17 Harry had of an orange, which he wished to divide equally between his two little sisters; can you tell me what part of an orange each one would receive? 18. Which is the most,,5 of 20, or ,25 of 40? 19. How many times can you draw of a gallon of cider from a barrel containing 30 gallons? How many times of ↑ gallon? How many times of a gallon? How many times of a gallon? 20. A man, failing in trade, is able to pay his creditors on ly $,33 on the dollar; how much will he pay on $3? On $4 On $12? On $13? On $300? 21. A man, failing in trade, was able to pay only $,163 on the dollar; how much would he pay on a debt of $4? $6? $10 $9? $20? $100? $600? 22. Two men bought a barrel of flour for $10; one gave $3. and the other $7: what part of the whole did each pay? What part of the flour must each have? 23. If 30 bushels of oats cost $10, what is that a bushel? What will 5 bushels cost? What will 20 bushels? 24. If 3 men mow a field in 8 days, how many men will mow the same in 2 days? In 1 day? In 4 days? 25. Two men, A and B, hired a pasture; A paid $3, and B $5; what fractional part of the whole did each pay? The profits from the pasture were $16; what was each man's share of the gain? 26. Three men, A, B, and C, are engaged in trade; A puts in $4, B $5, and C $6; they gained $60: what is each one's share of the gain? 27. Two men, A and B, hired a pasture for $12; A put in 1 cow 4 months, and B? cows 3 months: what ought cach to pay? 23. A merchant, hiving purchased a piece of broadcloth for $2 per yard, wishes to make 20 per cent. on it; what price must he ask for it? 29. William has (f a dollar, Thomas, and Harry; how many cents have ther in all ? 30. A merchant sold calico at $,22 per yard, and thereby gained 10 per cent.; what did it cost him per yard? 31. Harry, having of an orange, gave to Thomas, who gave of his part to his little brother, and kept the remainder himself; what part did he keep? How much is of? How much does of of from leave? 32. How much is 1 X of? (1) How much is 1 × & of Zi 33. What is the quotient of divided by ? 34. How much does exceed ,75? 35 How much does 36. How many strokes docs a regular clock strike in 2 hours? 3 h. 4 h.? 5 h.? 6 h.? 7h.? 8 h.? 9 h.? 10 h.? 11 h.? 12 h.? 24 h. ? 37. How many square feet in a board 12 inches wide, and 43 inches long? 36 in. long? 72 in. long? 38. What part of an acre of land is there in your father's garden, allowing it to be 4 rods long and 2 rods wide? 4 rods wide? 39. How many cord feet of wood are contained in a load 3 feet wide, 2 feet high, and of the usual length? How many feet in a load 6 feet high and 3 feet wide? 2 feet high and 6 feet wide? 4 feet high and 2 feet wide? 46 How many solid feet in a block 12 inches long, 12 inches thick, and 12 inches wide ? 12 inches long, 12 inches wide, and 6 inches thick? 41. How long will it take to count $1000, at the rate of 50 a. minute ? 42. What is the difference between 4 square feet and 4 fect square? 10 miles square and 10 square miles? 3 rods square. and 3 square rods? A parenthesis, enclosing several numbers, signifies that these numbers are to be taken together, or as one whole number; but, when performing subtraction and addition with these and other numbers, they may be taken either as before, or one by one, thus: (16+4) X3=60, read 16+4=20X360. ? A. 20. A. 2. A. 80, or 60+20. Or (163) 48. 43 12. Then, 48+ 1260, the same as befors 13. (9+3)+8= how many? 44. (9-3)-4= how many? 45. (155) X 4: how many 46. (155) X 4 = how many? 47. (93)÷3= how many? 48. (9-3)÷3= how many? 49. (12-8)÷(3+1)= how many? A. 40, or 60-20. A. 4, or 3+1. A line, or vinculum, drawn over numbers, is sometimes usen instead of a parenthesis. 50.48 x 12= how many? 9. 144, or 48 +96. 51. 2£48. X 2 = how much? A. 4£8s. 52. (2 s. 6 d.) X 2 53. (7 s. 6 d.) X 4: = = 54. 3 x 3 x 2 x 10 how much? how many? 55. How many minutes of motion make 2 degrees of motion! How many seconds of motion make 3 minutes of motion? 