decimal of a pound as follows: 16 s.8 £. and 1 s. 05 £. Then, 52 d. = 23 farthings, which, increased by 1, (the number being more than 12, but not exceeding 36,) is 024 £., and the whole is '874 £. the Ans. Wherefore, to reduce shillings, pence and farthings to the decimal of a pound by inspection,—Call every two shillings one tenth of a pound; every odd shilling, five hundredths; and the number of farthings, in the given pence and farthings, so many thousandths, adding one, if the number be more than twelve and not exceeding thirty-six, and two, if the number be more than thirty-six. T 77. Reasoning as above, the result, or the three first' figures in any decimal of a pound, may readily be reduced back to shillings, pence and farthings, by inspection. Double the first figure, or tenths, for shillings, and, if the second figure, or hundredths, be five, or more than five, reckon another shilling; then, after the five is deducted, call the figures in the second and third place so many farthings, abating one when they are above twelve, and two when above thirty-six, and the result will be the answer, sufficiently exact for all practical purposes. Thus, to find the value of '876 £. by inspection : 1. Find, by inspection, the decimal expressions of 9 s. 7 d., and 12 s. 02 d. Ans. 479 £., and ‘603 £. 2. Find, by inspection, the value of '523 £., and '694£. Ans. 10 s. 5 d., and 13 s. 104 d. 3. Reduce to decimals, by inspection, the following sums, and find their amount, viz.: 15 s. 3 d.; 8 s. 11 d.; 10 s. Amount, £1'833. 61 d.; 1 s. 81 d.; 1 d., and 24 d. 4. Find the value of '47 £. Note. When the decimal has but two figures, after taking out the shillings, the remainder, to be reduced to thousandths, will require a cipher to be annexed to the right hand, or supposed to be so. Ans. 9 s. 4 d. 5. Value the following decimals, by inspection, and find their amount, viz.: 785 £.; '357 £.; '916 £.; "74 £.; 5 £.; ‘25 £.; '09 £.; and '008 £. Ans. 3£. 12 s. 11 d SUPPLEMENT TO DECIMAL FRACTIONS. QUESTIONS. 1. What are decimal fractions? 2. Whence is the term derived? 3. How do decimal differ from common frac tions? 4. How are decimal fractions written? 5. How can the proper denominator to a decimal fraction be known, if it be not expressed? 6. How is the value of every figure determined? 7. What does the first figure on the right hand of the decimal point signify? the second figure? third figure? fourth figure? 8. How do ciphers, placed at the right hand of decimals, affect their value? 9. Placed at the left hand, how do they affect their value? 10. How are decimals read? 11. How are decimal fractions, having different denominators, reduced to a common denominator? 12. What is a mixed number? 13. How may any whole number be reduced to decimal parts? 14. How can any mixed number be read together, and the whole expressed in the form of a common fraction? 15. What is observed respecting the denominations in federal money? 16. What is the rule for addition and subtraction of decimals, particularly as respects placing the decimal point in the results? -multiplication? division? 17. How is a common or vulgar fraction reduced to a decimal? 18. What is the rule for reducing a compound number to a decimal of the highest denomination contained in it? 19. What is the rule for finding the value of any given decimal of a higher denomination in terms of a lower? 20. What is the rule for reducing shillings, pence and farthings to the decimal of a pound, by inspection? 21. What is the reasoning in relation to this rule? 22. How may the three first figures of any decimal of a pound be reduced to shillings, pence and farthings, by inspection? EXERCISES. 1. A merchant had several remnants of cloth, measuring as follows, viz. : How many yards in the whole, and what would the whole come to at $3'67 per yard? Note. Reduce the common fractions to decimals. Do the same wherever they occur in the examples which follow. Ans. 36'475 yards. $133'863+, cost. 2. From a piece of cloth, containing 36 yds., a merchant sold, at one time, 7 yds., and, at another time, 12ğ yds.; how much of the cloth had he left? Ans. 167 yds. 3. A farmer bought 7 yards of broadcloth for 8 £., a barrel of flour for 2£., a cask of lime for 13 £., and 7 lbs. of rice for £.; he paid 1 ton of hay at 37 £ 1 cow at 6., and the balance in pork at £. per lb.; how many were the pounds of pork? Note. In reducing the common fractions in this example, it will be sufficiently exact if the decimal be extended to three places. 