are regarded as decimal parts of a dollar. Thus the dime is 1 teoth, or 0.1 of a dollar, the cent 1 hundredth, or 0.01 of a dollar, and the mill 1 thousandth, or 0.001, of a dollar; and placing these together, dol. d. c. m. 1. ] 1 l, They might be read, one dollar, one dime, one cent and one mill, or, one dollar, eleven cents and one mill, or one dollar, one hundred and eleven mills, or thousandths. The place next to dollars, on the left, is eagles, and 11, may be read, 1 eagle and 1 dollar, or eleven dollars. Twenty-five eagles, 8 dollars, 4 dimes, 6 cents and 3 mills, may be written and read, 25 8. 4 6 3 258. 46 3 258. 463. Hence any sum in Federal Money may be regarded as a deciinal, or mixed number, and may be managed in all respects as such. Federal Money is usually denoted by the character, $, placed before the figures, and in reading it, dollars, cents and mills are the only denominations usually mentioned. ADDITION OF FEDERAL MONEY. 133. Rule.—The same as for the Addition of Decimals.(118) QUESTIONS FOR PRACTICE. 1. If I pay 4 dollars 62' 3. F holds a note against cents for a barrel of soap, G for one hundred seven 5 dollars 28 cents for a bar- ! dollars and six cents, one rel of flour, and 10 dollars | against H for forty-nine 8 cents for a barrel of pork, dollars seventeen cents, what do I give for the whole: and one against K for nine 4.62 dollar's ninety-nine cents; : 5.28 what is the amount of the 10.08 three ? Ans. $166.22. 4. A man bought 2} yds. Ans. $19.98=19 dolls. and I of broadcloth for $15.50, 6 98 cents. yds, of lutestring for-85.85, 2. A owes B 878, C 846. 7 yds. of cambric for $5.25, 27, D $101. 09, and E 828. 1 and trimmings to the a16; what is the amount of mount of $4.12: what was the four debts? the amount of the purchase : Ans. $253.52. Ang. $30.7%. 148 MULTIPLICATION OF FEDERAL MONEY, 134. RULE. The same as for the Multiplication of Decimals, (122). QUESTIONS FOR PRACTICE. 1. What will 34 yards 5. At 16 cents a pound, of cloth cost, at 37 cents what will 18 lbs. of butter per yard? cost ? what will 27 lbs. 0.37 cost! 6. What is the cost of 126 bushels of rye at 62 cents a bushel? Aus. 878.75. 111 7. If a person spend 6 cents a day, how much will $12.58 Ans. that be a year? 2. If a man purchase 4 Ans. $22. 811. handkerchiefs at 62 cents i 8. What cost 63 yards of each, 8 yds. ribbon at 17 calico at a quarter of a dolcents per yard, and 5 yds. of lár a yard ? Ans. $15.75. lace at 44 cents per yard, 19. What cost 1758 lbs. of what is the whole amount? tea at $1.15 per pound? Ans. 86.04. ! . Ans. 62021.70. 3. What will 156 yards 10. What cost 59 dozen of cloth cost at $1.67 per i of eggs at 59 cts. a dozen ? yard ? Ans, $260. 52. 11. What cost 87 bushels 4. What will 47 lbs. of of oats at 33 cts per bush. ? coffee cost at 22 cents per at 41 cts?, at 37 cts ? at 253 pound? Ans. $10.34. | cts? . SUBTRACTION OF FEDERAL MONEY. 135. RULE. The same as for the Subtraction of Decimals, (124). QUESTIONS FOR PRACTICE. : 1. A man bought a pair 3. A person having $200 of oxen for $76, and sold lost two dimes of it; how them again for $81.75; how much had he left ? much did he gain ? 4. A man bought 100 lbs. Ans. 85.75. of wool at 33 cts. a pound, 2. Take 1 mill from 8100 and sold the whole for $31. what reinains ? | 494, how much did he lose ? 5. A person bought 24 7. How much must be yards of cloth at $1.50 per added to 83 cents to make yard, and paid $26.55, how it 85 ? much remains unpaid ? 8. I bought 54 yds. of Ans. 89.45. cloth at 851 a yard, and 6. I bought 6 yards of paid six 5 dollar bills, who cloth at 76 cts. a yard, and I must receive change, and gave a 5 dollar bill, how how much? much change must I receive ? DIVISION OF FEDERAL MONEY. . 136. Rule.—The same as for the Division of Decimals.(128) QUESTIONS FOR PRACTICE. 1. If 24 lb. of tea cost, an estate of $35000; the 87.92, what is that a pound? l demands against the estate Ans. $0.33. | are $1254.65 ; the remain2. If 125 bushels of der, after deducting a legawheat cost $100.25, what i cy of 83075, is divided eis it a bushel ? qually among his 6 sons; what is each son's share ? 3. If $1268 be divided Ans 85111.725. equally among 15 men, what will each receive ? 1 6, If 121 acres of land Ans. $84.533. cost $78, how much is that į an acre ? 4. Six men, in company, buy 27 bushels of salt átl 7. Divide $7 between 9 81.67 a bushel, what did I men, what is each man's each man pay, and what share ? Ans. $0. 7777. was each's share of the salt? 8. 8-12 how much i Ans. $7.515, and his share Ans. 80.006. 41 bush. 9. 884+943--5=hor 5. A man dies leaving | much? 136, 137. 97 REVIEW. 