56. How many degrees is the circumference of the earth? 57. The earth, you know, turns round once in every 24 hours, or, in common language, the sun moves round the earth n that time; in what time, then, will the sun travel over 15° (degrees) and why? A. 1 hour for 360° 24 h.=159 4 min. 58. In what time will he travel over 1o (degree) of motion › A. 1 of 1 hour, or of 60 min., 59. In what time will he travel over 1' (minute) of motion? A. of 1 min., or of 60 sec., = 4 seconds. Q. By the foregoing we see that every degree of motion makes a difference in time of 4 minutes, and every minute of motion a difference of 4 seconds. Now, since longitude is reckoned in degrees, round the earth, can you tell me how to find the difference in time between one place and another, after knowing their difference in longitude? A. Multiply the difference of longitude in degrees and minutes by 4, the product will be their difference in time, in minutes and seconds. 60. What is the d.ference in time between two places, whose difference in longitude is 2° 4? A. 2° 4' x 4 = 8 minutes and 16 seconds, the difference in time. What, Is 10° ? 61. What is the difference in time between two places, whose difference in longitude is 5° 10? A. 20 m. 40 sec. when the difference of longitude is 8°? A. 32 m. A. 40 m. Is 15°? A. 60 m. 1 hour. Is 15° 15'? A. 1 h. 1 m. Q. The sun travels from east to west: which place, then, will have the earliest time? A. The one most easterly. 62. There are two places, the one situated in 10° E. longitude, and the other in 4° E. longitude; what is the difference in tine between these two places? When it is 24 minutes past 6 o'clock in the former, what hour is it in the latter? A. 24 minutes, difference in time; then, 100 being the most easterly place, it is there 24 minutes earlier than at 40; that is, when it is 24 minutes past 6 at 10, ut is only 6 at 40. 63. Boston is situated about 6° 40′ E. longitude from the city of Washington; when it is 2 o'clock at Washington, what o'clock is it at Boston? A. 26 m. 40 sec. past 2 o'clock. 64. "I recollect of reading a story once of a gentleman going to a foreign country, who had a fancy to look at a bright star every evening, at the same moment, with a certain lady whom he left behind, and they agreed to look at it at 9 o'clock;" but, it seems that, when the gentleman was in a different longitude, the time would, of course, be different; as, for instance, when he was in longitude differing 30° W. from where the lady was, she most probably had retired to rest, and was, perhaps, asleep, while he was gazing at the star. Can you tell me what o'clock it was, then, where she was? When he was 60° of W. longi tude from her, what hour of the night was it at the place where the lady resided? Exercises for the Slate. 1. Write down three millions, three hundred and three thou sand, three hundred and three. 2. What is the difference between 50 eagles and 4599 dimes 4 $40,10. 3. What number is that, which, being vided by 65, the quotient will be 42? A. 2730. 4. A captain, 2 lieutenants, and 30 seamen, take a prize worth $7002, which they divide into 100 shares, of which the captain takes 12, the two lieutenants each 5, and the remainder is to be divided equally among the sailors; how much will each man receive? A. Captain's share, $840,24, each lieutenant's, $350,10, and each scaman's, $182,052. 5. Bring $400 into crowns, at 6 s. 8 d. each. A. 360 crowns. 6 Washington was born A. D. 1732; how many years old would he have been, had he lived until the end of the year 1327? and how many seconds old, allowing the year to contain 365 days? A. 95 years, 2997972000 seconds. 7. The wheels of a cart are 5 feet in circumference, and that of a wheelbarrow 27 inches; how many more times will the latter turn round than the former, in going round the earth? How many more times in going through the earth, allowing the diameter to be of the circumference? A. 32292480 times round the earth, 10764160 times through it. 8. How many minutes is it from the commencement of the Christian era to the end of the year 1827? A. 960923920. 