$299.99, how much does one lay up more than the other? Ans. $39.87. 13. Bought a farm for $3946, and sold a part for $1426.82; what did the remaining part cost me? Ans. $2519.18. MULTIPLICATION OF FEDERAL MONEY. be re RULE.-Multiply as in simple numbers. The product will always be in the lowest denomination given, which may duced to dollars, cents, and mills, by the preceding rules. Ex. 1. What will 36 yards of cloth cost at $4.50 per yard? Ans. $162.00. PERFORMED. 2 7.0 0 1.3 5.0 1 6 2.0 0 The given price being 450 cents, the whole price is 16200 cents, which equals $162.00. 2. What will 29 pairs of shoes cost at $1.50 per pair? Ans. $43.50. 3. What will 35 pounds of beef cost at 8 cents per pound? Ans. $2.80. 4. Bought 280 reams of paper at $2.35 per ream; what was the whole cost? Ans. $658.00. 5. What cost 600 pounds of lard, at 15 cents per pound? Ans. $90.00. 6. Bought 15 tons of hay at $16.42 per ton; what was the whole cost? Ans. $246.30. 7. What cost 349 acres of land, at $15.49 per acre? Ans. $5406.01. 8. Bought 18 yoke of oxen for $72.50 per yoke ; what was the whole cost? Ans. $1305.00. 9. Bought 32 pounds of butter at 20 cents per pound; 45 pounds of loaf sugar at 18 cents per pound; 56 pounds of coffee at 15 cents per pound; 26 pounds of tea at $1.75 per pound; 21 cwt. of raisins at $6.75 per cwt.; 42 barrels of flour at $7.50 per barrel; and 29 pairs of boots at $4.50 per pair. What did the whole cost me ? Ans. $655.65. DIVISION OF FEDERAL MONEY. Division of Federal Money is employed whenever the cost of a number of articles, as yards, pounds, &c., is given, and the price of one required. RULE.-Divide the cost by the number of articles, and point off as many figures from the quotient for cents and mills, as there are in the given sum. If dollars only be given, and cyphers are added to complete the division, these cyphers must be regarded as cents and mills. Ex. 1. If 9 pounds of butter cost $225, what is the value of one pound? Ans. $0.25. 2. Sold 69 bushels of wheat for $625; what was the price per bushel? Ans. $9.057. 3. Paid $75.00 for 500 lbs. of butter; what was the price per pound? Ans. $0.15. 4. Paid $311.70 for 15 tons of hay; what was the price per ton? Ans. $20.78. 5. Paid $658 for 280 reams of paper; what did I pay per ream? Ans. $2.35. 6. Paid $505.44 for 144 lbs. of tea; what was the price of one pound? Ans. $3.51. 7. Paid $375 for 50 firkins of butter; what was the price per firkin? Ans. $7.50. 8. Paid $43.79 for 29 pairs of boots; what was the price per pair? Ans. $1.51. 9. Paid $2.80 for 35 lbs. of beef; what was the price per pound? Ans. .08. APPLICATION OF THE PRECEDING RULES. 1. A man dying, left an estate of $12000, which was divided equally among 7 children after his wife had received her third. What was the portion of the wife, and what did each child receive? Ans. $4000, wife's portion; $1142.857, each child's portion. 2. A man settling with his grocer, finds himself charged with 15 lbs. of tea at 75 cts. per pound; 42 pounds of brown sugar at 11 cts. a pound; 3 barrels of flour at $7.50 per barrel; 8 gallons of lamp oil at $1.25 per gallon; and 45 pounds of ham at 15 cts. per pound. He is also credited $11.62. How much does he owe his grocer? Ans. $43.50. 3. A man sells a horse for $84; 5 cows for $25 each; and agrees to take 80 sheep in pay. How much do the sheep cost him per head? Ans. $2.614. 4. A person agrees to furnish a grocer with 56 bushels of rye at 50 cts. a bushel, and to take his pay in coffee at 15 cts. a pound. How many pounds of coffee will he receive? Ans. 1863. 5. If I pay $21311 for 844 acres of land, what do I pay per acre? Ans. $25.25. 6. Bought 350 yards of cloth at $3 50 per yard. Of this I sold 200 at $5.00 per yard. How much money did I pay out; how much did I receive; how many yards had I left; and how much did it cost me per yard? Ans. I paid out $1225; I received $1000; 150 yards were left; and what remained cost me $1.50 per yard. 7. A man sold his farm for $8456, and his stock for $1560; at the same time he had on deposite in the bank, $872.97. He then purchased a house in the city, for which he paid $3845; he also purchased a horse and carriage for $392.53, and paid up his old debts to the amount of $1787. How much money had he left? Ans. $4864.44. 8. Suppose the man in the preceding sum had laid out the balance of his money in wagons, for which he paid $72 each; and that he took these wagons to the south and sold them for $97 each. How many wagons did he purchase, and how much did he gain by the transaction, allowing his expenses to have been $297.83? Ans. He purchased 67 wagons, and had $40.44 left; and he gained $1377.17. 