1. How has the foot usually been | 16. What is the rule for the mula divided ? tiplication of decimals? What the 2. What are the inconveniences rule for pointing? of these divisions ? 17. What effect has multiplica3. What would be a more conve- | tion by a decimal? Explain by exnient division? ample and diagram. 4. How might these divisions be 18. What is the rule for the submanaged? traction of decimals ? For the divi. 5. What name is given to num sion of decimals? bers, which express parts in this 19. What is the rule for pointing manner?(114) in each? 6. How are decimals distinguish-| 20. What is to be done if there ed from integers ? What are inte- are not so many figures in the quo. tient as the number of decimals re7. How would you write 12 feet quired ? and 3 tenths ? 21. When the decimal places in 8. Have figures in decimals a lo- ! the diyisor exceed those in the dical value? Upon what does it de- | vidend, what is to be done? pend? 22. When there is a remainder 9. What is the law by which / after division, how do you proceed? they diminish?(115) 23. What does a vulgar fraction 10. In what does the enunciation denote?(129) Explain by example, of decimals differ from that of whole 24. How then can you change a numbers ? vulgar fraction to a decimal ? 11. Do ciphers on the right hand 25. What is Federal Money? of decimals alter their value? What 1 26. What is the Table ? (p. 31.) does each additional cipher indi-1 27. Which is the unit money? cate?(116) 28. How may the lower denomi. 12. What effect have ciphers on nations be regarded ? Explain by the left hand of decimals? Why? example; and also the different 13. What are numbers made up methods of reading the same. of integers and decimals called ? 29. How then may Federal Mo.. (114) ney be regarded ? 14. From what is the word deci 30. How is it denoted ? mal derived ? A. From decimus, 31. What is the rule for the Ad(Latin) which signifies tenth. dition of Federal Money?_forMul. 15. 'What is the rule for the ad- tiplication ?--for Subtraction?-for dition of decimals? Where must | Division of Federal Money? the decimal point be placed ? SECTION IV. COMPOUND, OR COMPLEX, NUMBERS.. 137. Numbers are called Compound or Complex, when they contain units of different kinds, as pounds, shillings, pence and farthings ; years, days, hours, minutes and seconds, &c. Tables of Compound Numbers will be found in Part I. Sec. tion V. page 31, which should be thoroughly committed to memory, as by them all operations, performed with compound numbers, are regulated. 1. Keductioit. 138. Reduction is the method of changing numbers from one. denomination to another, without altering their value.(40) 1. In £4 8s. 5d. 3qrs. how many farthings; As £1-20s. there are 20 times as many shillings £ s. d. gr. as there are pounds; we therefore multiply the 4 8 5 3 pounds by 20, and to the product, 80s. join the 8s. making 889. Then because ls.=12d. there are 12 times as many pence as there are shillings : we 88s. therefore multiply the 88s. by 12, joining the 5d to 12 the product, and thus find £4 8s. 5d.=10610. Again, as 1d.=4qr. we multiply the pence by 4, 181 joining the 3 gr. to the product, and thus find 41. 3s. 5d. 3qr.=4247 farthings. This process is call ed Reduction Descending, because by it numbers 1061d. of a higher denomination are brought into a lower denomination. 4247qr. Ans. 2. In 4247 farthings how many pounds ? As it takes 4qr. to make 1 penny, there are evidently . 4) 4247 as many pence in 4247gr. as there are times 4 in that number. We therefore divide by 4, and the quotient 12) 1061-3qr. is 1061d. and 3 qr over. Then, as it takes 12 pence to make 1s. there will be as many shillings as there are 210) 8 8--5d. times 12 in 1061d.=88s. 5d. Again, as it takes 20s. to make 11. there will be as many pounds as there are 41. 85. times 20 in 88s.=41. 8s. Thus we find 42479r.=41. 8s. 5d. 3qr. This process is called Reduction Ascending, because by it a lower depomination is brought into a higher. By these examples it will be seen that Reduction Ascending and Descending mutually prove each other. As a process similar to the above may be employed in the Reduction'of time, weights and measures, as well as monies, it may be stated in the following general terms. 139. REDUCTION DESCENDING. | 140. REDUCTION ASCENDING. RULE.--Multiply the high-L RULE.--Divide the lowest est denomination by that num- | denomination by the number ber which it takes of the next | which it takes of that to make lower to make one in the next one in the next higher denohigher, adding the number, if ! mination ; and so continue to any, of the lower denomina- do, till you have brought it into tion; and so proceed to do, till the denomination required. it is brought as low as the question requires. |