do you reduce compound fractions to simple ones? Can you give one general rule for multiplying fractions, whole or mixed numbers, by fractions? DIVISION OF FRACTIONS. 5.- How do you divide a fraction by a whole number? a mixed number by a whole number? a whole number by a fraction? Explain, by an example, the method of dividing a fraction by a fraction, and give the rule. Give one general rule for dividing a fraction, a whole or mixed number by a fraction. How do you reduce complex fractions to simple ones? How do you find what part of one number another is ? LEAST COMMON MULTIPLE. - Define a multiple; a common multiple of two or more numbers; the least common multiple. When do you make use of the L. C. M.? Give and explain the first method of finding it; the second. What does the L. C. M. of prime numbers equal? COMMON DENOMINATOR. When are fractions said to have a common denominator ? In what operations upon fractions do we first reduce them to those having the same denominator? Can we change fractions to those of any denominator? How? (Ans. By dividing or multiplying the numerator by the same number by which we divide or multiply the denominator to produce the denominator required.) What denominator is generally chosen? Reduce a simple, a compound, and a complex fraction to those of the same denominator, explain the process, and give the rule. ADDITION AND SUBTRACTION OF FRACTIONS. - How do you add fractions of different denominators ? How do you subtract one fraction from another? How do you add mixed numbers? In subtraction of one mixed number from another, how do you proceed when the fraction in the subtrahend exceeds that in the minuend? G. C. D. AND L. C. M. OF FRACTIONS* D. of fractions? How do you find the L. How do you find the G. C. the G. C. D. of 4, § and 13, and explain. Find the L. C. M. of, §, and, and explain. 148. MISCELLANEOUS EXAMPLES. 1. Into strips of what widths may I cut cloth which is 36 inches wide, that none may be wasted, the width of the strips to be expressed in inches? 2. How many gallons in the largest vessel which will exactly measure 3 hogsheads, containing severally 128, 94, and 158 gal lons? * Optional, 3. What will 16 yards of cloth cost at $.53 a yard? 4. What cost 93 bushels of corn, at $.87 a bushel? 5. What cost 271 acres of land, at $313 per acre? 6 of 2 of 56 times what number equals 1? 7. I paid $.65 for 2 boxes of strawberries; what will be the cost of 45 boxes at the same rate? 8. What is my bill for 7 pear trees, $3 apiece for the trees, and $2 a dozen for setting? 9. What do I receive per pound by selling 15 pounds of coffee for $31? 10. of a man's property is in land, and is valued at $2324§; what is the value of his whole property? 11. Bought of an acre of land for $40.75; what would 1 acre cost at the same rate? 12. What costs 3 pieces of calico, 37 yards in a piece, at 194 cents per yard? 13. If 32 acres of land cost $1100, what costs 1 acre? 14. Sold my house and farm of 47 acres for $6150; allowing $3500 for the house, what did I receive per acre for the land? 15. How long will a barrel of flour last a family of 8 if it lasts 3 persons 4 months? persons, 16* What number is that from which if you take, the remainder will be? 17. What number is that to which if you add 97, the sum will be 124%? 18. What is that number to which if you add & of 261, the sum will be 147? 19. Bought 7 yards broadcloth at $5 per yard, 14 yards of kerseymere at $14 per yard, 43 yards of silk at $3 per yard, and yards of doeskin at $43 per yard, for which I gave in payment a $100 bill. What balance is due me? 20* I have paving stones 12 inches long and 10 inches wide, what must be the width of a walk which will just receive these stones, laid either lengthwise or widthwise? 21: What is the smallest sum of money which can be exactly paid in pieces of money worth either $.16 or $.12? 22. How long will 200 pounds of meat last 9 persons at the rate of 2 pounds a day for each person ? 23. What length of time would a man require to travel around the earth, the distance being 25000 miles, if he travel at the rate of 311⁄2 miles per day? 24. If a man can build 2 rods of wall in a day, how much can he build in 6 days? by 11? 26. What number is that of which exceeds 27. How many bushels of wheat can a man purchase for $2724, at 312 cents per bushel? 28. What is 29. What is ( of 4) (3 of 3)? 30. If I buy 125 bushels of corn at 413 cents per bushel, and sell it at 52 cents per bushel, what do I gain? 31. What number divided by equals 1254? 