denominator of the fraction in the subtrahend, and we have a new fraction }}, which we write at the right hand of the other 9, thus, 9jf. We then multiply the numerator and denominator of the subtrahend by 7, the denominator of the minuend, and we have another new fraction, {}, which we place at the right hand of the other 3, thus, 3t. It will now be perceived, that we have changed the fractions 94 and 3} to other fractions of the same value, having a common denominator. We now subtract as in question 26th by adding 1 (15) to } }, which makes us, and from this we subtract f'}; thus, =, we then carry the 1 we borrowed to the 3, 1+ 3 = 4, which we take from 9, and find 5 remaining. The answer therefore is 54. 33. 34. 35. 36. 37. From 124 163 19% 971 8713 Take 94 54 154 1831 191 211 336 7811 6 782 38. 39. 40. 41. 42. From 191 157 915 7115 6142 Take 7 음 81 315 1.511 1372 43. From a hhd. of wine there leaked out 12 gallons, how much remained ? Ans. 50%. 44. From $10, $24 was given to Benjamin, $31 to Lydia, $ 14 to Emily, and the remainder to Betsey ; what did she receive ? Ans. $31. Note. If it be required to find the difference between two fractions, whose numerators are a unit, the most ready way will be to write the difference of the denominators over their product. 45. What is the difference between fand + ? OPERATION. 7-3= 4 Ans. 7 X3=21 46. Take from }, from 4, from 1, + from . 47. Take from 1, from , from 1, from 48. Take from }, + from }, I'y from t, it from . Section 23. MULTIPLICATION OF VULGAR FRACTIONS. I. To multiply a fraction by a whole number, or a whole number by a fraction. Multiply the numerator of the fraction by the whole number, and under the product write the denominator of the fraction. 1. Multiply by 15. This question may 1 x lé = 105 = 134 Ans. alyzed as those in com pound fractions. 2. Multiply 11 by 83. OPERATION, be an OPERATION. 11 X 2=9=76Ans. 3. If a man receive it of a dollar for one day's labor, what will he receive for 21 days' labor ? Ans. $ 77. 4. What cost 56lbs. of chalk at of a cent per lb. ? Ans. $ 0.42. 5. What cost 396lbs. of copperas at ii of a cent per lb. ? Ans. $3,24. 6. What cost 79 bushels of salt at of a dollar per bushel ? Ans. $ 693. 7. Multiply 376 by 17. Ans. 243 17. 8. Multiply 14 by 189. Ans. 16614. 9. Multiply 471 by it Ans. 10. Multiply 871 by 27. Ans. 2377. 11. Multiply 114 by 365. Ans. 353147 12. Multiply 867 by 136 Ans. 6336 II. To multiply a mixed number by a whole number, or a whole number by a mixed number. 13. Multiply 4 by 7. Ans. 325 8 . OPERATION. In performing this question, we say 7 times 3 fifths are 21 fifths, and 21 fifths are equal to 4. We write down the and carry the 4 to the product of 7 times 4= 32. Hence the following 324 Ans. RULE. Multiply the numerator of the mixed number by the whole number, and divide the product by the denominator of the fraction.; and, as many times as it contains the denominator, so many units must be carried to the product of the integers. If, after division, any thing remains, lei it be a numerator, and the divisor a denominator to a fraction to be affixed to the product. 14. Multiply 9by 5. Ans. 463. 15. Multiply 12by 7. Ans. 881 16. Multiply 814 by 9. Ans. 801 17. Multiply 7} by 10. Ans. 713. 18. Multiply 118 by 8. Ans. 949. 19. What cost 74 lbs. of beef at 5 cents per pound ? Ans. 3781. 