 8 8 ! 8 6434.49 67 !72!3 7! ! 24 7 2 ! 2 ! 2 ! 3 74" 12 #" 2 # 12 ! 2 24 19. % % & 7 '& 5 ' 7 ! 5 35" 6 #" 22 # 6 ! 22 2 ! 3 ! 2 ! 11 4 35. % % 511 ! 3 ! 5& 11 '& 15 ' 11 ! 15" 9 #" 7 # 9 ! 7 63 20. % % & 10 '& 4 ' 10 ! 4 403!4!51" 12 #" 5 # 12 ! 5 36. % % & 45 '& 4 ' 45 ! 4 3 ! 3 ! 5 ! 4 3" 1 # 8 1 8 !1 8 21. 8 ! % ! & 11 ' 1 11 1 ! 11 11" 17 #" 72 # 17 ! 72 17 ! 8 ! 9 8 837. % % 19 ! 17& 9 '& 17 ' 9 ! 17" 2 # 3 2 3! 2 6 22. 3 ! % ! & 7 ' 1 7 1! 7 723.24.25.26.27." 39 #" 11 # 39 ! 11 3 ! 13 ! 11 3 338. % % 111 ! 13& 11 '& 13 ' 11 ! 1344 6 4 ! 6 24!6 ! 55 1 5 !1 555 5 5 ! 5 25!5 ! 88 1 8 !1 813 5 13 ! 5 65! 9 4 9 ! 4 3629.5 353 5! ! 6 4 2" 3 4 830.7 1872 ! 3 ! 3 21" " 12 5 2 ! 2 ! 351040.85 12 5 ! 17 2 ! 2 ! 3 17! ! 176 10 2 ! 32!5142. 4 "2 323 2! ! 9 5 3 " 3 5 151 414 1! ! 8 7 2 " 4 7 1421 16 3 ! 7 4 ! 4 12! ! 124 747141. 12 "6 7 6 ! 7 42! 5 5 5 ! 5 2528.39.43.6315 2 ! 2 ! 33 !530 " 4212 ! 3 !7 782!22!2!28 " 9212 ! 2 ! 23 239 16 25! !15 3 83 " 3 2 " 2 " 2 "25 "5 !!3"532"2"210 101
Chapter 244.45.Fractions and Mixed Numbers: Multiplication and Division49 4 207 "72 " 2 2 "2" 5! ! !!8 5 72"2"25714 141! 1 54. # &" 10 %1 1 1 1 1 1 1 1 1' ' ' ' ' ' ' '10 10 10 10 10 10 10 10 101 1,000,000,000 5 10 7 5 2 ! 5 7 5" " "" 2 21 5 2 3 ! 7 5 321 1 1!1"55. % # 9 9 81&9'55 18 2446.!!9 32 115" 112 "3"32 " 2 " 2 "3 !!3 " 3 2 " 2 " 2 " 2 "21115 247.921 1 1!1"56. % # 4 4 16&4'33 3 3 27!3"57. % # # 2 2 2 8&2'7 3735 3! !5 !! 10 282! 5 2!2! 7 1 834 4 4 64!4"58. % # # 3 3 3 27&3'11 21123 ! 5 11! ! 15 !! 48.18 202 ! 3 !3 2!2! 5 11250.3333! 3" ! 4 3 "59. 4 # % # % 33 27& 4' & 1 4 '10014 2 " 2 " 5 " 5 3" 7 2 " 7! 21! !!49.49257"715"524 241! 2" ! 5 2 "60. 5 # % # % 23 8& 5' & 1 5 '385 2 ! 19 11 5 5" 11 " "" 52219 2 ! 11 1 19 11221 11!1 3" ! 1 "61. # % % # & 9 5 ' & 15 ' 15 15 22531 1 11!1"51. % # # & 10 ' 10 10 10 1000312" 10 1 # " 1 #2 1 11!62. % % ! 30 30 900& 3 100 ' & 30 '41 1 1 11!1"52. % # # # & 10 ' 10 10 10 10 10,0001061 1 1 1 1 1!1"53. % # # # # #101010 10 10 10 10& '1 1,000,000321121 " 21 8 # 1 6! % ! 263. ! 3 & 4 7' 3 131631 " 24 30 # 1 18! ! 364.% !6 & 5 8 ' 6 116411
Section 2.4321117376. A 28 ! 3 "28 9 2166.# % # 6 &2'6 4 22411 !8" 1 5 875. A bh (5) % # # 4 yd 222 &5' 2 1 516 ! 1 "16 1 265.# % # 9 &2'9 8 92Multiplication of Fractions and Applications111 ! 16 bh (3) # &22 " 9%1181 3 16 82 ' ' or 2 mm 22 1 93367.13177. A l ! w 68.3 1 1" cm 24 3 41188 378. A l ! w " 3 " 8 m 233 169.179. A l ! w 70.13 15 195" in.216 16 256123 3 23 2" ft80. A l ! w 24 4 3248111 11 871. A bh (11)(8) ! ! 44 cm 2222 1 1181. A (8)(4) (8)(4) 32 4 ! 4 32 1622 48 yd1111 15 1272. A bh (15)(12) ! !222 1 12 90 in.6182. A (8)(3) (8)(3) 24 4 ! 3 24 122 36 m 2141 ! 7 1 ! 2 72(6) # & (6) # & 3' 3'2 " 3% 2 " 3%333 7 3 2 ' ' 7 2 9 cm 21 3 1 3111 8 873. A bh (8)(8) ! ! 32 m 2222 1 183. A 111!7"1 7 1 774. A bh % (1) # # ft 222& 4'2 4 1 81 ! 9 1 ! 15 915(8) # & (8) # & 4 ' 4 '2 " 4% 2 " 4 %444 9 4 15 ' ' 9 15 24 m 21 4 1 484. A 65