9. Jacob, by contract, was to serve Laban for his two dasghters 14 years; when he had accomplished 10 years, 10 mo., 10 weeks, 10 days, 10 hours, 10 minutes, how many minutes had he then to serve ? A. 1416350. 10. Reduce to its lowest terins. A. 11. What is the value of of a cwt.? A. 1 qr. 20 lbs. 12. What is the amount of ,5,05,005,555,18765 and 8567: A 8568,29765 82 13. Divide by . . . 14 From 17 take of of 14. 9. 127. 15. Reduce 550 to a mixed number. A. 4518. 16. What is the value of,425 of a pound? 9. 8 s. 6 d. 17. Reduce 14 s. 6 d. 3 qrs. to the decimal of a pound. A.,7281+. 18. From,1 of a pound, take,0678 of a pound. A.,0322. 19. If you give $60 for 25 yards of cloth, what will 1 yard cost? A. $2,40. 20. A merchant sold 8 bales of linen, 6 of which contained 15 pieces each, and in each piece were 40 yards; the other 2 bales contained 12 pieces each, and in each piece were 27 yards, what did the whole amount to, at $14 per yard? A. $5310. 21 A man, dying, left $10024 to his wife and 2 sons, to be divided as follows: to his wife, to his eldest son of the remainder, and to his youngest son the rest: what is the share of each? A $3759 to his wife $2506 to his eldest son, $3751 to his youngest 22. A farmer sold a grocer 20 bushels of rye, at $,75 per bushel; 200 lbs. of cheese, at 10 cents per lb.; in exchange for which he received 20 gallons of molasses, at 22 cents per gal lon, and the balance in money; how much money did he re ceive? A. $30,60. 23. A has 150 yards of linen, at 25 cents per yard, which he wishes to exchange with B for muslin at 50 cents per yard; how much muslin must A receive? A. 75 yds. 24. A gave B 500 yards of broadcloth, at $2,50 per yard, fo 600 umbrellas; what were the umbrellas apiece? A. $2.0834.. 25. A farmer sold a grocer 20 bbls. of apples, each barrel con taining 3 buskels, at 40 cents per bushel; (24) 30 bushels of corn, at 30 cents per bushel; (27) 500 lbs. of cheese, at 8 cents per pound; (40) 200 lbs. of butter, at 17 cents per pound; (34) 75 bushels of turnips, at 19 cents per bushel; (1425) 40 bushels of barley, at $1 per bushel; (50) 25 bushels of rye at 95 cents per bushel; (2375) and, in exchange, the farmer has received 2 bbls. of cider brandy, at 42 cents per gallon, (2646) 1 bbls. of flour, at $8 per barrel; (35) 60 gallons of molasses, at 34 cents per gallon; (2040) 40 gallons of wine, at $1,50 per gallon; (60) 10 lbs. of tea, at 73 cents per pound; (730) $40 in cash; and he agrees to take up wha. is still due him in rice at 7 cents per pound; how many pounds of rice must the gro cer give the farmer to balance the account? A. 340 lbs. 9 oz. 27 dr 26. What quantity of cider, at $1,20 per barrel, will buy 2 barrels of rum, at $2 per gallon? A. 105 bbls. 27. A man exchanged 40 bushels of salt, at $1,50 per bushel. for 200 bushels of oats, at 25 cents per bushel; how much was the balance in his favour? A. $10. 28. A sold B 16 cwt. of sugar, at 84 cents per pound; (14784) 20 bbis of flour, at $114 per barrel; (225) 17 chests of tea, each containing 8 cwt., at 53 cents per pound; (807296) 30 tierces of rice, at $36 per tierce; (1080) for which B gave up A his note of $400, that had been on interest 6 yrs. 7 mo. 15 days; (559) in addition to which B gave A 700 dozen of wax candles at $1,14 per dozen; (798) and for the balance A consents to take B's note, payable in 21 years, without interest; but B, un expectedly receiving some money, wishes to advance the cash, instead of giving his note; what sum of ready money ought B to pay A, discounting at 54 per cent.? A. $7181,362+ 29. A had 200 bbls. of flour, at $10,50 per bbl., for which B gave him $1090 in money, and the rest in molasses, at 20 cents per gallon; how many hogsheads of molasses did he receive? A. 80 hhds. 10 gals |