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48. Divide 6780D, among 15 men.

Ans. 452 each 49. Divide 975 pounds of flour among 25 persons.

Ans. 39 pounds each. 50. Divide 100786 pounds by 43. Ans. 2343, 37 rem. 51. Divide 1600 bushels of wheat among 40 men.

Ans. 40 bush, each 52. There are 24 hours in a day; how many days are there in 7248 hours ?

Ans. 302. 53. There are 60 minutes in an hour ; how many hours in 97680 minutes ?

Ans. 1628 hours. 54. There are 365 days in a year; how many years in 3285 days?

Ans. 9 years. 55. There are 63 gallons in a hogshead; how many hogsheads in 8796 gallons ?

Ans. 139, 39 rem 56. At 12 cents per pound, how many pounds can you have for 1728 cents ?

Ans. 144 pounds. 57. If the dividend is 4200, and divisor 48, required the quotient ?

Ans. 87, 21 rem. 58. If the divisor is.25, and the dividend 5025, what is the quotient?

Ans. 201. 59. If you sell 84 bushels of wheat for 150 cents a bushel, and take your pay in cloth at 4D. a yard, how many yards will you have ?

Ans. 311. 60. Divide 256976: by 41.

6267, 29 rem. 61. Divide 997816 by 59.

16912, 8 rem. 62. Divide 6283459 by 29.

216671. 63. Divide 37895429 by 112.

338352, 5 rem. 64. Divide 29070 by 15; by 18 (+ quot.)

3553. 65. Divide 29070 by 19; by 17.

3210 66. Divide 10368 by 27; by 36.

672. 67. Divide 10368 by 54;) by 18.

768. 68. Divide 2688 by 112; by 224.

36. 69. Divide 101442075 by 4025.

25203. 70. Divide 978098745 by 78978.

APPLICATION OF THE PRECEDING RULES.

1. If you add 476, 361, 842, together, and divide their amount by 20, what number will result ?

Ans. 83, 19 rem. 2. A. has 2 farms, one of 732 acres, the other 241 acres ; if he should divide the land equally among his 7 sons, how many acres would each receive ?

Ans. 139.

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3. A gentleman has 2 sons and 1 daughter; he is worth 697833D.; he will give his daughter 232611D., and his sons may share the remainder between them; was the estate equally divided ?

4. If you multiply 1750 by 17, and divide it by 16, what will be the result ?

Ans. 1859, 6 rem. 5. Divide 420D, among three men and a boy.

6. If you purchase 120 pounds of flour for 7D. and sell it for 6 cents a pound, will you gain or lose, and how much?

7. Make out a bill of the following articles, namely: 18 pounds of nails at 14 cents per pound; 47 pounds of sugar at 11 cents per pound; 5 gallons.of molasses at 44 cents per gallon; 4 pounds of tea at 75 cents per pound ; 9 yards of calico at 22 cents per yard; and 2 brooms at 25 cents each.

Ans. 15D. 37c. 8. A gentleman has 4 notes of hand : the first is for 474D. 20c.; the second for 760D. 42c.; the third for 285D. 68c.; the fourth for 369D. 31c.; when received, he must pay a debt of 1562D. 96c. ; how much will remain ?

Ans. 326D. 65c. 9. What is the amount of 40 bushels of corn at 84 cents a bushel ; 25 bushels of rye at 97 cents a bushel; and 30 bushels of wheat at 1D. 25c. a bushel ?

Ans. 95D. 35c. 10. What is the quotient of 55 multiplied by 22 and = 15 ?

Ans. 80, 10 rem 11. Purchased 1 set of chairs for 4D. 25c.; table 7D. 50c.; bureau for 27D. ; a watch for 60D. 50c.; writing-desk for 18D.; a clock for 40D.; required the amount. Ans. 157D. 250.

12. A gentleman of Philadelphia lately purchased 4 tracts of unimproved land in the western country; in the first tract there are 2780 acres ; in the second, 4027 acres ; third, 3012 acres ; fourth, 8760 acres, all of which is worth 5D. per acre ; he will divide all the lands among his 3 sons; how many acres did he purchase, and how much land will each son receive, and how much is it all worth?

Ans. He purchased 18579 acres; each son will receive 6193 acres; worth 92895D.

13. A farmer has 3764 acres of land ;' he will sell A. 642 acres, B. 224 acres, C. 180 acres, and D. 354 acres ; the remainder is to be equally divided among his 4 children; how much land will each receive, and how much will each share be worth at 65D. an acre ?

Ans. 591A.; worth 38415D, 14. If you sell 44 bushels of oats for 35c. per bushel, 25 bushels of corn for 76c. per bushel, and 6 cords of wood for 4D. por cord, how much would you receive ? Ans. 58D. 40c.

15. Required the amount of the following articles, namely: I set of knives and forks at 3D. ; 1 Cashmere shawl at 75D.; 47 yards Irish sheeting at 90c. per yard; 7 yards of broadcloth at 6D. per yard; one Russian hat at 5D.; 11 yards of silk at 2D. per yard ?

Ans. 189D. 30c. 16. A gentleman deposited in bank, at one time 4638D., at another 216D., at another 8329D., at another 1212D.; required the amount in bank.

Ans. 14395D. 17. A ship in sailing to a distant part of the world : from one port to another was 6243 miles, to another port 4123 miles, to another 9401 miles, and thence home 130 miles ; required the number of miles she sailed.

Ans. 19897. 18. Supposing you gain 34568D., then 1245D., again 2467D., and then lose 2365D.; again, you gain 41210D., and then lose 39300D. ; how much will you have left?

19. A man gains 367D., then loses 423D.; a second time he gains 875D., and loses 912D.; he then gains 1012D. ;' how much has he gained in all ?

