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 2 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. 504 224 2. Reduce, 1, and 1 432 7 504 to a common denominator. 8. How much is and and added together? 1 Which is greater, P* SECTION 29. 1. A farmer raised 142 bushels of corn in ne field, and 2371⁄2 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. 2. A faim is divided into three lots;— the first lot containing 46 acres, the second 50% acres, and the third 62 acres. 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 437 from 16592. 6. If 6 gallons of wine should leak from a cask containing 53 gallons, how many gallons would remain ? 7. Add together 623 and 113; 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 barrels to another. What quantity of flour had he then remaining? SECTION 30. : Suppose I have 16 dollars; to how many men can I 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 3 contained in 4? contained in 7?? Direction. Reduce and to a common denomina tor, and then divide one numerator by the other. 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 months, how many barrels will he drink in 10 SECTION 31. REVIEW. 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 $14, 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 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? how 13. (§ 25.) is equal to how many ninths? many thirty-sixths? how many seventy-fifths? 14. (§ 26.) Reduce the two fractions, 3 and 4, to their lowest terms, and then add them together. 15. (§ 27.) Suppose a farm to contain 98 acres of land; how many acres are there in 1⁄2 of the farm? 16. (§ 28.) Add together, and and 1; then subtract from the sum;- what is the remainder? 17. (§ 29.) If and of a number be subtracted from itself, what part of that number is the remainder? 18. (§ 30.) If the mail-stage run 95 miles in 1 hour, how many hours will it be in running 175 miles? RETROSPECTIVE OBSERVATIONS. A fraction is rendered greater by increasing the numerator, and smaller by increasing the denominator. To multiply a fraction by a whole number,- Either multiply the numerator, or divide the denominator. To divide a fraction by a whole number,- Either divide the numerator, or multiply the denominator. When a number is multiplied by 1, the product is equal to the multiplicand. Therefore, when a number is multiplied by a fraction, which is less than 1, the product must be less than the multiplicand. To multiply a whole number by a fraction,― Multiply by the numerator, and divide by the denominator. Dividing a number by 1, gives a quotient equal to the dividend. Therefore, dividing a number by a proper fraction, must give a quotient greater than the dividend, because, the fraction being less than 1, is contained a greater number of times in the dividend. To divide a whole number by a fraction,—Multiply by the denominator, and divide by the numerator. To multiply a fraction by a fraction,-Multiply numerator by numerator, and denominator by denominator. To divide a fraction by a fraction,-Multiply the numerator of the dividend by the denominator of the divisor, for a numerator; and multiply the denominator of the div idend by the numerator of the divisor, for a denominator 19 19. Multiply the fraction, 2, by 38. 203 23. Multiply the fraction, 16, by the fraction, 71. 26. What is the quotient of 45 SECTION 32. multiplied by 8? divided by 32? MISCELLANEOUS EXAMPLES. 1. Suppose a man can perform a journey in 14 days and 3 hours, travelling 9 hours a day; in what time can he perform the journey, travelling 11 hours a day? 2. A trader gave $75 for 56 gallons of wine, and lost 11 gallons by leakage. At how much per gallon must he sell the remainder, to get the whole cost? 3. Suppose a retailer to pay $165 for a ton of sugar, at what price must he sell it per pound, in order to gain 10 per cent. on the cost? 4. What quantity of salt, worth 62 cents per bushel, must be given in exchange for 258 pounds of pork, worth 9 cents per pound? 5. What is the profit on 400 hogsheads of molasses, purchased in New Orleans at 12 cents per gallon, [63 gal. in each hhd.], freighted to New York at $3.50 per hhd., and sold at 24 cents per gallon; 3gal. 2qt. having leaked from each hhd. on the passage? 6. If a pint of rum a day will kill a man in a year and a half, how many men would a cargo of 600 hogsheads kill in the same time? 7. If 11 young men can become fools by drinking 6 bottles of wine, at $3 a bottle, what would it cost a dinner party of 25, to become fools in like manner? 8. If a man's expenses be $1.40 a day, and his income $700 a year, what will he lay up in 7 years? 9. A and B are laborers-A earns $19.50 a month, and B earns $16.25; but A gives B of his earnings. What will each lay up in 14 months? 10. Find the difference between of 91, and 7 of 91. |