20. What cost 237 bbs. flour at $6 per barrel ? Ans. $ 1411. 21. What cost 8yds. cloth at $5 per yard ? Ans. $ 417 22. What cost 9 barrels of vinegar at $ 6% per barrel ? Ans. $ 573. 23. What cost 12 cords of wood at $6.374 per cord ? Ans. $ 76.50. 24. What cost 11cwt. of sugar at $ 9% per cwt. ? Ans. $ 1031. 25. What cost 43 bushels of rye at $ 1.75 per bushel ? Ans. $7.653. 26. What cost 7 tons of hay at $ 117 per ton ? Ans. $83. 27. What cost 9 doz, of adzes at $ 10% per doz. ? Ans. $953. 28. What cost 5 tons of lumber at $3} per ton ? Ans. $ 153. 29. What cost 15cwt. of rice at $ 7.62; per cwt. ? Ans. $ 114.375 30. What cost 40 tons of coal at $8.374 per ton ? Ans. $ 335.00. III. To multiply simple fractions. 31. Multiply 1 by t. Ans. Tz: This question may be anal{ x = = 72 Ans. yzed in the same manner as in compound fractions. Hence the following OPERATION. RULE. CANCELLED. Х Multiply the numerators together for a new numerator, and the denominators together for a new denominator ; then reduce the fraction to its lowest terms. 32. Multiply by Ir. Ans. 11° OPERATION. 8 56 7 7 7 Ans. 8 11 88 11 11 11 33. Multiply & by . Ans. 1 34. Multiply 13 by . Ans. . 35. Multiply 19 by $3. Ans. } 36. Multiply 14 by 17. Ans. 1 37. Multiply by Ir Ans. T&T 38. Multiply by Ans. 39. What cost } of a bushel of corn at of a dollar per bushel ? Ans. I of a dollar. 40. If a man travels & of a mile in an hour, how far would he travel in }} of an hour ? Ans. I of a mile. 41. If a bushel of corn will buy To of a bushel of salt, how much salt might be bought for at of a bushel of Ans. At of a bushel. Note. If there be mixed numbers in the question, they must be reduced to improper fractions, and compound fractions must be reduced to simple fractions. 42. Multiply 43 by 63. corn ? 43. Multiply 7} by 84. Ans. 6076 44. Multiply 47 by 9. Ans. 457 's: 45. Multiply 114 by 8%. Ans. 9935. 46. Multiply 123 by 113. Ans. 1475. 47. What cost 7 cords of wood at $ 5% per cord ? Ans. $ 4131 48. What cost 7 yds. of cloth at $34 per yard ? Ans. $ 2513 49. What cost 64 gallons molasses at 23 cents per gallon? Ans. $ 1528. 50. If a man travels 34 miles in one hour, how far will he travel in 97 hours ? Ans. 3472 51. What cost 36110 acres of land at $ 25% per acre ? Ans. $ 9167313. 52. If of of a dollar buy one bushel of corn, what will 7 of 1 of a bushel cost ? Ans. 17 of a dollar. 53. How many square rods of land in a garden, which is 971 rods long, and 494 rods wide ? Ans. 481036 rods. 54. If of 4 of is of an acre of land cost one dollar, how much may be bought with of $ 18 ? Ans. 167 acres. Note. The following questions are to exercise the foregoing rules. 55. What are the contents of a field 76,25 rods in length and 18 rods in breadth ? Ans. 8A. 3R. 304p. 56. What are the contents of 10 boxes which are 7 feet long, it wide, and 14 feet in height? Ans. 16917 cubic feet. 57. From 11 of an acre of land there were sold 20 poles and 200 square feet. What quantity remained ? Ans. 2R. Ip. 227 ft. 58. What cost 7 of an acre at $ 1.75 per square rod ? Ans. $ 236.9215 59. What cost is of a ton at $ 154 per cwt. ? Ans. $ 49.731%. 60. What is the continued product of the following numbers 143, 114, 5%, and 101 ? Ans. 9184. 61. From Ty of a cwt. of sugar there was sold of it; what is the value of the remainder at $0.12 per lb. ? Ans. $3.57. |