Hence we derive the following RULE. 1. How must the several denominations be placed? A. One above another, the highest at the bottom. II. How do you divide? A. Begin at the top, and divide as in Reduction; that is, shillings by shillings, ounces by ounces, &c., annexing ciphers. III. How long do you continue to do so? A. Till the denom inations are reduced to the decimal required. More Exercises for the Slate. 2. Reduce 7 s. 6 d. 3 qrs. to the decimal of a pound. A.,378125 £ 3. Reduce 5 s. to the decimal of a pound. 5. Reduce 2 qrs. 3 na. to the decimal of a yard. A. ,003125 £. A.,6875 yd. 6. Reduce 2 s. 3 d. to the decimal of a dollar. A.,7375 lb 9. Reduce 8 £, 17 s. 6d. 3 qrs. to the decimal of a pound. A. 8,878125 £. a unit, is, by being in the second place, of; then and added together, thus, £%+3=35=35, Ans. Hence, to find the value of a mixed repetend-First find the value of the repeating decimals, then of the other decimals, and add these results together. 2. Change,916 to a common fraction. A. Fob+980=838=11. Proof, 1112= =,916. 61 3. Change 203 to a common fraction. A. 8. To know if the result be right, change the common fraction to a decimal again. If it produces the same, the work is right. Repeating decimals may be easily multiplied, subtracted, &c. by first reducing them to their equal common fractions. 1 LIX. To reduce Decimals of higher Denomina tions to Whole Numbers of lower Denominations. This rule is the reverse of the last. Let us take the answer to the first example. Reduce,775 £ to whole numbers of lower denominations. OPERATION £,775 20 s. 15,500 12 d. 6,000 In this example,775 £, reduced to shillings, that is, multiplied by 20, gives 15,5, (for ciphers on the right of a decimal are of no value;) then the decimal part ,5×12=6,00 =6d. Ans. 15 s. 6 d. Hence we derive the following RULE. I. How do you proceed? A. Multiply the given decimal as in Reduction; that is, pounds by what makes a pound, ounces by what makes an ounce, &c. II. How many places do you point off in each product for decimals? A. As many as there are decimal places in the given decimal. III. Where will you find the answer? A. The several denominations on the left hand of the decimal points will be the answer. More Exercises for the Slate. The following examples are formed by taking the answers in the last rule; of course, the answers in this may be found in the examples of that. The examples in each are numbered so as to correspond. 2. Reduce ,378125 £ to whole numbers of lower denominations. (For ans. see ex. No. 2, ¶ LVIII.) 3. What is the value of 25 £ of a pound? 8. What is the value of ,7375 of a pound Troy? Application of the two foregoing Rules. 1. What will 4 yards of cloth cost, in pounds, at 7 s. 6 d. a 78. 6d., reduced to a decimai,=,375 £× 4 yds.: yard? £1,500 20 10,000 Ans., 1 £ 10 s = 2. At $6 a cwt., what will 2 cwt. 2 qrs. of rice cost? A. $15. 3. At $20 a ton, what will 15 cwt. 2 qrs. of hay cost? A. $15,50 4. What cost 6 cwt. 0 qr. 7 lbs. of sugar, at $11,25 a cwt. A. $68,203+ 5. What cost 60 gals. 1 pt. of rum, at $,78 a gallon? A. $46,897. 6. At $1,25 a bushel, what will 36 bu. 0 pk. 4 qts. cost? A. $45,156,25 7. At $4,75 a yard, what will 26 yds. 2 qrs. of broadcloth cost? A. $125,87. 8. At 2£, 10 s. a cwt., what will 6 cwt. 3 qrs. of rice cost? 2 £, 10 s. =2,5 £, and 6 cut. 3 grs.=6,75 cut. ; then, 6,75X 2,5=16,875 £×20= 17,5 s.X12=6 d. Ans. 16 £, 17 s. 6 d. 9. What will 6 gallons, 2 qts. of brandy cost, in pounds, at 15 shillings a gallon? A. 4£. 