Chapter 2Fractions and Mixed Numbers: Multiplication and Division21255 1685. ! 16 ! 1088 122 40 3692.! (40)(36) ! ! 96033 1 11140 36 14401440 960 480The amount left is 10 gal.2750Frankie mowed 960 yd 2 . He has 480 yd 2left to mow.33 11,00086.!11,000 ! 8250441121 1 1!1"93. (a) % # 6 6 36&6'The cost is 8250.87.1 1 1! 4 2 81Jim ate of the pizza for breakfast.8(b)22 2 4!2"94. (a) % # 7 7 49&7'188.1 2 1! 4 5 102(b)1of the sample has O negative blood.103, 275, 00089.22 9,825,000! 9,825,000 !3131 6,550,000There are 6,550,000 viewers.3 3 3 9190. 3! ! or 24 1 4 4491Nancy spendsor 2 hr a day.4422 1200! 1200 ! 80033111 1 1 ! 255 5 596.11 11 ! 10010 10 1097.648 8 8 ! 819 9 998.93 3 3 ! 42 2 2130011 1200Second place: ! 1200 ! 300441100.142 2 2 ! 497 7 795.99.40091. First place:11 1 1 ! 366 6 61 11 11 11, , , 2 4 2 ! 2 8 4 ! 2 16 8 ! 211The next number is .16 ! 2 322 22 22, , 3 9 3 ! 3 27 9 ! 3The next number is10011 1200Third place:! 1200 ! 1001211216622 .27 ! 3 81
Section 2.5101.1!1" 1# 2 % 8 & 161! 1 " 1# 8 % 2 & 16They are the same.Section 2.5102.Division of Fractions and Applications2!1" 2 1# 3 % 4 & 12 61!2" 2 1# 4 % 3 & 12 6They are the same.Division of Fractions and ApplicationsSection 2.5 Practice Exercises1. Page 143Answers will vary.10.11 10 10! 10 " 11010 1 102. To find the reciprocal of a nonzerofraction, interchange the numerator anddenominator.11.11 3 3!3 " 133 1 323.12. (a) Yes,9 22 18! 511 5135.(b) Yes,35(c) Yes,16124 74.! 37 8112111(d) No,34 5! 25 171!7" 3 7 76. 3 # % # &6' 1 6 213.8714.6515.91016.51417.1418.19215! 5 " 8 5 7. 8 # % #& 24 ' 1 24 33! 2 ! 7 148. # & # & 1" 7 % " 2 % 14! 9 ! 5 459. # & # & 1" 5 % " 9 % 452 211is undefined.019. No reciprocal exists.67
Chapter 2Fractions and Mixed Numbers: Multiplication and Division20. No reciprocal exists.21.22.131535. 7 2 7 3 21 ! 3 1 2 236. 4 3 4 5 20 ! 5 1 3 3210 1 10 1837. ! 209 18 9 123. multiplying124. multiplying12 52 122 2!2! 3 8 ! ! 25.15 12 15 5 3 ! 552526.4 1 4 338. ! 43 3 3 1111 6 11 5 55 ! 3 5 3 6 1827.7 2 7 5 35 ! 13 5 13 2 2628.8 3 8 10 80 ! 7 10 7 3 2143 12 439. 12 ! 164 1 3138 24 540. 24 ! 1551 81729.14 6 14 5 35 ! 3 53 6 931212 1 341. 4 ! 55 4 531230.11 3 11 4 22 ! 2 4 2 3342020 1 4 242. 5 ! 66 5 6 31531.32.1115 3 15 2 ! 52 2 2 311119 99 2 1 ! 10 2 10 9 55122215130 15 30 82 ! 44.40 840 15 513 3 3 4 1233. ! 14 4 4 3 1234.19 189 25 1 ! 43.50 25 50 18 4109139 1000 90 ! 45.100 1000 100 13136 6 6 5 30 ! 15 5 5 6 30168