32. What are the contents of 3 floors measuring as follows: 13 square yards, 32 square yards, and 493 square yards? X33. The product of three numbers is 74; two of them are 84 and 6; what is the third? 34. Exchanged 42 tubs of butter, averaging 481⁄2 pounds, at 21 cents per pound, for 42 barrels of flour, at $93 per barrel, and received the balance in cash; required the balance. 35. I have three boxes of cloth, each containing 12 pieces, each piece containing 44 yards, weighing 33 pounds to the yard; what is the weight of the whole? 36. What will 423 quires of paper weigh at 3 pound per quire? 37. A grocer has five casks of raisins of the following weights: 115 pounds, 1172 pounds, 99 pounds, 100 pounds, and 1211 pounds; what is the average weight per cask? 38. What is the cost of the above at 83 cents per pound? 39. Owning of a paper-mill, I sold of my share for $1750; what is the value of the whole mill at the same rate? X 40. A man sold 50 yards of cloth at the rate of 14 yards for 2 dollars; what did he receive for it? 41 Mr. Gray raised 212 bushels of potatoes, of which h stored in 4 equal-sized bins; what did each bin hold? He sold the other at the rate of 3 bushels for 2 dollars; what did he receive for the potatoes which he sold ? 42. If of a ton of lead cost $134, how many ounces of gold at $194 per oz. will pay for one ton of lead? of a ton for 12 tons 43. When hay was $15 per ton, I gave of coal; what was the coal worth per ton? 44. If of a yard of cloth will pay for six hats worth $41 per dozen, what is the price of the cloth per yard? 45. If of an acre of land cost $280, what will 5g acres cost? 46. If a man walks 9 miles in 24 hours, how far will he walk in 4 hours? 47. At the rate of 4 miles an hour, what time will be re quired to walk 122 miles? 48. In 1860, I purchased sold in 1862 at 90 cents. cotton at 83 cents a pound, which i What did I gain on 1000 lbs. ? 49. If a man can earn $2 per day, how many days' work will he have to give for a suit of clothes, of which the coat cost $25, the pants $81, and the vest $51? 39 50* The longest canal in the world, is the Grand Canal in China; + to +14 + of its length is 331388 miles; what is its entire length? Ans. 650 miles. 51. If of of a ship cost $42,000, what is of her worth? 52. In a certain manufactory, of the operatives are Germans, Dutch, Scotch, English, Canadians, and the remainder, 140, native Americans; what is the whole number, and the number of each nationality? 8 53. of my money is in gold, of the remainder in silver, and the balance, $360, is in bank notes; how much money have I in all? + 54. If 17 boxes of raspberries cost $2.834, what part of a box can I buy for 12 cents? 55. If a body in falling descends 16 feet in the first second of time, three times 16 in the next second, and five times 16 feet in the third second, how far will it fall in three seconds? 56. Owing a man in Paris 1325 francs, I have shipped to him $375 worth of rice. If the franc is worth 183 cents, how much have I overpaid him in Federal money? 57. 7 oz. of gold are to be divided among 3 men and a boy,— the boy to have half as much as a man; what will each have? X58* If the wages of a man per month are $354, and if the wages of 3 boys are equal to the wages of 2 men, what will be the wages of 10 men and 30 boys for a month? 59. What is that number to which if g of itself be added the sum will equal 64? Ans. 40. 60* If from 5 times a certain number 193 is subtracted, and the remainder is 184, what is the number? 61. I sold my watch for $72, which was more than I gave for it; what did it cost me? 62. Bought a horse and saddle for $75, giving as much for the saddle as for the horse; what was the cost of each? 63. A boy, being asked the age of his dog, replied, "If of his age be added to his age, the sum will be 13 years." What was his age? 64. Being asked the age of his father, he said, "If 12 years were added to of his age, the sum would equal of his age." What was his age? Ans. 48 years. 65. Being asked his own age, he answered, "If added to of my age, the sum would equal What was his age? 2 years were of my age." Ans. 16 years. 66. A can build a wall in 3 days, and B can do the same work in 4 days. What part of the work can each do in one day! What part can both do in one day? In how many days car both do it working together? 67. C can do a piece of work in 5 days, and What time will be required for both to do it? Ans. 14 days D in 8 days Ans. 3 day |