17 s. 6 d. REDUCTION OF CURRENCIES. LX. An apology may by some be deemed necessary for the omission, in this work, of much that is contained in other treatises, respecting what is called " the currencies of the different United States." The athor, however, deems it rather necessary to apologize for introducing the subject at all. Those merely nominal currencies, originally derived from Great Britain, have long been obsolete in law, and ought to become so in practice. So long, however, as that practice continues, it may be necessary to retain a brief notice of it in elementary works. Note. It was not intended that the following Table should be exact in every particular to a mill, but enough so, to correspond with the pecuniary calculations current among men of business; and, as such, it will be committed to memory more easily. The design of the Table is not that it should be learned by rote, but by actual calculations from a few data; thus-as 1 far. is of a cent, then 2 farthings are. Again, as 3 d. is 4 cents, and 3s. are 50 cents, then 3 s. 3 d. are 54 cents. It would be well for the teacher to direct the attention of the pupil to this object by explanations. 6. d. d. cts 2 and 6 are 30 or 42 2 yards of tape cost in 2. What will 2 sticks of twist cost, in cents, at d. a stick? Atd. a stick? At d. a stick? 3. At 7 d. a piece, how many cents will buy 1 inkstand? Will buy 2? Will buy 3? 4? 5? 6? 4. How many cents must you pay for 2 rulers, at 9 d. a iece? For 4? For 6? For 8? For 16? For 24? For 5. What will 2 yards of lace come to in cents, at 1 s. 6 d. a yard? What will 3 yards? What will 4 yards? What will 6 yards? 6. When oats are 3 s. 6 d. a bushel, how many cents will buy 2 bushels? 7. When rye is 3 s. a bushel, how many cents will buy 2 bushels? How many 3 bushels? How many 4? How many 8? 8. When corn is 4 s. 6 d. a bushel, what are 2 bushels worth in cents? What 4 bushels? What 8 bushels ? bushels? 9. How many cents make a dollar? A. 100. What 12 10. If a Latin Grammar cost 6 shillings, how many dollars will buy 2? How many 4? How many 6? How many 8? How many 20? 11. What will 2 barrels of flour come to, at 30 shillings pe barrel? What will 3? What will 6? What will 7? 12. If you buy a book for 1 shilling and 6 pence, and give the bookseller a fifty-cent piece, how many cents in change mus ` he give you? 13. If you buy a Latin Grammar for 4 shillings and 9 pence, and give the bookseller 1 dollar, how many cents must he pay you? 14. If you have 4 pence a week, how many weeks will come to a dollar? How many to 2? How many to 3? 15. If I pay 1 s. 6 d. for 1 meal of victuals, how many meals can I have for a dollar? For 2 dollars? For a dollar? For of a dollar? For 3 dollars? For 4? 16. When broadcloth is 12 s. a yard, for how many dollars can you buy 2 yards? How many 3? How many 5? 17. You buy a hat for 18 shillings, and give the store-keeper a five dollar bill; how many dollars must he give you in change? 18. How many cents are 2 s. 2 d. ? 2 s. 7 d. ? 2 s. 5 d.? 2 s. 10 d. ? 3 s. 1 d. ? 3 s. 5 d. ? 3 s. 8 d. ? 4 s. 2 d. ? 4 s. 10 s. 6 d. ? 12 s. ? 14 s. 6 d. ? 17 s. 6 d.? 18 s. ? 42 s.? 48 s.? 54 s. Q. What is that, which you have now been doing, called? A. Reduction of Currencies. Q. Are pounds, shillings, pence and farthings the same in all countries? A. They are the same in name, but not in value. Q. What was their value formerly in England and her American colonies? A. The same. Q. What has occasioned the difference in value? A. The legislatures of these colonies emitted, or put in circulation, bills, which depreciated in value in various degrees. Q. What is the number of shillings, which it takes, in any state, to make a dollar, called? A. The currency of that state. Q. How many shillings make a dollar in the New England states, Virginia, Kentucky, and Tennessee? A. 6 shillings. Q. What name does the currency of these states take? A The New England currency. NEW ENGLAND CURRENCY.-To reduce this Currency to Federal Money, and Federal Money again to the same Currency. Q. What part of a pound is $1 or 6s. of this currency? A. 21%; decimally,=,3. 1. How many dollars in 3 £. 8 s. 3 d.? By reducing 3£. 8s. 3d. to decimals, by T LVIII, we have 3,4125£. Now, since every 3 of a pound is a dollar, it is crident, that, as many times as ,3 is contained in 3,4125£, so many dollars there will be, thus : |