Section 2.561004242 1 656. 7 ! 1111 7 111000 10 1000 3 300 ! 46.17317 10 17114511Division of Fractions and Applications816 2 16 5 4057. ! 3 53 2336 936 2547. ! 205 255 911217 1 17 4 17 ! 58.8 4 8 1 213 17 13 10 2648. ! 5 10 5 17 17212111 1659. ! 16 ! 288 17 1 7 4 749. ! 8 4 8 1 2123122 960.!9 ! 633 17 5 7 3 7 ! 50.12 3 12 5 201415 2 551.! 8 9 3661.22 5 2 ! 11 555! ! 7 1672 ! 8 5662.40 18 5 ! 8 3 ! 6 48! ! 21 25 3 ! 7 5 ! 5 35411 4 1! 52.16 3 12116 8 33 63. 8 !3 1 16 24224 6 453. 6 ! ! 83 1 3115 5 44 64. 5 !4 1 15 313254. 12 !5 12 5 ! 106 1 665.12262by , and 6! 6 multiplies331322122 6multipliesby . So ! 6 ! 433 136255.1616 1 2 8 ! 55 8 511122 1 1and 6 ! .33 6 9369
Chapter 2Fractions and Mixed Numbers: Multiplication and Division222multiplies 8 by , and 8 33332 8 2 16multiplies 8 by . So 8 ! ! 23 1 3 327 ! 1 7 ! 1 1 7 1 # & # ' & 72.8 " 2%8 " 2 2% 8 466. 8 !17 4 7 ' 8 1 242 8 3and 8 ! 12.3 1 2212717167. 54 2 9 54 ! 3 9 27 921 3721 2 27 1 3! 7 9 7171294001 22468. 48 3 8 48 ! 8 8 16 856 8756 3 216 1 2 ! 7 8 725647121113 6 5 3 7 5 7 5 7 ! ! ! ! 5 7 3 5 6 3 10 3 62170.222! 75. ! 63 9 ' 4 63 ' 4 ' 4 ! 7 ' 4#&#" 8 4 &%#" 2 &%" 8 9%169.2! 74. ! 5 2 5 ' 3 ! 5 5 ' 5#&#" 12 3 &%#" 8 &%8 8" 12 2 %116243 12! ! ! 3 373. 2 8 2 ' 3 3#" 5 3 &%#" 5 8 &%#" 20 &% 20 ' 2017 7 4 49 4 ' ' ' 492 2 1 4 1221115 35 1 5 16 1 2 1 1 ! !! ! 8 16 4 8 35 4 7 4 1417322! ! ! 76. 25 50 '8 # 25 ' 9 & '8 3 '8#" 3#" 2 &%9 &%" 3 50 %212! 3 9 3 3 999 71. # & ' 14 8 8 14 64 14" 8%9 1492 '7 7 ' ' 64 92 ' 32 932223 3 8 9 8 ' ' ' 182 2 1 4 1170
Section 2.54215 " 2 %20 15 " 2 2 % 2077.! ' ! ! 16 # 3 &21 16 # 3 3 '& 213 16 385. 16 ! ! 124 1 4115 4 20 3 !5 420 ! ! 16 9 21 4 ! 4 3 ! 3 215 20 5 21 !12 21 12 205 3 !7 7 ! 3 ! 4 4 ! 5 16The stack will be 12 in. high.65 24 586. 24 ! ! 3041 41Yes, the books will take up only 30 in.928 " 3%13 8 " 3 3 % 1378.! ' ! ! 27 # 4 &18 27 # 4 4 '& 188 9 138913 ! ! 27 16 18 3! 9 2 ! 8 18 Division of Fractions and Applications2 18 387. (a) 18 ! 273 1 2127 commercials in 1 hr1 13 1 18 1 3! 63 ! ! 6 18 6 13 6 13 13(b) 27 24 648648 commercials in 1 day1 20 2 ! 402 1 140 commercials in 1 hr288. (a) 20 9 1 9 879. ! 184 8 4 11(b) 40 24 960960 commercials in 1 day280.4 1 4 6 ! 83 6 3 189. (a)1182 36 381. 36 ! 5431 2111 240,000! 240,000 !10101240,000 10 24,000The down payment is 24,000.8000Li wrapped 54 packages.22 24,000! 24,000 ! 16,0003312013 60 482. 60 ! 8041 3Ricardo’s mother will pay 16,000.1(b) 24,000 16,000 8000Ricardo will have to pay 8000.She can sell 80 parcels of land.83 1 3 1683. ! 24 cups of juice2 16 2 1(c) 240,000 24,000 216,000He will have to finance 216,000.1255 15 10084. ! 125 cm4 100 4 1171
