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40. 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 feet square? 10 miles square and 10 square miles? 3 rods
square and 3
A parenthesis, enclosing several numbers, signifies that these numbers are to be taken toget or as one whole number; but, when performing subtraction and alldition with these and other numbers, they may be taken either as before, or one by one, thus :
(16 + 4) X3= 60, read 16 +4= 20 X3= 60. Or, (16 x 3) = 48. 4X3= 12: Then, 48 + 12 = 60, the same as bofore. 43. (9+3)+8= how many ?
A. 20. 44. 19-3) —4= how many ? A. 2. 45. (15+5) X4=how many ? A. 80, or 60+20. 46. (15--5) x 45
A. 40, or 60 — 20. 47. (9+3)=3 how many?
.A. 4, or 3 +1. 48. (9-3)=3= how many ? 1. 2, or 3 - 1. 49. (12—8)=(3+1)=how many ? A. 1, or 3 -- 2.
A line, or vinculum, drawn over numbers, is sometimes used instead of parenthesis.
50. 4+8 X 12 = how many ? A. 144, or 48 +96.
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 inoves round the earth in that time ; in what time, then, will the sun travel over 15° (degrees) ? and why? A. 1 hour for 360° -- 24 h.
A. Its of 1 hour. or its of 60 min., = 4 min. 59. In what time will he travel over 1' (minute) of motion?
A. I's of 1 min., or I'5 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 minule of motion a differ
ence of 4 seconds. Now, since longitude is reckoned in degrees, round the earth, can you tell me how to find the difference in time be. tween 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 difference in time between two places, whose difference in longitude is 20 4' ? A. 20 4 X 4 = 8 minutes and 16 seconds, the difference in time.
61. What is the difference in time between two places, whose difference in longitude is 5o 10 ? A. 20 m. 40 sec. What, when the difference of longitude is 8o? A. 32 m. Is 10° ? 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 4o E. longitude'; wh is the difference in time 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, 10° being the most easterly place, it is there 24 minutes earlier than at 4°; that is, when it is 24 minutes past 6 at 10°, it is only 6 at 4o.
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, wit tain 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. longitude 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 ? A. $40,10.
3. What number is that, which, being divided 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? 4. Captain's share, $840,24 ; each lieutenant's, $350,10, and each seaman'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 haye been, had he lived until the end of the year 1827: and how many seconus old, allowing the year to contain 3654 days? A. 95 years, 2997072000 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. 960928920.
9. Jacob, by contract, was to serve Laban for his two daughfers 14 years; when he had accomplished 10 years, 10 mo., 10 weeks, 10 days, 10 hours, 10 minutes, how many ininutes had he then to serve ? A. 1416350.
10. Reduce to its lowest terms. A. 42. 11. What is the value of of a cwt.? A. 1 qr. 20 lbs. 12. What is the amount of ,5 ,05 ,005 ,555 ,13765 and 8567 ?
A. 8568,29765. 13. Divide gs by T. A. 14. From 175 take ţ of of 14.1. A. 1274. 15. Reduce to a mixed number. A. 4513 16. What is the value of ,425 of a pound? A. 8s. 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 ,0673 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, $3759 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 gallon, and the balance in money; how much money did he receive? 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, for 600 umbrellas; what were the umbrellas apiece? A. $2,083+.
25. A farnier sold a grocer 20 bbls. of apples, each barrel containing 3 bushels, at 40 cents per bushel-24; 30 bushels of corn, at 90 cents per bushel-27 ; 500 lbs. of cheese, at 8 cents per pound-40; 200 lbs. of butter, at 17 cents per pound34; 75 bushels of turnips, at 19 cents per bushel-1425; 40 bushels of barley, at $14 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 ; 4 bbls. of flour, at $81 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 what is still due him, in rice, at 7 cents per pound; how many pounds of rice must the grocer give the farmer to balance the account?
A. 340 lbs: 9 oz. 2 dr. 26. What quantity of cider, at $1,20 per barrel, will buy ? 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 favor? A. $10.
28. A sold B 16 cwt. of sugar, at 84 cents per pound-14784; 20 bbls. 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 В gave up A his note of $400, that had been on interest 6 yrs. 7 mo. 15 days559; in addition to which В 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, unexpectedly 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 53 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. 30. A has linen cloth, worth $,20 per yard, but, in bartering, he will receive $,30; B has broadcloth, worth $4,60 per yard, ready money: at what price ought B to rate his broadcloth, to be in proportion with A's bartering price ?
$,20 : $4,60 : : $,30 : $6,90, Ans. Or, multiply $,30 by the ratio of 20 to $4,60, that is, 23; thus, 23 x 30 = $6,90 ; for, $4,60 being 23 times as much as 20, it is plain that 23 times $,30, A's bartering price, will give B's bartering price, Ans. $6,90.
31. A merchant, in bartering with a farmer for wood at $5 per cord, rated his molasses at 25 dollars per hhd., which was worth no more than $20 ; what price ought the farmer to have asked for his wood to be equal to the merchant's bartering price ? A. $6,25.
The last ten examples are proper questions in a rule usually called Barter.
32. What number is that, which, being multiplied by 15, will make ? A. b
33. What number is that, which, being divided by 15, will make ? A.
34. What decimal is that, which, being multiplied by ,625, will make ,25 ? A. ,4.
35. At $,75 per bushel, how much rye can be bought for $150 ?-200. For $600 ?-800. For $75 -100. A. 1100 bushels.
36. (800+12+88) • (50-5) =how many ? A. 20. 37. (i+14) =(3,55,-55) =how many ? A. 23.
38. Two persons depart from one place at the same time; the one travels 35, and the other 40 miles a day; how far are they distant at the end of 10 days, if they both travel the same road? and how far, if they travel contrary directions ? A. 50, and 750 miles.
39. Two men, A and B, traded in company; A put in $700 for 8 months, and B $1280 for 10 months; they gained $500 : what was the share of each ? A. A's share, $152,173; B's share, $347,826 +.
40. How many cord feet of wood are contained in a load 8 feet long, 4 ft. 6 wide, and 5 ft. 3' high? A. 111. ft. or 11 ft. 9/91.
41. What is the difference in time between two places, whose difference of longitude is 40° 7-2,40. 50° ?-3,20..60° ?-4. A. 10 h.
42. What time is it in 150 W. longitude, when it is 6 o'clock in 15° E. longitude ? A. 4 o'clock.
43. If a cow yield 16 qts. of milk in a day for 240 days, and 20 qts. make 1 pound of butter, or 10 pounds of cheese, how