OBS. If either of the given numbers have no cents expressed, it is customary to supply their places by ciphers. 2. A man owing $57.35, paid $17.93: how much does he still owe? Ans. $39.42. 3. A grocer bought two hogsheads of molasses for $68.90, and sold it for $79.26: how much did he gain by the bargain? 4. A man owed a debt of $105, and paid all but $23. 67: how many dollars did he pay ? 5. A merchant bought a quantity of silks for $237.63, and sold it for $196.03: how much did he lose? 6. A drover bought a flock of sheep for $357, and sold them for $17.33 less than he paid for them: how much did he sell them for? 7. What is the difference between 365 dolls. 7 cts. and 208 dolls. 20 cts. ? 8. From 1 cent subtract 6 mills. 9. From 1 dollar, 6 cts. and 7 mills, take 89 cts. and 3 mills. 10. From 96 dollars, 6 cents, take 41 dolls., 63 cents, and 8 mills. 11. From 100 dollars, 10 cents, and 3 mills, take 1 cent and 5 mills. 12. From 1000 dollars, 6 cents, take 100 dolls. and 5 mills. MULTIPLICATION OF FEDERAL MONEY. 213. In Multiplication of Federal Money, as well as in simple numbers, one of the given factors must always be considered as an abstract number. (Art. 45. Obs. 2.) Ex. 1. How much will 5 yards of cloth cost, at $1.75 per yard? QUEST. 212. How is Federal Money subtracted? How point off the remainder? Obs. When either of the given numbers have no cents expressed, how is their place supplied? 213. In Multiplication of Federal Money, what must one of the given factors be considered? Operation. $8.75 Ans. If 1 yard costs $1.75, 5 yards will obviously cost 5 times as much. Hence, we multiply the price of 1 yard by the number of yards, and point off two figures for decimals in the product. (Art. 191.) 2. How much will 15.8 yards of fringe cost, at 12 cents per yard? Operation. 15.8 Reasoning as before, 15.8 yards will cost 15.8 times 12 cents. But in performing the multiplication, it is more convenient to make the 12 cents the multiplier, and the result will be the same as if it was placed for the multiplicand. (Art. 47.) Point off the product as before. $1.89 6 214. Hence, when the price of one article, one pound, one yard, &c., is given, to find the cost of any number of articles, pounds, yards, &c. Multiply the price of one article and the number of articles together, and point off the product as in multiplication of decimals. (Art. 191.) 3. Multiply $45.035 by 6.2. Ans. $279.217. 215. From the preceding illustrations we derive the following GENERAL RULE. Multiply as in simple numbers, and point off the product as in multiplication of decimal fractions. (Art. 191.) OBS. 1. When the price or the quantity contains a common fraction, the fraction should be changed to a common decimal. (Art. 197.) 2. In business operations, when the mills in the answer are 5, or over, it is customary to call them a cent; when under 5, they are disregarded. QUEST.-214. When the price of 1 article, 1 pound, &c., is given, how is the cost of any number of articles found? 215. What is the rule for Multiplication of Federal Money? Obs. When the price or quantity contains a common fraction, what should be done with it? 4. What will 10 lbs. of beef cost, at 6 cents a pound? Solution. 6 cts.=.065, and .065 × 10=.65. 5. What cost 14 lbs. of starch, at 10 Ans. 65 cents. cts. per pound? 6. What cost 15 pounds of sugar, at 94 cents a pound? 7. What cost 25 gals. of molasses, at 183 cts. a gallon? 8. What cost 234 lbs. of raisins, at 8 cts. per pound? 9. What cost 33 lbs. of candles, at 12 cts. per pound? 10. What cost 164 lbs. of hyson tea, at 564 cts. a pound? 11. What will 83 lbs. of beef cost, at $4.623 per hund. ? 83 Analysis. 83 pounds are of 100 pounds; therefore 83 pounds will cost of $4.625; and 3 of $4.625 4.625x83 100 Operation. $4.625 83 13 875 3 70 00 100 83 We multiply the price of 100 ($4.625) by 83, the given number of pounds, and the product $383.875, is the cost of 83 lbs. at $4.625 per pound. But the price is $4.625 per hundred; consequently the product $383.875 is 100 times too large, and must therefore be divided by 100, to give the true answer. But to divide by 100, we simply remove the decimal point two places towards the left.(Art. 195.) $3.83 875 Ans. 12. What will 825 feet of boards cost, at $6.75 per 1000? Operation. 6.75 8 25 33 75 135 0 5400 $5.568 75 1000 Reasoning as before, 825 feet will cost 825 of $6.75. We multiply the price of 1000 feet by the given number of feet, and divide the product by 1000. To divide by 1000, we remove the decimal point three places towards the left. (Art. 195.) Hence, 216. To find the cost of articles bought and sold by the 100, or 1000. Multiply the given price by the given number of articles ; then if the price is for 100, divide the product by 100 ; but if the price is for 1000, divide it by 1000. (Art. 195.) 13. At $4.50 per 1000, what will 1250 bricks cost? 14. A farmer sold a quarter of beef, weighing 256.5 pounds, at $5.37 per 100: how much did he receive for it? 15. At $4.624 per hundred, what will 1675 pounds of pork cost? 16. What cost 2129 feet of spruce boards, at $18.25 per 1000? 17. How much will 456 yards of shirting cost, at 12 cts. per yard? 18. What cost 156 lbs. of chocolate, at 15 cents a pound? 19. What cost 235 pounds of cheese, at 64 cents a pound? 20. What cost 175 dozens of eggs, at 10 cents per dozen ? 21. At 47 cents per bushel, what will be the cost of 300 bushels of corn? 22. What will 153 lbs. of sugar cost, at 82 cents per pound? 23. What will 1500 pounds of butter cost, at $8.50 per hundred ? 24. What cost 28500 feet of timber, at $3.76 per 100 ? 25. What cost 8230 feet of mahogany at $70.20 per 1000? 26. What cost 7630 bunches of hemlock shingles, at $3.50 per 1000 ? 27. What cost 15024 bunches of pine shingles, at $8.37 per 1000? 28. At 16 cts. a pound, what will 219 pounds of honey cost? QUEST.-216. How do you find the cost of articles bought and sold by the 100, or 1000? 29. At $2.67 per yard, what will 400 yards of cloth cost? 30. At $5 per barrel, what will 1560 barrels of flour cost? DIVISION OF FEDERAL MONEY. Ex. 1. A man bought 6 hats for $25.68: how much did they cost apiece? Operation. Proof. $4.28 6 $25.68 If 6 hats cost $25.68, 1 hat will cost one sixth of $25.68. Divide as in sim ple numbers, and point off two decimal figures in the quotient. (Art. 194.) If 1 hat costs $4.28, 6 hats will cost 6 times as much; and $4.28×6=$25.68, which is the cost. Hence, 217. When the number of articles, pounds, yards, &c., and the cost of the whole are given, to find the price of one article, pound, &c. Divide the whole cost by the whole number of articles, &c., and point off the quotient as in division of decimal fractions. (Art. 194.) 2. How many yards of cloth, at $3.13 per yard, can be bought for $20.345 ? Operation. Since $3.13 will buy 1 yard, 3.13)20.345(6.5 Ans. $20.345 will buy as many yards 18 78 1 565 1 565 as $3.13 is contained times in $20.345. Divide as in simple numbers, and point off one decimal figure in the quotient. (Art. 194.) Proof-$3.13x6.5=20.345. Hence, QUEST. 217. When the number of articles, pounds, &c., and the cost of the whole, are given, how is the cost of one article found? |