Chapter 290. (a)Fractions and Mixed Numbers: Multiplication and Division711 18,000! 18,000 !1212118,000 12 1500The down payment is 1500.111 42 792. (a) ! (24 18) ! (42) !666 11Josh has read 7 pages.(b) (24 18) 7 42 7 35He still must read 35 pages.75011 1500! 1500 ! 750221217 1 7 893. ! 144 8 4 1Althea’s parents will pay 750.1(b) 1500 750 750Althea will have to pay 750.She can prepare 14 samples.2(c) 18,000 1500 16,500She will have to finance 16,500.7 1 7 1694. ! 148 16 8 11391. (a)Tony must make 14 strikes.1 9 3! 3 4 495. The length is 12 ft, because1She plans to sell(b) She keeps13123acre.430 5 30 2 5 ! 6 2 12 ! ! 122 1 51 5 14m, because78 12 !4 148 14 ! ! 1 141 2 !7 72of the land.396. The width is2 9 31! or 1 acres3 4 22Problem Recognition Exercises: Multiplication and Division ofFractions1. (a)8 6 8 3 ! 2 16! ! 3 5 3 552. (a)10 12 10 3 ! 4 40! ! 3 773 7(b)6 8 3 ! 2 8 16! ! 5 35 3 5(b)12 10 3 ! 4 10 40! ! 7 3773(c)8 6 8 5 2 !4 520 ! ! 3 5 3 63 2 !3 9(c)10 12 10 72 !5 735 ! ! 3 73 123 2 ! 6 18(d)6 8 6 3 2 !3 39 ! ! 5 3 5 85 2 ! 4 20(d)12 10 12 32 !6 318 ! ! 737 107 2 !5 3572
Problem Recognition Exercises: Multiplication and Division of Fractions9 12 9 3! 4 9273. (a) 12 ! ! ! 8 1 81 2! 427. (a)(b)99 129 3! 4 27!12 ! ! 88 1 2! 4 12(b)(c)12 (d)99 13 !3 13 12 ! ! 88 128 3 ! 4 329 12 8 3 ! 4 832 ! ! 8 1 91 3 !3 333 15 3 3! 5 9!15 ! ! 955 1 5 11(c)3 15 5 3 !5 5 2515 ! ! 255 1 31 3 1(d)33 1 3 11 15 ! ! 55 15 5 3 !5 255. (a)(b)1 2 1613 4 ! 2 !2 ! ! !12 3 21 3 ! 4 2212 211 2 16 1 3 21 ! !(d)12 3 21 12 2 161 3 21 21 ! ! 3 ! 4 2 16 1288. (a)5 5 25! 6 6 365 6 1! 16 5 1(c)5 5 5 6 1 ! 16 6 6 5 1(d)5 6 5 5 25 ! 6 5 6 6 361 2 16 1 2 21! ! !12 3 21 12 3 161 2 3 !7 7 ! ! 12 3 2 !8 96(c)3 15 3 3! 5 3 94. (a) 15! ! ! 95 1 51 5 1(b)1 2 161 2 4 !48! ! ! ! 12 3 21 3! 4 3 21 189(b)1 7 2 1 7 3 1 7 3 7! ! ! !! 2 9 3 2 9 2 2 3 ! 3 2 12(c)1 7 2 1 9 2 1 3 !3 2 3 ! ! ! !! 2 9 3 2 7 3 2 7 3 7(d)1 7 2 1 9 3 27 ! ! 2 9 3 2 7 2 289. (a)(b)9!0 089(b) 0 ! 089(c) 0 Undefined898(d) 0 0 ! 0896. (a)(c)(d)731 7 27! ! 2 9 3 2791 9 6 1!6! ! !104 10 1 49 2 !3 127 !! 10 1 2 ! 2 2091 9 6 4!6 ! !104 10 1 19 2 ! 3 4 108 !! 52 !5 1 191 9 1 1 6! ! !104 10 6 43! 3 1 1 3 !! 10 2 ! 3 4 8091 9 1 4 6 ! !104 10 6 13! 312!2 3 !! 152 !5 2 ! 3
