9. (§ 21.) A ship's crew used 14 casks of water, during a passage of 5 months, from Calcutta to New York. How much did that quantity allow them per month? 10. (§ 22.) If 7 barrels of flour cost 30 dollars, what will 9 barrels cost at the same rate? 11. (§ 23.) A man purchased a farm, containing 98 acres; but not being able to pay for the whole, he sold off of the land. How many acres did he sell? 12. (§ 24.) If a mill grind 9 bushels of corn in & of an hour, how many bushels will it grind in 1 hour? 13. (§ 25.) If pen-knives are worth of a dollar apiece, and pencils 20 of a dollar apiece, how many pencils must be given in exchange for 3 knives? 14. (§ 26.) Reduce to its lowest terms. do you reduce a fraction to its lowest terms? How 15. (§ 27.) A man, owning of an acre of land, sold of what he owned. What part of an acre did he sell? 16. (§ 28.) Change and to a common denomina tor. How do you change fractions to a com. denom. › 17. (§ 28.) John gave of a dollar for a book, and of a dollar for a slate, and then sold them both for of a dollar. Did he gain or lose?- How much? 18. (§ 29.) 23 tons of it. A farmer cut 183 tons of hay, and sold 19. (§ 30.) When coffee is of a dollar per pound, how many pounds can be bought for 1⁄2 of a dollar? 20. (§ 30.) A tenant raised 583 bushels of corn, gave his landlord of it for the use of the land. many bushels had the tenant for himself? SECTION 32. MISCELLANEOUS EXAMPLES. and How 1. The Gulf Stream is a current in the ocean, running 3 miles an hour. If a steam boat, whose engine propels her 12 miles an hour, should run in the stream, with the current, what distance would it move in 8 hours? 2. If the above steam boat were running against the current, what distance would it move in 8 hours? 3. A trader bought 25 barrels of flour, paying 7 dollars a barrel for 11 barrels of it, and 9 dollars a barrel for the remainder. What did the whole cost? 4. What sum of money must be divided among 10 men, so that each man shall receive 194 dollars? 5. Suppose a man can perform a journey in 8 days, travelling 10 hours a day,-in how many days can he perform it, travelling 12 hours a day? 6. Henry reads 12 pages in the same time that Willam is reading 7 pages; how many pages will Henry read while William is reading 60 ? 7. If 72 dollars be divided equally among 9 sailors, how many weeks' board, at 3 dollars a week, will each sailor's share pay for? 8. A man failed in trade, and could pay only 4 dollars on every 9 dollars that he owed. How much did he pay on a debt of 100 dollars? 9. There is a pole standing in a pond, so that of it is under the water, and 3 feet of it is above the water. How long is the pole? 10. A pole is standing so that of it is in the mud, of it is in the water, and 2 feet of it is above the waWhat is the length of this pole? ter. 11. If A borrow of B, 8 bushels of wheat, when the price is 9 shillings a bushel; how much wheat must A return, when the price is 7 shillings a bushel? 12. A trader, having 100 dollars, laid out of his money for narrow-cloth at 5 dollars a yard, and the remainder for broad-cloth at 7 dollars a yard. How many yards did he buy of each sort? 13. If 2 bushels of apples will fill a barrel, how many bushels will it take to fill 8 barrels ? 14. John can pick a quart of berries in an hour; Ann can pick twice as fast;-how many can both pick in an hour? In what time would they pick 10 quarts? 15. How many bushels of corn must a miller grind, to get 1 bushel for himself—allowing, that he takes 2 quarts from every bushel before grinding it, and, that 32 quarts make a bushel? Suggestion. He gets 2 qts. for grinding less than a bush. Η 16. If 1 monitor can mend 2 pens in a minute, how long will it take 3 monitors to mend 28 pens? 17. It is worth as much to pasture 1 cow, as 5 sheep. If I pay 1 dollar a month for pasturing a cow, what must I pay for pasturing 35 sheep, 7 months? 18. If 3 horses eat 1 ton of hay in 1 month, how long will 5 tons last 4 horses? 19. A drover sold a cow for 20 dollars, and, in so doing, he gained a sum equal to of what he had paid for the cow. How much had he paid for her? 20. Suppose a man,can dig a trench in 4 days, and a boy in 6 days;- what part of it can each dig in 1 day? What part of it can both together dig in 1 day? In what time can they both finish it? 21. Suppose a cistern has one tap that will discharge it in 5 hours, and another in 7 hours,-in what time will they both discharge it? 22. If 1 man can perform a piece of work in 35 days, in what time can 6 men perform it? 23. If 4 men drink a barrel of cider in 20 days, in what time will 9 men drink the same quantity? 