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 three first figures of any decimal of a pound be reduced to shillings, pence and farthings, by inspection? the 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, 73 yds., and, at another time, 12 yds. ; how much of the cloth had he left? Ans. 16'7 yds. 3. A farmer bought 7 yards of broadcloth for 8 £., a barrel of flour for 2 £., a cask of lime for 18 £., and 7 lbs. of rice for £.; he paid 1 ton of hay at 37% £ 1 cow at 64 £., 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. Ans. 108 lb. 4. At 12 cents per lb., what will 372 lbs. of butter cost? Ans. $47182. 5. At $17'37 per ton for hay, what will 113 tons cost? Ans. $201 92§. 6. The above example reversed. At $201'92 for 11 tons of hay, what is that per ton? Ans. $1737. 7. If '45 of a ton of hay cost $9, what is that per ton? Consult ¶ 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 $69'875 for 5 cwt. 1 qr. 14 lbs. of raisins, what is that per cwt.? Ans. $13. 11. What will 2300 lbs. of hay come to at 7 mills per lb. ? Ans. $16'10. 12. What will 7654 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? 15. At $1'92 per bushel, how bought for $72 ? 16. At $9272 per ton, how chased for $60′268 ? Ans. $6. much wheat may be Ans. 1 peck 4 quarts. much iron may be purAns. 13 cwt 17. Bought a load of hay for of $16 per ton; what was the weight of the hay? $9'17, paying at the rate Ans. 11 cwt. 1 qr. 23 lbs. 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 $1'80 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 $2'215 per gal., what cost 34 qts.? 23. At $96'72 per ton for pot-ashes, what will § of a tou 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? chased for $2? 27. If 14 cwt. of 28. If a ton of 29. At 27 £.10 pot-ashes cost 19£.pot-ashes cost 27 £. 5 s., what is that 10 s., what will 14 per ton? yard cost? cwt. cost? a ton for pot-ashes, what quantity may be bought for 19 £. 5 s.? Note. 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 3 £. 2 s. 3 d. 33 q.; what was that per ounce ? grs. for 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 ¶ 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. 178. 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, 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. 88., called New York currency. New Jersey, S. Carolina and Georgia, } 1 dollar is reckoned in 7 s. 6 d., called Pennsylvania currency. 4 8. 8 d., called Georgia currency. 1. Reduce 6£. 11 s. 61 d. to federal money. Note. To reduce pounds, shillings, pence and farthings, in either of the above-named currencies, to federal money,First, reduce the shillings, pence and farthings (if any be contained in the given sum) to the decimal of a pound by in spection, as already taught, TT 76. 6£. 11 s. 64 d. = £6'576. English money.-Now, supposing the above sum to be English money,-1£. is 20 s. = 240 pence, in all the above currencies. 1 dollar, in English money, is reckoned 4 s. 6 d = 54 pence, that is, of 1 pound. Now, as many times as, the fraction which 1 dollar is of 1 pound, English money, is contained in £6'576, so many dollars, it is evident, there must be; that is,-To reduce English to federal money,-Divide the given sum by, the quotient will be federal money. £6'576 English money. 40 9) 263'040 29'226 federal money, Answer. Note. It will be recollected, to divide by a fraction, we multiply by the denominator, and divide the product by the numerator. CANADA CURRENCY.-Supposing the above sum to be Cana da currency,-1 dollar, in this currency, is 5 s. = 60 pence, that is, of 1 pound. Therefore,-To reduce Cana da currency to federal money,-Divide the given sum by †, and the quotient will be federal money; or, which is the same thing,-Multiply the given sum by 4. £6'576 Canada currency. 4 $27'304 federal money, Answer. |