Chapter 210. (a)(b)(c)(d)Fractions and Mixed Numbers: Multiplication and Division4 12! 2110 2! !10 !! 5 205 2 ! 10 1514. (a)4 14 1 11! 10 !! 5 205 4 !5 10 250(b)4 14 20 2 ! 5 160 !10 ! ! 5 20115 1 1604 14 20 1 10 ! !5 205 1 102! 2 4! 5 18 !! 1 2 !5 55(c)(d)111 2 !8 142 ! 4 ! 4 ! 16 ! !6661 2 !38 3116(b) 42 4 ! 4 16 ! 16 ! 6 9666115. (a)22!1 332 2(b) 1! 3 322(c) 1 3323 3(d) 1 1! 32 211. (a)12. (a)6 10 11 1 1 2 ! 77 2 1411 2 2!2 ! 77 1 71 1 1! 7 2 141 1 1 2 2 ! 7 2 7 1 72(c)" 1%4 1 1 4414! ' ! ! 1 6 6 36 4 ! 9 9# 6&2(d)6 12 !3 13! ! 1 101 2 !5 5! 1 4 ! 1 1 4 ! 1 4 # & # ' & # &1 " 6 6 % 1 " 36 %" 6%4 36 ' 1441 1216. (a)10 1 2 !5 15(b) 10 6 ! ! 1 61 2 !3 3(c) 6 !10 60(d) 10 ! 6 60! 1 2 1 1 2 1#" 2 &% ' 3 2 ' ' 3 622! 1 2 1 1 3 3(b) # & ' ' 3 2 2 2 8" 2%2113. (a) 8 8 ! 4 3241 8(b) 8 ! 24 4(c) 8 4 2(d) 8 ! 4 32(c)1 " 2%1 2 2 2! ' ! ! 2 # 3&2 3 3 92(d)741 ! 2 1 ! 2 2 1 4 # & # ' & 2 " 3%2 " 3 3% 2 91 9 9 ' 2 4 8
Section 2.6Section 2.6Multiplication and Division of Mixed NumbersMultiplication and Division of Mixed NumbersSection 2.6 Practice Exercises4 1 ! 7 4 1111. 1 7771. Chapter Review Exercises, pages 157 160Chapter Test, pages 160 161Cumulative Review Exercises,pages 161 162Answers will vary.1 4 ! 8 1 3312. 4 88815 252.! 6 9 2713. 63213 10 26! 3.5 991213120 10 20 32 ! 4.939 10 3642 7 42 2 12 ! 5.11 2 11 7 111915. 4 39!36393415121531!211!101421115252 14 2 13 ! 7.1818 13 18 9! 2 "! 1 " 12 37 37' 17. # 2 # 3 5% 5 &% 12 & 5 121175 37!3528. 1. Multiply the whole number by thedenominator.2. Add the result to the numerator.3. Write the result from step 2 over thedenominator.2 3 ! 5 2 179. 3 55510. 256516. 2812514. 11 57!55213232 1 86. 4 ! 1515 4 151277!617!1257 2 ! 10 7 27 10101075 725
Chapter 2Fractions and Mixed Numbers: Multiplication and Division13312192 39!219!181 1912115221 5 7 5 519. 2 ! ! 3 7 3 7 31 12312 7217112 372145!145!418 3! 2"26. 2 % # 3 # 83 1& 3'1 4 49 4 720. 6 ! ! 8 78 7 232 7!619! 1 29 10 14525. # 7 & '10 ' 4 12" 4%113 5!322! 2 ! 1 26 2724. # 8 & # 2 & ' 183 13" 3 % " 13 %! 1 "! 3 " 26 15 39' 18. # 5 # 3 2% 5 &% 4 & 5 4527. 4 ! 0 0811228. 0 ! 61 0101! 1 ! 1 7 15 15129. # 3 & # 2 & ' 722" 2% " 7% 2 71238 921. 4 ! 9 ! 3899 1111! 3 ! 1 13 5 13530. # 1 & # 1 & ' 18" 10 % " 4 % 10 4 82110 622. 3 ! 6 ! 2033 12111! 2 ! 2 ! 4 27 2 9 54431. # 5 & # & # 1 & ' ' 225" 5 % " 9 % " 5 % 5 9 5 25! 3 ! 1 83 16 8323. # 5 & # 5 & ' 3" 16 % " 3 % 16 311273 83!623!212 27237111! 1 ! 3 ! 8 49 11 8 77132. # 6 & # 2 & # & ' ' 198 4 744" 8% " 4% " 7 %76