Ans. 919D. 20. A farmer agrees to furnish a merchant 40 bushels of rye at 60 cents a bushel, and take his pay in coffee at 16 cents a pound; how much coffee will he receive ? Ans. 150 pounds.

21. A farmer sold 3 cows at 25D. each, and 1 pair of oxen at 65D., he agrees to take in payment 60 sheep; how much per head do his sheep cost him?

Ans. 2D. 33c. .3+ 22. The exports of the United States from October, 1841, to October, 1842, were as follows: of products of the sea, 2823010 D.; of the forest, 5518262D.; of agriculture, 73688113; of manufactures, 10940611D. The total value of the imports for the same period was 100162087D. How much did the total value of the imports exceed that of the exports ?

23. If M. R. is worth fourteen millions, two hundred and fifty thousand D., how many men could he make comfortably rich by giving them 25 thousand D. each?

Ans. 570. 24. A celebrated personage of England has a salary of seven hundred and fifty thousand dollars annually; how much is that daily, and how many teachers would it pay at a salary of 500D. a year? Ans. daily income 2054D. 79c. 4+ 1500 teachers. 25. What cost 6400 yards of riband at 25c. per yard ?

Ans. 25= D. 4)6400=1600D. 26. What cost 3600 yds. at 12£c. a yard? 12}= D. 8)3600. 27. What cost 2400 pounds of cheese at 61c. a pound?

Ans. 61=1 D. 16)2400. 28. What cost 600 bushels of potatoes at į of a dollar a bushel ?

Ans. 3)600=2000. 29. What cost 50 bushels of wheat at 1D. 25c. a bushel ?

Ans. 62D. 50c 30. Supposing 1800 apple-trees to be planted in 72 rows, how many trees are there in each row ?

Ans. 25. 31. A merchant bought 8200 barrels of flour; he then sold 3756 barrels; he again bought 5000 barrels, after which he sold 4879 barrels; how many has he on hand ?

Ans. 4565. 32. A man sets out on a journey, intending to travel 2450 miles; how far must he go every day to perform the journey in 50 days?

Ans. 49 miles. 33. The quotient of an operation in division is 1763, the dividend 8435955 ; required the divisor.

Ans. 4785. 34. What number is that which, being multiplied by 7969, the product will be 1864746 ?

Ans. 234.

REVIEW.

What is Long Division? What is the rule? At which hand of the dividend must the divisor be written ? Why do you begin at the left hand of the dividend to divide ? Ans. Because numbers decrease, &c. Under this rule, where must the quotient be written? How many figures of the dividend must first be taken? How can you find the one half of any nuinber? one fourth? one sixth ? one eighth ? &c. How many rules have you now been through ? Name. them? Why are they called the principal or fundamental rules of the science ? Ans. Because they are the foundation of all the other rules, and by their use and operation all calculations in arithmetic are performed. Perform the following examples on the slate, as the signs indicate : 87834+284+65+32+100=88315 Ans. 876345723 -267001345=609344378 Ans. 692784578 X 27839421= 19286721529249338 Ans. 202884150:-4025=50406 Ans. 2600-600=2000-+1828=3828 Ans. 9788 X 97:29 X 17+ 79--400 X 92.

35. From 95,000,000 take 18,999,999; from 777,777 688,888

36. If a miller should purchase 578 bushels of wheat for 482D., and sell 482 bushels for 375D., how many bushels will he have left, and what sum will he have paid for the quantity remaining ?

Ans. 96 bushels ; paid 107D. 37. From eleven millions take eleven hundred and eleven.

Ans. 10998889. 38. What is the difference between 84 and 76 ? 90 and 22 ? 400 and 380 ? 7868 and 9897 ?

Methuselah died aged 969 years, and Adam aged 930; what is the difference of their ages ? How many years were required to have extended the life of Methuselah to 1000 ? How many for Adam? How many years are their united ages ? How many years since the death of Adam? How long from the death of Adam to the deluge? How many years from the deluge to the present time? In what year was America discove ered by Columbus ? How many years since ? years since the declaration of independence ? How are you pleased with the science of Arithmetic ?

How many

DECIMAL FRACTIONS, Adapted to the Currency of the United States. We now come to treat of Decimals in connexion with the currency of this country, by which it is believed that calculations generally, at least where money is concerned, will be much facilitated, and bring to view a better and easier method of computation than has heretofore been in general use. That fractions must of necessity occur in almost every transaction, none will presume to deny, and all will admit that no part of the science of Arithmetic is more difficult of comprehension to the juvenile mind than fractions, especially those termed vulgar; but in this treatise, this part of Arithmetic is introduced in a pleasing and agreeable manner, particularly calculated to attract the attention : of youth, and overcome every obstacle and difficulty; and the author entertains the belief that he has in part succeeded.

DECIMAL is derived from the Latin word decem (signifying ten, because they increase and decrease in a tenfold proportion, like whole numbers), and is a part of a whole number, or unit, which is distinguished by a period, decimal point, or separatrix, placed at the left of the figure or figures, thus: .5=jo, or one half; .25=10=twenty-five hundredths=one quarter ; 6.8, six and eight tenths ; .15=105=fifteen hundredths; .144= 140, one hundred and forty-four thousandths, &c.; the number above ihe line, 144, is called the numerator, and the number below the line, 1000,

is called the denominator, and must consist of one place more than the numerator, and shows the number of parts into which a unit or anything is divided, thus, if you own 25 parts in 100 parts, you own one fourth, because 25 X4=100==

the numerator and denominator being alike, are equal to 1 The word fraction implies broken parts of a unit or whole number

25

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