are regarded as decimal parts of a dollar. Thus the dime is 1 tenth, 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 1 1, 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, decim 258. 463. Hence any sum in Federal Money may be regarded as a decinal, 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 dollars ninety-nine cents; what is the amount of the three ? Ans. $166.22. 4.62 5.28 10.08 4. A man bought 24 yds. Ans. $19.98-19 dolls. and of broadcloth for $15.50, 6 98 cents. 2. A owes B $78, C 846. 27, D $101. 09, and E $28. 16; what is the amount of the four debts? Ans. $253.52. yds. of lutestring for $5.85, MULTIPLICATION OF FEDERAL MONEY. 134. RULE. The same as for the Multiplication of Decimals. (122). QUESTIONS FOR PRACTICE. 1. What will S4 yards of cloth cost, at 37 cents per yard? 0.37 34 148 111 $12.58 Ans. 2. If a man purchase 4 handkerchiefs at 62 cents each, 8 yds. ribbon at 17 cents per yard, and 5 yds. of lace at 44 cents per yard, what is the whole amount? Ans. $6.04. 3. What will 156 yards of cloth cost at $1.67 per yard? Ans, $260. 52. 4. What will 47 lbs. of coffee cost at 22 cents per pound? Ans. $10.34. 5. At 16 cents a pound, what will 18 lbs. of butter cost? what will 27 lbs. cost? 6. What is the cost of 126 bushels of rye at 62 cents a bushel? Aus. $78.75. 7. If a person spend 61 cents a day, how much will that be a year? Ans. $22. 811. 8. What cost 63 yards of calico at a quarter of a dollar a yard ? Ans. $15.75. 9. What cost 1758 lbs. of tea at $1.15 per pound? Ans. $2021.70. 10. What cost 59 dozen of eggs at 59 cts. a dozen? 11. What cost 87 bushels of oats at 33 cts per bush. ? at 41 cts Pat 37 cts P at 253 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 of oxen for $76, and sold them again for $81.75; how much did he gain? Ans. $5.75. 2. Take 1 mill from $100 what remains? 3. A person having $200 lost two dimes of it; how much had he left? 4. A man bought 100 lbs. of wool at 33 cts. a pound, and sold the whole for $31. 494, how much did he lose? 5. A person bought 24 yards of cloth at $1.50 per yard, and paid $26.55, how much remains unpaid? Ans. $9.45. 6. I bought 6 yards of cloth at 76 cts. a yard, and gave a 5 dollar bill, how much change must I receive? 7. How much must be added to 83 cents to make it $5? 8. I bought 5 yds. of cloth at $5 a yard, and paid six 5 dollar bills, who must receive change, and how much? DIVISION OF FEDERAL MONEY. 136. RULE.-The same as for the Division of Decimals.(128) QUESTIONS FOR PRACTICE. 2. If 125 bushels of wheat cost $100.25, what is it a bushel ? 3. If $1268 be divided equally among 15 men, what will each receive? Ans. $84.533. 4. Six men, in company, buy 27 bushels of salt at 81.67 a bushel, what did each man pay, and what was each's share of the salt? Ans. $7.515, and his share 4 bush. an estate of $35000; the demands against the estate are $1254.65; the remainder, after deducting a legacy of $3075, is divided equally among his 6 sons; what is each son's share? Ans $5111.725. 6. If 12 acres of land cost $78, how much is that an acre? 7. Divide 87 between 9 men, what is each man's Ans. $0.7773. share? 8. Show much? 5. A man dies leaving much? REVIEW. 1. How has the foot usually been divided? 2. What are the inconveniences of these divisions? 3. What would be a more convenient division? 4. How might these divisions be managed? 5. What name is given to numbers, which express parts in this manner?(114) 6. How are decimals distinguished from integers? What are integers? 7. How would you write 12 feet and 3 tenths? 16. What is the rule for the multiplication of decimals? What the rule for pointing? 17. What effect has multiplication by a decimal? Explain by example and diagram. 18. What is the rule for the subtraction of decimals? For the division of decimals? 19. What is the rule for pointing in each? 20. What is to be done if there are not so many figures in the quotient as the number of decimals required? 21. When the decimal places in 8. Have figures in decimals a lo- the divisor exceed those in the dical value? Upon what does it de-vidend, what is to be done? pend? 9. What is the law by which they diminish ?(115) 10. In what does the enunciation of decimals differ from that of whole numbers ? 11. Do ciphers on the right hand of decimals alter their value? What does each additional cipher indicate?(116) 12. What effect have ciphers on the left hand of decimals? Why? 13. What are numbers made up of integers and decimals called? (114) 14. From what is the word decimal derived? A. From decimus, (Latin) which signifies tenth. 15. What is the rule for the addition of decimals? Where must the decimal point be placed? 22. When there is a remainder after division, how do you proceed? 23. What does a vulgar fraction denote?(129) Explain by example. 24. How then can you change a vulgar fraction to a decimal? 25. What is Federal Money? 26. What is the Table? (p. 31.) 27. Which is the unit money? 28. How may the lower denominations be regarded? Explain by example; and also the different methods of reading the same. 29. How then may Federal Mo.. ney be regarded? 30. How is it denoted? 31. What is the rule for the Addition of Federal Money?-for Multiplication?-for Subtraction?-for Division of Federal Money? 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. Keduction. 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; £ s. d. gr. 20 88s. 12 181 88 1061d. 4247qr. Ans. As £1-20s. there are 20 times as many shillings as there are pounds; we therefore multiply the pounds by 20, and to the product, 80s. join the 8s. making 889. Then because 1s. 12d. there are 12 times as many pence as there are shillings: we therefore multiply the 88s. by 12. joining the 5d to the product, and thus find £4 8s. 5d.=1061d. Again, as 1d.-4qr. we multiply the pence by 4. joining the 3 qr. to the product, and thus find 41. 8s. 5d. 3qr. 4247 farthings. This process is called Reduction Descending, because by it numbers of a higher denomination are brought into a lower denomination. 2. In 4247 farthings how many pounds? 4) 4247 12) 1061-3qr. 20)88-5d. As it takes 4qr. to make 1 penny, there are evidently as many pence in 4247qr. as there are times 4 in that number. We therefore divide by 4, and the quotient is 1061d. and 3 qr over. Then, as it takes 12 pence to make 1s. there will be as many shillings as there are times 12 in 1061d. 88s. 5d. Again, as it takes 20s. to make 1. there will be as many pounds as there are times 20 in 88s. 41. 8s. Thus we find 4247qr.-4. 3s. 5d. 3qr. This process is called Reduction Ascending, because by it a lower denomination is brought into a higher. By these examples it will be seen that Reduction Ascending and Descending mutually prove each other. 41. 8s. 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. RULE.-Multiply the highest denomination by that number which it takes of the next lower to make one in the next higher, adding the number, if any, of the lower denomination; and so proceed to do, till it is brought as low as the question requires. 140. REDUCTION ASCENDING. RULE. Divide the lowest denomination by the number which it takes of that to make one in the next higher denomination; and so continue to do, till you have brought it into the denomination required. |