Section 2.6Multiplication and Division of Mixed Numbers121 1 13 1 13 244. 6 ! 132 2 2 2 2 173 17 11 17 4 34! 33. 1 2 104 10 4 10 11 551534. 51725121 2 4 2 4 7 14245. 1 ! 43 7 3 7 3 2 331 3 51 3 51 4 344 ! 610 4 10 4 10 3 551311 5 15 5 15 13 394! 546. 2 7 13 7 13 7 5778 1 53 4 53 3 53535. 5 1 ! 49 3 9 3 9 4 12121317 2 7 1 7347. 3 2 ! 122 1 2 2 44143 64 13 64 5 641236. 12 2 ! 455 5 55 13 13131214 3 14 1 14548. 4 3 ! 133 1 3 3 99811 5 17 5 16 406 237. 2 1 !2 16 2 16 2 17 17172319 849. 4 ! 8 ! 3844 112137 38 19 38 12 244 ! 438. 7 1 5 12 5 125 1955Tabitha earned 38.11350028 10,50050. 2 ! 10,500 ! 28,000331211 9 9 9 439. 4 2 ! 224 2 4 2 91115The land will cost Kurt 28,000.517257 25 12851! 64251. 25 ! 25 102210 151 35 7 35 3 51 ! 240. 5 2 63 6 36 7 22212741. 0 6 012Average Americans consume 6425942. 0 1 0112123 20 63 105! 10552. 6 !15 3413 4115 1 17 1 17 643. 2 ! 176 6 6 6 6 11Kayla is paid 105.1771lb.2
Chapter 2Fractions and Mixed Numbers: Multiplication and Division121 6 9 6 8 16159. 6 1 ! 58 1 8 1 9 333 1 7 1 7 453. (a) 1 ! 7 weeks old4 4 4 4 4 1311 1 17 1 (b) 2 8 4 8 41 8 7 8 3 24360. 8 2 ! 33 1 3 1 7 77117 4 171 ! 8 weeks old8 1222192 7 2 27 94!2 ! 161.3 10 3 10 551137 3 7 1 754. 1 3 ! 44 1 4 3 127Each child will inherit million.12514 1 4 41 41562.!5 ! 63 8 3 866217 28 41 28 24 672 ! 24 1 24 1 41 4116 164116The roll is 16ft long.4155. 28 163. 41!0 0122116 664. 5 ! 6 ! 3233 1177171 1456. (a) Lucy: 35 ! 14 " 49722 1121 9 21 1 71! 165. 10 9 22 12 9 66135185 10Ricky: 42 ! 10 " 42522 166.497 425 72Lucy earned 72 more than Ricky.267. 0 9 031(b) 497 425 922Together they earned 922.1131 3 5 3 2368. 2 ! 82 8 2 8 5 202411 11 11 11 10! 257. 2 1 5 10 5 10 5 1112 8 2 17 34!1 ! 7 9 7 9 6331 12 1 31! 169. 12 ! 8 1 8 221523 5 15 11 557! 658. 3 ! 1 4 6 4 68842 20 2 82! 270. 20 ! 151 15 332378
Section 2.6Multiplication and Division of Mixed Numbers3871. 6 0 is undefined.91172. 0 ! 2 08131221179. 12 ! 25 3183845 281211180. 38 12 3321513511881. 56 3 17661974. ! 1 ! 4 ! 14 31 11 14#" 5 6 &% #" 1 7 &% #" 33 &% 6 ' 7 '3362 314 318 9911182. 25 !18 4665251 11 57 4 9 75. 7 1 2 834 8 3 4191113183. 3257 3 4 193 ! ! 28 4 9 88 113185. 11 ! 41 480248225 7 16 10 5!! 8 40 21 24 1217199 12 21261461540484. 106 41 296753155 25 40 2176. 3 5 1 87 16 87 16581It takes 3 gallons of gas for Sara to get toand from work.3 5 15It costs Sara 15 each day.73. ! 2 ! 7 ! 3 17 7 15 21' #" 3 5 &% #" 34 &% #" 3 4 &% 5 '834 4 111 129 43 129 2 ! 378. 64 21 22222 4381586. 9 ! 28 2809327377. The perimeter of the garden is2(20) 2(15) 40 30 70 ft.141 70 5 70 470 1 ! 564 1 41 5156 bricks will be needed.56 3 168The total cost is 168.79
Chapter 2Fractions and Mixed Numbers: Multiplication and DivisionChapter 2Review Exercises13416. 7 941!724!2131!283Section 2.11.122.4753(b) Improper3. (a)16(b) Proper6.18. 21, 51, 1200237or 28819. 55, 140, 260, 120020. 58, 124, 140, 260, 1200717.or 16621. Prime1 6 ! 7 1 438. 6 77722. Composite44 4 112 11 ! 5 2 579. 11 55523. Neither24. Neither11 1 17 1 17 410. 4 ! 174 4 4 4 4 125. 22222112.60Section 2.2715511. 9 47!452376017. 26 1582!15622!0224. (a)5.1345292481632642 ! 2 ! 2 ! 2 ! 2 ! 2
