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Note.- When the operation is performed by short division, let the several quotients be placed under their respective denominations.

9. Divide 151£. 19s. 11 d. by 9. Ans. 16£. 175. 9£d. 10. Divide 350£, 17s. 3 d. by 519.

Ans. 135. 64d. 11. Divide 225£. 1s. 101d. by 63. Ans. 3£. 11s. 5 d. 12. Divide 159£. 4s. 9d. by 12.

Ans. 13£. 5s. 4d. 13. Divide 75£. 6s. 6d. by 4.

Ans. 18£. 16s. 7}d. 14. Divide 111£. 8s. 11d. by 7. 15. Divide 159£. 4s. 9d, by 12. 16. Divide 1581b. 9oz. 1dwt. 21gr. by 9. 17. Divide 111lb. 11oz. 17dwt. 9gr. by 7. 18. Divide 183 Ton, 1cwt. 2qr. 11lb. 4oz. by 11. 19. Divide 105 Ton, 7cwt. Oqr. 6lb. 8oz. by 8. 20. Divide 191h. 93. 43. 23. 9gr. by 8. 21. Divide 335yd. 2qr. Ona. Ošin. by 7. 22. Divide 215m. 7fur. 1rd. 14ft. 6in. by 12. 23. Divide 149deg. 8m. Ofur. Ord. lyd. 1ft. 6in. by 9. 24. Divide 97deg. 55m. 7 fur. 35rd. 4ft. 2in. 1bar. by 6. 25. Divide 181A. BR. 11p. 6yd. 4ft. 41in. by 11. 26. Divide 31 cords, 83ft. 1332in. by 4. 27. Divide 209hhd. 55gal. 3qt. Opt. 1gi. by 7. 28. Divide 35 Tun, 3hhd. 4 gal. 2qt. by 9. 29. Divide 56hhd. 45gal. by 8. 30. Divide 118bu. 1pk. 5qt. by 6. 31. Divide 255chald. 24bū. Bpk. 1qt. by 7. 32. Divide 110y. 343d. 3h. 41m. 12sec. by 8.

33. A man divides his farm of 214A. 3R. 12p. equally between his 9 sons. How much does each receive ?

34. If one man perform a certain piece of labor in 3da. 16h. 54m., how long would it take 12 men to perform the same work?

35. A farmer has 29 bushels of rye which he wishes to put into 8 bags, how much must each bag contain ?

CASE 11.

When the quantity is a composite number, proceed as in the following

EXAMPLE.

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36. If 42 yards of cloth cost 14£. 3s. 6d., what is the value of 1 yard ?

Ans. 6s. 9d. £. 7)14 3 6 In this question, we find the component parts 6)2 0

of 42 are 6 and 7; we therefore first divide the 6

price by 7, and then divide the quotient by 6. 0 6 9 From the above, we deduce the following

RULE.

Divide the dividend by one of the component parts, and the quotient thence arising, by the other, and the last quotient will be the answer to the question.

NOTE. – To find the true remainder; multiply the last remainder by the first divisor, and to the product add the first remainder.

37. If 16 yards of velvet cost 2£. 18s. 8d. what will 1 yard cost ?

38. If 72 yards of broadcloth cost 71£. 14s. Od. what is the value of 1 yard ?

39. If 84 yards of cotton cost 8£. 1s. Od. what will 1 yard cost?

40. If 90 hogsheads of sugar weigh 56T. 13cwt. Sqr. 10lb. what is the weight of 1 hogshead ?

41. What will be the price of 1 sheep if 18 cost 5£. 4s. 3d. ? 42. If 21 yards of cloth cost 10£. 8s. Bd. what is the price of 1 yard ?

43. What is the value of 1 hat when 22 cost 12£. 13s. Od. ?

44. When 96 shares of a certain stock are valued at 1290£. 4s. Od., what would be the cost of 1 share ?

45. If 120 spoons weigh 321b. 9oz. 15dwt., what does 1 weigh?

46. If a man in 1 month travel 746m. 4fur. 40rd, how far does he go in 1 day?

47. If the earth revolve 15° on its axis in 1 hour, how far does it revolve in 1 minute ?

48. Divide 1275A. 2R. 16p. 22yd. 8ft. 32in. equally between 32 men.

49. If a man walk round the earth in 2y. 68da. 19h. 54m.; how long would it take him to walk 1 degree, allowing 3651 days to a year?

The following questions are to be performed as the second example of this section.

50. If 53 tons of iron cost 1001£, 9s. 70. what is the value of 1 ton ?

51. If 57 gallons of wine cost 23£. 11s. 5fd. what cost 1 gallon?

52. Divide 3419A. 2R. 23p. by 29.

53. If 89 pieces of cloth contain 3375yds. Sqr. Ina. Ofin. how much does 1 piece contain ?

54. If 59 casks contain 44hhd. 52gal. 2qt. 1 pt. of wine, what are the contents of 1 cask ?

55. If a man travel in 1 year (365 days) 6357m. 5fur. 14rd. 11fft., how far is that per day?

56. When 175gal. 2qt. of beer are drunk in 52 weeks, how much is consumed in 1 week ?

57. When 17 sticks of timber measure 15T. 38ft. 1074in., how many feet does 1 contain ?

58. Divide 132 cords, 2ft. by 17.
59. Divide 89hhd. 54gal. by 39.
60. Divide 179bu. Bpk. 1qt. by 53.
61. Divide 275chald. 17bu. equally between 17 men.