4. At 124 cents per lb., what will 37 Ans. 1084 lb. lbs. of butter cost? Ans. $4'7182. 5. At $17'37 per ton for hay, what will 111⁄2 tons cost? Ans. $201 92§. 6. The above example reversed. At $ 201'92 of hay, what is that per ton? for 111⁄2 tons Ans. $1737. 7. If '43 of a ton of hay cost $9, what is that per ton? Consult T 65. Ans. $20. 8. At 4 of a dollar a gallon, what will '25 of a gallon of molasses cost? Ans. $1. 9. At $9 per cwt., what will 7 cwt. 3 qrs. 16 lbs. of sugar cost? Note. Reduce the 3 qrs. 16 lbs. to the decimal of a cwt, extending the decimal in this, and the examples which follow, to four places. Ans. 71'035+. 10. At $69875 for 5 cwt. 1 qr. 14 lbs. of raisins, what is per cwt.? Ans. $13. that 11. What will 2300 lbs. of hay come to at 7 mills per lb.? Ans. 16'10. 12. What will 765 lbs. of coffee come to, at 18 cents per Ans. $13779 Ib.? N* 13. What will 12 gals. 3 qts. 1 pt. of gin cost, at 28 cents per quart? Note. Reduce the whole quantity to quarts and the decimal of a quart. Ans. 14'42. 14. Bought 16 yds. 2 qrs. 3 na. of broadcloth for $100′125; what was that per yard? Ans. $6. 15. At $192 per bushel, how much wheat may be bought for $72? Ans. 1 peck 4 quarts. 16. At $9272 per ton, how much iron may be purchased for $60'268 ? Ans. 13 cwt. 17. Bought a load of hay for $9'17, paying at the rate of $16 per ton; what was the weight of the hay? Ans. 11 cwt. 1 qr. 23lbs. 18. At $302'4 per tun, what will 1 hhd. 15 gals. 3 qts. of wine cost? Ans. $94'50. 19. The above reversed. At $94'50 for 1 hhd. 15 gals. 3 qts. of wine, what is that per tun? Ans. $302'4. Note. The following examples reciprocally prove each other, excepting when there are some fractional losses, as explained above, and even then the results will be sufficiently exact for all practical purposes. If, however, greater exactness be required, the decimals must be extended to a greater number of places. 20. At $180 for 31 qts. of wine, what is that per gal. ? 22. If of a ton of potashes cost $60'45, what is that per ton? | 21. At $2215 per gal, what cost 34 qts. ? 23. At $96'72 per ton for pot-ashes, what will § of a ton cost? 24 If '8 of a yard 25. If a yard of 26. At $25 per of cloth cost $2, cloth cost $2'5, yard, how much what is that per what will '8 of a cloth may be puryard? yard cost? chased for $2 ? 27. If 14 cwt. of 28. If a ton of pot-ashes cost 19 £. pot-ashes cost 27£. 5 s, what is that 10 s., what will 14 per ton? Note. cwt. cost? 29. At 27 £.10 a ton for pot-ashes, what quantity may be bought for 19 £. 5 s.? After the same manner let the pupil reverse and prove the following examples: 30. At $18'50 per ton, how much hay may be bought for $12'025? 31. What will 3 qrs. 2 na, of broadcloth cost, at $6 per yard? 32. At $22'10 for transportation of 65 cwt. 46 miles, what is that per ton? 33. Bought a silver cup, weighing 9 oz. 4 pwt. 16 grs. for 3 £. 2 s. 3 d. 33 q.; what was that per ounce ? 34. Bought 9 chests of tea, each weighing 3 cwt. 2 qrs. 21 lbs. at 4 £. 9 s. per cwt.; what came they to? 35. If 5 acres 1 rood produce 26 quarters 2 bushels of wheat, how many acres will be required to produce 47 quarters 4 bushels? A quarter is 8 bushels. Note. The above example will require two operations, for which consult T 65, ex. 1. 36. A lady purchased a gold ring, giving at the rate of $20 per ounce; she paid for the ring $125; how much did it weigh? REDUCTION OF CURRENCIES. ¶ 78. Previous to the act of Congress in 1786 establishing federal money, all calculations in money, throughout the United States, were made in pounds, shillings, pence and farthings, the same as in England. But these denominations, although the same in name, were different in value in dif ferent countries. England, Nova Scotia, Virginia, Kentucky, and Thus, 1 dollar is reckoned in 4 s. 6 d., called English, or sterling money. 5 s. called Canada currency. 6 s., called New England currency. 8 s., called New York currency. |