9. On the first of Jan. a spendthrift was in possession of $3860.90 after 30 days he had only $1680 remaining; how much had he spent during the whole time; and how much daily? Ans. Whole sum, $2180.90; daily, $72.696. 10. A man bought 20 pounds of coffee, for 15 cents a pound; and 18 pounds of sugar, at 12 cts. a pound. He paid 96 cents in cash, and the balance in butter at 20 cents a pound; how much butter did it take? Ans. 21 pounds. 11. How much tea worth 56 cents a pound must be given for 16 sacks of salt, worth $2.87 per sack? Ans. 82 pounds. QUESTIONS.-What is Federal Money? What are its denominations? How do they increase in value? Repeat the table. What are the coins of the United States? What are the gold coins? What are their values? What are the silver coins? What are their values? Are the four-pence half-penny and the nine-penny pieces, American coin? What are the copper coins? Are the gold and silver coins pure metal? What is their composition? By what word is the purity of a metal expressed? What does that word express? If a quantity of gold be said to be 18 carats fine, what is meant? Suppose it be said to be 22 carats fine, what is meant? How may the denominations of Federal Money be added? Which is the unit money? What are dimes, cents, and mills? How is the dollar or unit figure always shown? How does the period always stand? What is the first figure on the left of the point? The second? How are they usually read? How are the figures on the right of the point read? How are cents converted into mills? How are dollars converted into cents? What is the rule for the addition of Federal Money? How is the decimal point placed? What is the rule for the subtraction of Federal Money? How is the point placed? What is the rule for the multiplication of Federal Money? How many figures are cut off from the right of the product? When is division of Federal Money employed? What is the rule? How many figures do you point off in the quotient? If dollars only are given and cyphers are added, how are they to be regarded? CANCELING. In all arithmetical operations, it is important not only to know how to solve a proposition, but also, how it may be done most expeditiously. The object of this rule is to acquaint the scholar with a principle by which peculiar expedition is attained in the solution of such sums as involve in their operation both multiplication and division. This principle is founded on the following facts: First. The value of any quotient depends on the ratio, or relative size of the numbers divided; that is, if the dividend be three times as large as the divisor, the value of the quotient is 3; and if it be four times as large, the value is 4, &c. Second. If two or more numbers are to be multiplied together, and their product divided by any other number, the true result is obtained by first dividing one of these numbers by the dividing number, and then multiplying the quotient by the remaining number or numbers. Thus, if it be required to multiply 8 by 4 and to divide the product by 2, first divide 8 by 2 and multiply the quotient by 4; thus, 8÷2-4, and 4 × 4=16. The advantage of this process will be more obvious if we take large numbers. Suppose we wish to multiply 288 by 16, and to divide the product by 144. The usual process would be thus: But by first dividing, the operation is much abbreviated; thus: 144) 288(2 0 0 0 and 16×2=32. By the usual method, 37 figures are required; by the other, only 18. There is still another advantage. The scholar can see at a glance that 144 is contained in 288, twice; and that twice 16 is 32; so that an operation, which is long and protracted, is often reduced nearly or quite to a mental operation. Third. When any large number is to be divided by the product of two or more smaller numbers, it may be divided by each number separately. This needs no explanation; it is the same as dividing by the component parts of any number, instead of the number itself. Fourth. When the operation is of such a nature as to require the product of several numbers to be divided by the product of several other numbers, these numbers may be divided before multiplication, and their quotients used instead of the numbers themselves. For illustration, suppose the product of 36 and 42 is to be divided by the product of 6 and 7. The usual mode of operation would be as follows, viz.: 4 2 252 126 1 5 1 2 dividend. |