34. Change 91 pounds, to pounds, ounces, and drams. 35. Reduce of a mile to furlongs, rods, feet, &c. 36. In 10 acres, how many acres, roods, rods, &c. 37. How many dimes, cents, and mills, in of $1? 38. In of a dollar, how many cents and mills? 39. Suppose sugar to be $12 per hundredweight, what quantity can be purchased for $113? SECTION 28. COMMON DENOMINATORS. When two or more fractions have the same number for a denominator, this number is called their Common Denominator. Fractions having different denominators, must be reduced to a common denominator, before addition or subtraction can be performed on them. RULE FOR REDUCING FRACTIONS TO A COMMON DENOMINATOR. Multiply each numerator into all the denominators except its own, for a new numerator. Then multiply all the denominators together for a common denominator, and place it under each new numerator. 1. Reduce,, and, to a common denominator. 4 10 2. Reduce, 1, and 3. Reduce and to 4. Reduce! 1 and 5. 2949 Reduce 4 1 2 ,,, and 6. How much is 2 and 432 504 504 to a common denominator. 7. How much is 12 and 1 added together? 1 P* SECTION 29. 1. A farmer raised 1427 bushels of corn in ne field, and 237 bushels in another. How many bushels did he raise in both fields? The learner may reduce the fraction in his answer, to its lowest terms, in this, and all future examples. 62 acres. 2. A farm is divided into three lots;― the first lot containing 46 acres, the second 50% acres, and the third How many acres are there in the farm? 3. Add together 441 and 65 and 255613. 4. If 6 be taken from 8 how much will remain ? 5. Subtract 4373 from 1659. 6. If 6 gallons of wine should leak from a cask containing 53 gallons, how many gallons would remain ? 7. Add together 623 and 11372; and then subtract from the sum 4502. 8. Three soldiers shared a loaf of bread as follows:the first took of it, the second took of it, and the third took the remainder. What fractional part of the loaf did the third soldier receive? 9. A trader having 25 barrels of flour, sold 8 barrels to one man, and 911⁄2 barrels to another. What quantity of flour had he then remaining? I SECTION 30. Suppose I have 16 dollars; to how many men can give of a dollar apiece? 2. How many times is contained in 16? 3. How many pairs of gloves can I buy for 18 dollars, the price being of a dollar a pair? 4. Divide 18 by ; that is, reduce 18 to fourths, and find how many times 3-fourths is contained therein. 5. Divide 46 by ; that is, find how many times the fraction is contained in 46. 6. If a man walk 1 mile in of an hour, what distance will he walk in 4 hours? 7. How many times is 8. How many times is 3 contained in 4? contained in ?? Direction. Reduce and to a common denomina tor, and then divide one numerator by the other. 3 9. How many times is contained in ? 10. How many barrels of flour can be bought for 38 dollars, at 4 dollars per barrel? 11. How many times is 25 contained in 912? 12. How many times is 6 contained in 42? Direction. Reduce the two fractions to a common denominator; then reduce the mixed numbers to improper fractions, and divide one numerator by the other. 13. If a barrel of cider will last a man 3 how many barrels will he drink in 10 SECTION 31. REVIEW. months? months, 1. (§ 13.) Suppose a man to earn 95 cents per day, how many days would it take him to earn $43.16? 2. (§ 14.) How many pounds of sugar can be bought for $145, when the price is of a dollar a pound? 3. (§ 15.) If 1 yard of silk cord cost of a dollar, what is the price of 75 yards, at the same rate? 4. (§ 16.) If 14 yards of cloth be cut from a piece containing 52 yards, how much will be left? 5. (§ 17.) If a pound of shot cost of a dollar, what will be the cost of 17 pounds, at the same rate? 6. (§ 18.) How much corn will grow on 140 acres of land; allowing each acre to produce 34 bushels? 