point, and you have 6 yards; then multiply by 9, because 9 feet make 1 yard, and count off as before, which gives 0 feet, yet the remaining decimal of a foot must be reduced to inches, 144 being equal to 1 foot, and you have 64 inches. Thus we find that .9075 of an acre is equal to 3 roods, 25 poles, 6 yards, O feet, 64 inches. 24. What is the value of .046875 of a pound avoirdupois ? Thus, .046875 × 16=750000 × 1612.000000 drams, Ans. 25. What is the value of .617 of a cwt.? Ans. 2 qr. 13 lb. 1 oz. 10 dr. 26. What is the value of .569 of a year of 365 days? Ans. 207 da. 16 ho. 26 min. 24 sec. 27. Find the proper quantity of .9071 of an acre. 28. Find the value of .76442 of a pound troy. Ans. 9 oz. 3 dwt. 11 gr. 29. What is the value of .875 of a yard? Ans. 28 po. 2 yds. 1 ft. 11 in. + 31. Find the proper quantity of .897 of a degree. To reduce a Vulgar Fraction to its equivalent decimal. RULE III. 1. Annex ciphers to the numerator, and then divide it by the denominator. 2. There must be as many places pointed off in the quotient as you annex ciphers to the given numerator; if there should not be so many places of figures in the quotient, the deficiency must be supplied by prefixing ciphers at the left hand of the quotient; if the numerator is larger than the denominator, there must be a whole number, or whole number and decimal. 32. Reduce to a decimal having the same value? 8)1.000 When you wish to reduce several denominations to the decimal of a larger denomination, still retaining the same value, how do you procced? (See rule, &c.) In question 1st the quotient is .875; what do you understand by this? Ans. Eight hundred seventy-five thousandths of an acre, which is equal to 140 rods : that is, 140 rods bear the same proportion to 160 rods, or one acre, as. 875 does to .1000, or $75, or 875 to 1000, &c. Suppose the number at the left of the decimal point in the dividend had been more than 160 (the divisor) would the quotient have been a decimal ? Ans. In that case it must have been a whole number and decimal, but after a decimal figure is brought down for a new dividend that quotient figure will be a decimal, as there can be no decimal in the quotient until there is one in the dividend. How do you reduce a decimal to its proper value? (See the rule.) Can you explain the first example? Wherein does this rule differ from the one immediately preceding it? Ans. It is the very reverse of the first, and they reciprocally prove each other. How do you reduce a vulgar fraction to its equivalent decimal? What is the rule? What do you understand by numerator? Ans. It is the number above the line, thus 1, which serves as the common measure to others. What is the meaning of denominator? Ans. It is the number below the line, thus and is the number of parts a unit, or anything, is divided into, and gives the name or denomination of the parts. What is understood by the expression of D.? 25 D.? Ans. Seven eighths of a dollar, or 87.5 cents, and the other is twentyfive hundredths, which is 25 cents. If you owned of the capital in trade, what part would be yours? Ans. Two thirds (3); that is, the stock would be divided into 24 shares, and I should have sixteen of them, and 16 is two thirds of 24. Suppose the stock divided into 32 shares, what part would then be yours? Ans. One half, because is equal to one half. If divided into 64 shares how much? Ans. One fourth (1); for as the de nominator increases, the value of the numerator decreases in the same proportion; and the same of the denominator, for 32, in stead of being one half as above, it would be just 4 times as much-D2.00, or my share would be 4×16=64, which is more than the given capital. What is this last (32) fraction called? Ans. An improper fraction. Why? Ans. Because the numerator is larger than the denominator, consequently the fraction expresses one whole, or more than one whole number, as =1, 102, &c. Any number may be expressed or written fractionwise, whether it be a whole number, decimal, or vulgar fraction, retaining its value, thus: 150-50-30; 28 ==.06974; 32÷8=-1.25; 746-1989, &c. NOTE. This part of arithmetic is fully explained in its proper place. (See Vulgar Fractions.) APPLICATION OF THE RULES OF DECIMALS, &c. 1. Add 16,7 days, 1825, 1475 together. 