24. If 9 men can do a piece of work in 5 days, in how many days will 7 men do the same work? 25. A farmer kept his sheep in four pastures-In the first pasture he had of his flock; in the second, f; in the third, ; and in the fourth he had 32 sheep. How many sheep had he? 26. There is a school, in which of the scholars read in the Classical Reader, read in the National Reader, read in Pierpont's Introduction, and 36 little boys read in the Young Reader. How many scholars are there in the school? 27. If a post 4 feet high cast a shadow 3 feet, at noonday, what is the height of a steeple, that casts a shadow 90 feet, at the same time. 28. A and B are laborers-A earns 10 dollars a month, and B 9; but A gives of his earnings to B. What will each lay up in 3 months? 29. If 12 men can perform a piece of work in 6 days, in what time would 10 men perform the work? 30. How many men must be employed, to dig a trench in 3 days, that 6 men can dig in 4 days? 31. Suppose 2 men start from the same place, and travel in opposite directions, one at the rate of 5 miles an hour and the other as fast;- how far apart will they be in 11 hours? 32. A fox has 35 rods the start of a greyhound, but the hound runs 10 rods while the fox runs 7. How many rods must the hound run to catch the fox? 33. A started on a journey, and travelled 5 miles an hour-B started on the same journey, 2 hours after, and travelled 7 miles an hour. In how many hours 71⁄2 did B overtake A? 34. A jockey paid 9 times as much for his horse as he did for his saddle; he paid 3 times as much for his saddle as he did for his bridle; and for his bridle he paid 5 dollars. What did the whole cost? 35. Suppose a man can reap of a field of wheat in a day, and his son can reap of it in a day;- what part of it can they both reap in a day? In what time can they both reap the whole? 36. A boy being asked how much money he had, replied, "If I had as much more, and as much more, and as much more as I really have, I should then have 70 cents.' How much must he have had? 37. A gentleman paid 85 dollars for 5 weeks' board of himself, his son, and one servant, at a hotel- His own board cost twice as much as his son's, and his son's cost three times as much as the servant's. What was the expense of each, per week? 88 NOTE TO TEACHERS. The teacher should now be provided with "A KEY TO THE NORTH AMERICAN ARITHMETIC," otherwise he must lose much time in examining operations. The KEY is a small book designed exclusively for teachers, and contains answers to all the examples in the Written Arithmetic. If the KEY cannot be obtained at every place where the Arithmetic is for sale, it may still be obtained from the publishers of the Arithmetic, and from the principal book-stores in the larger cities and towns. A variety of expedient methods may be pursued, in examining written operations in arithmetic; and perhaps no one system can be adopted, from which it will not be found advantageous, occasionally, to depart. My own practice for several years, with occasional variation, has been as follows. A certain number of examples having been assigned for a lesson the day previous, each scholar is supposed to be prepared with the solutions upon his slate, and the class are paraded for recitation. Every scholar passes his slate into the hands of the scholar next above him, except the head scholar, who hands his to the foot scholar. The first scholar then reads from the slate he holds, the answer to the first example; and the teacher, holding the key, declares the answer to be right, or wrong. When the answer has been pronounced right, it is the duty of every scholar who finds a different answer upon the slate he holds, to signify it, and the error is noted against the owner of the slate. The first example being disposed of, the answer to the second example is read by the second scholar, and disposed of in like manner. Thus the reading of answers goes through the class, and each scholar detects the errors of his neighbour. Individual scholars are occasionally called upon to explain their work in a particular example, and to give their reasons for the operation adopted. By this mode of examination, the work of a large class is particularly inspected, in nearly the same time that would be required to inspect the work of one scholar. Besides the advantage of despatch in this mode of examination, the exercise itself is beneficial to the pupils. Each scholar acts the part of an inspector--he is interested to be critical-he acquires a facility in deciphering the work of others and thus his perceptive powers are cultivated, and a habit of alertness is attained. Before the learners attempt to perform operations by figures, they should be able to write figures with facility, and to arrange them regularly. To attain this object, the arrangement of figures below, may be repeatedly copied upon the slate, until a good degree of despatch and accuracy is acquired. |