Composite 3 19 57 37. Prime 38. Prime 39. Neither 40. Neither 41. Composite 11 11 121 42. Composite 3 23 69 43. Prime 44. Prime 45. Composite 3 13 39 46. Composite 7 7 49 47. There are two whole numbers that are neither prime nor composite, 0 and 1. 48. False; the square of a
Fractions Prerequisite Skill: 3, 4, 5 Prior Math-U-See levels Epsilon Adding Fractions (Lessons 5, 8) Subtracting Fractions (Lesson 5) Multiplying Fractions (Lesson 9) Dividing Fractions (Lesson 10) Simplifying Fractions (Lessons 12, 13) Recording Mixed Numbers as Improper Fractions (Lesson 15) Mixed Numbers (Lessons 17-25)
(a) Fractions (b) Proper, improper fractions and mixed numbers (c) Conversion of improper fractions to mixed numbers and vice versa (d) Comparing fractions (e) Operations on fractions (f) Order of operations on fractions (g) Word problems involving fractions in real life situations. 42
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
Estimating with Fractions and Mixed Numbers – all operations Add and Subtract Fractions and Mixed Numbers Multiplying Fractions and Mixed Numbers Dividing Fractions and Mixed Numbers Grade 7 (cont.) Ratios Unit Rates Proportions
10 IXL Practice SOL 6.4: The student will demonstrate multiple representations of multiplication and division of fractions. Multiply fractions: Multiply fractions -with models (Sixth grade V.5) Divide fractions: Divide by fractions -with models (Sixth grade W.1) Divide fractions: Reciprocals (Sixth grade - W.2) SOL 6.6.a: The student will multiply and divide fractions and mixed
counting unit fractions by folding fraction strips. Fifth grade fractions worksheets encourage your child to work with probability, mixed fractions, and number patterns. Try our fifth grade fractions worksheets. shading fractions worksheet tes. 6th Grade Fractions Worksheets Grade
Mixed Numbers & Improper Fractions Mixed Numbers- are a number that has a mixed number and a fraction. example: Improper Fractions- are fractions in which the numerator is larger than the denominator. example: You can easily go from a mixed number to an improper fraction .or an improper fraction to a mixed number. Let’s start by going from .
Understanding fractions Finding equal fractions Simplifying and expanding fractions Identifying improper fractions and converting it to a mixed number Identifying a mixed number and converting it to an improper fraction Highlights include the following: Fractions are a part of a whole.