2. A. purchased 4 hogsheads of molasses: the first contained 62 gallons; second, 72, 2657 gallons; third, 50 fourth, 55,75 gallons; how many gallons in all? gallons; Ans. 240.6157. 3. What is the amount of one and five tenths; forty-five and three hundred and forty-nine thousandths; and sixteen hundredths ? Ans. 47.009. 4. What is the difference between 4.75 minutes and 6.25 minutes? 5. From .65 cwt. take .125 cwt. 7. What will 9.7 lb. of sugar cost at D0.07 per Ans. 1.5 mi. Ans. .525. Ans. 172.78. lb. ? Ans. D0.67.9. 8. At D0.90 per bushel, what will 7.25 bushels cost? 9. What is the quotient of 1561.275÷24.3? 10. What is the quotient of .264÷2? Ans..132. 11. What decimal is equal to ? 12. What decimal is equal to ? Ans. D6.52.5. Ans. 64.25. Ans. .25 .175. 13. What decimal is equal to ? Ans. .3333, circulating rept. 14. What is the value of 2 yds. 3 na. French calico, at 70 c. per yd. Ans. D1.53.125. ? 15. What cost 2 cwt. 17 lb. of chocolate, at 15D. per cwt.? 2.151786 × 15-D32.27.6790. Ans. 16. What cost 1.25 tons of hay, at 11D. per ton? Ans. 13D. 75c. 17. If 31.25 yds. cost 75D. how much is it per yard? Ans. D2.40. 18. If 35 bushels of wheat cost D97.50, what did 1 bushel cost? Ans. D2.78.5+ 19. What is the cost of 1 gall. and 1 pt. of wine at D1.75 per gall. ? Ans. D1.96.875. sell it for 12.5c. 20. If I pay 14D. for 112 lb. of sugar, and per pound, do I gain or lose, and how much? 21. If I pay 7D. for 80 pounds of flax, and sell it for 8c. per pound, do I gain or lose, and how much? 22. When rye is selling at D1.25 per bushels can I have for D62.50. Ans. Loss 60c. bushel, how many Ans. 50 bushels. 23. A gentleman bequeathed his estate of one hundred thousand dollars to his son and daughter; the son was to have 15 thousand, 15 hundred and 15 dollars more than the daughter; required the share of the daughter. Ans. 41742.50. 24. If the sum of 33485D. was expended in the purchase of United States land, at D1.25 per acre, how many acres would it purchase? Ans. 26788 acres. 25. Then if you should sell the 26788 acres for D2.5 per acre, how much would you gain? Ans. 33485D. 26. If you should buy a chest of tea containing 135 lb. for 150D., and sell the same for D1.30 per lb., what would be the difference? Ans. Gain D25.5. 27. If a pipe of wine contains 126 galls., how many pints are in the pipe, and what is it worth at 14.5c. per pt.? Ans. 1008 pints, worth D146.16. 28. A farmer purchased 120 sheep, for which he paid D1.75 per head, and 47 young cattle at D14.50 per head; he sold the sheep for D2.14 per head, and the cattle for 14D. per head; did he gain or lose, and how much? Ans. Gained D23.30. 29. A certain field will produce 127 bushels of grain; how much will a field produce, just seven and a half times as large? Ans. 952.5 b. 30. A. and B. start from the same place; A. goes east 17 days, at the rate of 39 miles per day; B. goes west at the rate of 43 miles per day for 14 days; how many miles will each travel, and how many distant from each other? Ans. A. 663 m., m., distance, 1265 m. B. 602 31. If 57 yards of cloth cost 197D., what cost 1 yard? 32. If 18 yds. 1 qr. of cloth cost D91.16, what is the cost of 1 yd.? 33. If you have 7D. and pay away .07, how much will re main ? 34. What is the value of 23 grains of silver, at 14D. per lb troy? 35. If you earn 1D. and 1m. per day, how much is that in one year? 36. John Armstrong, Dr. To 1 pound of tea at D1.56c. To 4 bushels of oats at 50c. D19.72. 38. How many quarts in 7 hogsheads? in 18? in 27 ? in 34 ? 39. How much is a hogshead of molasses worth, at 9c. per quart? at 14? 40. A cask of sugar weighs 5 cwt., what is it worth at 12c. per pound? Ans. D70.00. 41. If .25 of a yard is worth D0.25, what cost 17.5 yards? what cost 27.25 yards? 42. How many cubic inches in 5 feet? in 11 feet? in 40 ft.? 43. How many inches in 35 poles? in 65 poles? in 75 poles? |