7. (§ 19.) If a man's expenses be $46.247 for 12 of a year, what will be his expenses for 1 year? 8. (§ 20.) of 71 is equal to what improper frac tion? Then of 71 is equal to what mixed number? 9. (§ 21.) Suppose 42 men to share equally in a prize of $1000; what is the share of one man? 10. (§ 22.) If a man can cut 46 cords of wood in 14 days, how many cords can he cut in 60 days? 11. (§ 23.) Suppose a man can build a mile of wall in 310 days; in what time can he build of a mile ? 12. (§ 24.) A man bought a quantity of flour, for domestic use, and in 36 days he found that of it was consumed. How long would the whole last? 50. What is the interest of $21, for 2 months, at 7 per cent. per annuni? 51. What is the interest of $4291, for 3 months, at 5 per cent. per annum? 52. At 4 per cent. per annum, what is the interest of $122.75 for 4 months? for 5 months? for 6 months? for, 7 months? for 8 months? for 9 months? for 10 months? What is the amount for 11 months? 53. What is the interest of $14.50, for 1 year and 1 month, at 6 per cent.? 54. What is the interest of $19.25, for 3 years and 2 months, at 8 per cent.? 55. What is the amount of $458, for 2 months, at 7 per cent.? years and 3 56. What is the amount of $8.75 for 5 years and 4 months, at 4 per cent.? 57. What is the amount of $91.50, for 2 years and 7 months, at 8 per cent.? 58. What is the interest of $81, from February 7, 1832, to August 7, 1835, at 6 per cent.? 59. Suppose a promissory note of $145, to be dated, January 15, 1831; what will be the amount of that note, October 15, 1834; the rate being 6 per cent.? At 60. A owed B $96, on interest at 6 per cent. the end of 2 years, A paid the interest then due, and $25 of the principal: at the end of 3 years and 11 months, he paid the whole debt. What was each payment? 2 When interest is to be computed for any number of days,- First find the interest for 1 month; then take 30 of a month's interest for 1 day; or 15 for 2 days, 35 or 10 for 3 days; or for 4 days; or for 5 days; or for 6 days; and so on. 30 6 In the following operations, in this section, all fractions of a cent may be disregarded: this being the common practice in business. 61. What is the interest of $231, for 7 days, at 6 per cent. per annum? Direction. First find the interest for 1 year; then for f of a year or 1 month; and then for of a month. 62. What is the interest of $75, for 10 days, at 6 per cent. per annum ? 63. What is the interest of $254 for 21 days, at 6 per cent. per annum? 64. What is the interest of $110, for 5 months, and 8 days, at 6 per cent. per annum ? 65. What is the interest of $34 for 1 year, 3 months, and 25 days, at 6 per cent. per annum ? 66. What is the interest of $91.18, for 3 years, 2 months, and 13 days, at 6 per cent. per annum ? Several other methods are practised by merchants, in computing interest; among which, are the following. When the rate is 5 per cent.-Divide the principal by 20, and the quotient is the interest for 1 year. 67. What is the interest of $4207, for 2 years, at 5 per cent. per annum ? 68. What is the interest of $951.17, for 4 years, at 5 per cent. per annum ? When the rate is 6 per cent.-Multiply the principal by half the number of months in the time, divide the product by 100, and the quotient is the interest. 6 6 4 69. What is the interest of $119, for 16 months, at per cent. per annum ? 70. What is the interest of $96.48, for 10 months, at per cent. per annum ? 71. What is the amount of $27.56, on interest 6 months, at 6 per cent. per annum? 72. What is the interest of $133.24, for 11 months, at 6 per cent. per annum? To find the interest for DAYS, the rate being 6 per cent. Multiply the principal in dollars by the number of days, divide the product by 6, and cut off one figure from the right of the quotient. The rest of the quotient figures express NEARLY the interest, in cents. 73. What is the interest of $249, for 75 days, at 6 per cent. per annum? 74. What is the interest of $5824, for 21 days, at 6 per cent. per annum ? |