CASE III.

When the value of a fractional part is required.

RULE.

Multiply the price by the numerator, and divide by the denominator, but if the price of a fractional part be given, and it is required to find the value or integer, multiply the price by the denominator and divide by the numerator.

EXAMPLE.

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62. If the whole of a ship and cargo be valued at 2346£. 128. 8d. what is worth ?

Ans. 1759£. 19s. 6d. £. 2346 12 8

3 4) 7039 13 0

1759 19 6

63. Bought § of a lottery ticket, which drew a prize of $1500; what was my share of the prize money? Ans. $ 937.50.

64. If is of an estate be valued at $ 1728.50, what is the value of the whole ?

Ans. 2963.14. 65. A vessel and cargo is valued at $ 10.000, and of the cargo was sold for $ 5780; what was the value of the vessel ?

Ans. $ 2775.00.

SECTION XI.

MENTAL OPERATIONS IN FRACTIONS.

Note:— The pupil is requested, before he commences the mental operations of Fractions, to examine carefully the definitions on page 78.

1. If į of a barrel of cider cost 2 dollars, what will a barrel cost ?

2. Boughts of a barrel of flour for 2 dollars, what would be the price of a barrel ?

3. If į of a yard of cloth cost 3 dollars, what will cost ? What will cost ? What will a yard cost ?

4. If} of a barrel of flour cost 2 dollars, what will cost ? ? ? ? ? ? ? ? 5. If of a pound of pepper cost 3 cents, what will % ? ?

6. Bought of a barrel of sugar for 2 dollars, what was the price of 1? 1?1?10?

7. If a man bought of a firkin of butter for 7 cents, what did the whole firkin cost ?

8. Bought ia of an acre of land for 5 dollars, what was the price of an acre? Of 2 acres ? Of 10 acres ? Of 20 acres ?

9. Bought of a pound of ginger for 4 cents, what did a pound cost?

10. Bought is of a chest of tea for 5 dollars, what did so cost ? ? ? ? 18?

11. Bought t of a load of hay for 3 dollars, what did the load cost ? What did 2 loads cost ?

12. If į of a cask of wine cost 9 dollars, what was that a cask ?

13. 2 is of what number? 4? 5? 6? 8? 9? 10? 12? 14. 4 is of what number ? 5? 6? 8? 9? 11? 15? 16? 15. 6 is of what number? 7? 8? 9? 11? 13?18? 20? 16. 7 is of what number? 4? 5? 6? 8? 11? 15? 25? 17. 9 is of what number? 7? 2? 8? 11? 12? 13? 17? 18. 8 is of what number? 7? 11? 12? 15? 10? 11? 25? 19. 10 is of what number? 6? 7? 8? 9? 11? 15? 18? 20. 12 is of what number? 14? 15? 16? 17? 18? 19? 21. 11 is of what number? 6? 3? 2? 1? 7? 18? 14? 22. 14 is of what number? 11? 12? 13? 15? 16? 17? 23. 15 is of what number? 21? 18? 13? 14? 17? 19?

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24. 7 is to of what number? 10? 11? 12? 16? 18? 13? 25. 8 is ļ of what number? 6? 7? 6? 5? 2? 7? 18?

26. If z of a pound of sugar cost 4 cents, what will { of a pound cost? What will a pound cost? 4 is of what number?

27. If of a pound of nutmeg cost 6 cents, what will of a pound cost? If of a pound cost 2 cents, what will a pound cost? 6 is of what number?

28. If; of a cwt. of starch cost 10 dollars, what will of a cwt. cost? What will a cwt. cost? 10 is of what number?

29. If of a barrel of molasses cost 4 dollars, what is the value of į of a barrel? If í of a barrel cost 2 dollars, what will a barrel cost? 4 is z of what number?

30. If of a pound of candles cost 15 cents, what will } of a pound cost? If į of a pound cost 3 cents, what will a pound cost? 15 is į of what number?

31. Bought of a pound of mace for 20 cents, what was the cost of of a pound? If of a pound cost 4 cents, what will a pound cost? 20 is of what number?

32. If it of a pound of opium cost 55 cents, what will is of a pound cost? If ja pf a pound cost 5 cents, what will a pound cost? 55 is 11 of what number?

33. 6 is 3 times what number?- 9? 12? 15? 18? 21? 24? 34. 15 is 3 times what number? 20? 25? 35? 65? 70? 35. 20 is 4 times what number? 4? 8? 12? 16? 40? 50? 36. 21 is 7 times what number? 14? 28? 56 ? 63? 70? 37. 24 is 2 times what number? 26? 30? 372 39? 40? 38. 25 is 5 times what number? 80 ? 85? 95? 100? 200? 39. 3 is 6 times what number? 18? 21? 28? 31? 40? 60? 40. 18 is 9 times what number? 6? 7?18? 30? 37? 28?

41. If 6 be į of some number, what will be of the same number? If 3 be of a number, what is that number?

42. 3 is į of what number?

43. If of a pound of sugar cost 12 cents, what will of a pound cost? If of a pound cost 2 cents, what will a pound cost?

44. If I of a pound of nutmegs cost 20 cents, what will ji cost? If i cost 5 cents, what will a pound cost? 20 is îi of what number?

45. If, of a quarter of veal cost 64 cents, what will of a pound cost? If į of a pound cost 8 cents, what will a pound cost? 64 is , of what number?

46. Bought of a ton of potash for 84 dollars, what did ;

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