19. The proprietor of a vineyard sold in equal quantities to 25 of his customers, 42834 gal. 1 qt. 1 pt. of wine; how much did each purchase? Ans. 1713 gal. 1 qt. 1 pt.

20. Divide 540 yards, 3 qr. 1 nl. by 28. Ans. 19 yards, 1 quarter, 1

nail.

21. Divide 51 acres, 1 rood, 11 poles, by 51. Ans. 1 acre, 1 pole.

22. Divide 307 gallons, 1 pint, by 63. Ans. 4 gallons, 3 quarts, 1 pint.

23. If seven casks weigh 2 tons, 7 cwt. 3 quarters, 14 lb., what does 1 cask weigh? Ans. 6 cwt. 3 quarters, 10 lb.

24. If 6 lb. of tea cost 11. 7s., what will 1 lb. cost? Ans. 4s. 6d.

25. If 9 pair of gloves cost 17. 8s. 10 d., what is that per pair? Ans. 3s. 24d.

26. Bought 12 lb. of beef for 4s. 3d. What did it cost the lb.? Ans. 44d.

27. Bought 24 gallons of rum for 167. 15s. 6d. What did it cost per gallon? Ans. 13s. 11 d.

28. If 29 yards of cloth cost 57. 2s. 11d., what cost 1 yard? Ans. 3s. 6d.

29. A piece of land containing 45 acres is let for 1137. 12s. 6d. What is it let at per acre? Ans. 27. 10. 6d.

30. If a man spends 1287. 11s. 2d. in 12 months, what is that per month? Ans. 107. 14s. 3d. 31. Three men make an adventure, each equally concerned, whereby they clear 740i. What was each man's share of the gain? Ans. 2467. 13s. 4d. 32. What is the value of 1 yard of cloth, when 84 yards cost 51l. 7s. 3d.? Ans. 12s. 2 d.

33. A prize of 38501. is to be equally divided among 742 sailors. What is each man's share. Ans. 51. 3s. 94d..

34. A gentleman has 560l. 12s. a-year. How

much is that a-month, a-week, and a-day? Ans. 467. 14s. 4d. a-month; 10l. 15s. 74d. §. a-week; 17. 10s. 8d. §. a-day.

When the Divisor is of different denominations.

RULE. Reduce both the Divisor and Dividend to the same denomination, and then proceed as in Simple Division.

35. A gentleman distributed 67. 12s. among some poor people, and gave each 5s. 6d. How many poor were there? Ans. 24.

36. The revenues of an infirmary amount to 11527. 10s. 6d. How many patients will it maintain, when each patient requires 97. 10s. 6d. ? Ans. 121.

37. A farm is let at 17. 2s. 6d. per acre, and the rent amounts to 5697. 16s. 3d. How many acres does it contain? Ans. 506 acres, 2 roods.

38. How long must a tradesman work, who gains 1s. 4d. a-day and spends 74d., in order to pay a debt of 201. 17s. 24d.? Ans. 589 days.

SUPPLEMENT TO COMPOUND MULTIPLICATION
AND DIVISION.

I. When the Multiplier contains a fraction. RULE. First multiply by the whole number, then multiply by the upper figure of the fraction, and divide by the lower figure, and add the Quotient to the former Product.

39. What cost 83 yds. at 14s. 6d.? Ans. 67. 1s. 97. ૐ.

40. What cost 12 lb. at 6s. 2d.? Ans. 37.18s. 74d. 41. What cost 14ğ yards at 11s. 93d.? Ans. 81. 12s. 9od..

42. What cost 293 bushels of wheat at 15s.63d.? Ans. 221. 16s. 6d.

43. What cost 46 cwt. of hay at 6s. 72d.? Ans. 151. 8s. 24d. §.

44. Multiply 20 lb. 2 oz. 7 dwt. 21 gr. by 4§. Ans. 92 lb. 11 oz. 5 grs.

45. Multiply 24 cwt. 1 qr. 14 lb. 10 oz. by 8%. Ans 202 cwt. 1 lb. 2§ oz.

46. Multiply 20 m. 3 fur. 30 po. 2 yds. by 938. Ans. 197 m. 7 fur. 1 yd.

47. Multiply 120 yds. 2 qr. 1 nl. by 10. Ans. 1259 yds. 3 nl.

48. Multiply 40 ac. 3 ro. 30 po. by 113. Ans. 467 ac. 3 ro. 174 po.

49. Multiply 57486 gallons, 3 quarts, 1 pint of wine by 7. Ans. 440732 gallons, 2 quarts, 1 pint.

II. When the Divisor contains a fraction.

RULE. Multiply both the Divisor and Dividend by the under figure of the fraction, adding the upper figure to the Product of the Divisor, then divide the Product of the Dividend by the sum.

50. Bought 174 bolls of potatoes for 87. 12s. 6d. What did they cost per boll? Ans. 10s.

51. Bought 13 yds. of cloth for 157. What did it cost per yard? Ans. 11. 2s. 6d.

52. Bought 22 stones of beef for 121. 6s. 84d. What did it cost per stone? Ans. 10s. 10d. žę.

53. Divide 2767. 16s. Sd. among 5 men and a boy, and give the boy of a man's share. Ans. A man's share, 481. 17s. Od. 14. Boy's share, 321. 11s. 41d. 19.

54. Divide 2007. 14s. 6d. among 9 men and 7 women; and give a woman of a man's share. Ans. A man's share, 137. 10s. 74d. §§. A woman's 117. 5s. 6d. 6.

55. A, B, and C, have a ship in company: A has, B, and C they receive of freight for a voyage, 1147. 8s. 4d. What is each man's share of the freight? Ans. A's share, 717. 10s. 24d. B's 28% 12s. 1d. C's 147. 6s. Ojd.

SIMPLE PROPORTION

Teaches from three given numbers to find a fourth. Of the three given numbers two are always of the same kind, the other is of the same kind as the fourth, or number required in the question.

RULE 1. Put down that number which is of the same kind with the number required for the third term.

2. Consider whether the answer ought to be greater or less than this number; if greater, make the greater of the two remaining numbers the second term, and the less the first; but if less, make the less of the two remaining numbers the second, and the greater the first term.

3. If the first and second terms are of different denominations, reduce them to the same, and the third to the lowest denomination mentioned in it.

4. Multiply the second and third terms together, and divide their product by the first; the quotient will be the answer in the same denomination to which the third term was reduced, and it may either be brought to a higher or reduced to a lower denomination, according as the answer requires.

PROOF. Invert the question.

NOTE 1. Multiply and divide as in Compound Multiplication and Division, when found convenient.

2. When the first number is 1, the answer is found by Multiplication. When the second or third number is 1, then the answer is found by Division.

3. If the first number, and either the second or third, can be exactly divided by the same divisor, let them be divided, and the quotients used instead of the original numbers.

4. To find a common measure: Divide the Divisor by the Remainder continually till nothing remain, the last Divisor