2 times 99+ 33. have 155 times 99. times 99. Now, by adding 153 times 99 to 2 times 99, we The following exhibits a convenient form for writing the work : — 153/78 155 33 = 15533 The full explanation is the same as that already given The necessary numerical operations are as follows: Separating the hundreds from the tens and units by a vertical line, we add the number at the right of the line to that at the left. This gives 153 +78 = 231 = first remainder. Writing this beneath the dividend, and adding as before. we have 2 +31 = 33, which, being less than 99, is the final remainder. The sum of the numbers at the left of the line, or 153 +2 155, the quotient. = (b.) In a similar manner we can divide by 999, 9999, &c. Let the pupil find, if he can, the application of a similar principle to the division by 98, 97, 96, &c.; also to 998, 997, &c., and afterwards perform the following examples: What is the quotient 3. Of 18673899? 4. Of 49763842 999? 6. Of 984298748399999? 7. Of 5478398? 8. Of 298763796? 9. Of 248763997? 10. Of 698743259998? 97. To divide by any convenient fractional Part of 10, 100, or 1000. (a.) Since 100 ÷ 25 = 4, 900 ÷ 25 must equal 9 times 4; 170025 must equal 17 times 4; 4960025 must equal 496 times 4. (b.) Since 100 ÷ 12 = 8, 3800 121 must equal 38 times 8; 49700 12 must equal 497 times 8, &c. (c.) Since 1000 ÷ 1258, 479000125 must equal 479 times 8; 3785000125 must equal 3785 times 8, &c. (d.) These principles are applied in the following pro cesses. 1. What is the quotient of 9738 25? Solution. 9738, 9700 + 38. But 970097 times 100 97 times 4 times 25 = 388 times 25; and 38 = 113 times 25. Hence, 9738 + 388 +118=38913. 25 = 1. A man bought a house lot and garden for $1378.24; he paid $4796.87 for building a house, $1274.38 for building a stable and carriage house, $438.47 for fencing the lot, $578.37 for laying out the garden and grounds, $1287.63 for a span of horses and a carriage, $1328.56 for furnishing his house, and then had $47289.43 left. How much money Idid he have at first? 2. Mr. French bought a house for $6742.38, and after paying $138.47 for having it painted, and $527.94 for repairs, he sold it for $8472. Did he gain or lose, and how much? 3. Mr. Hall bought 437 cords of wood at $3 per cord, and sold it at $4.75 per cord. What did he gain by the speculation? 4. A man started on a journey of 1164 elled 37 miles per day for the first 21 days. would it take him to finish the journey if he the rate of 43 miles per day? miles, and travHow many days should travel at 5. Bought 43 acres of land at $28.73 per acre, and sold it at $37.73 per acre. How much did I gain? 6. I bought 487 yards of cloth at $2 per yard, and €27 yards at $4 per yard; I sold the whole of it at $4 per yard. How much did I gain? 7. A trader bought 528 barrels of flour at $7 per barrel, 875 barrels at $8 per barrel, and 497 barrels at $9 per bar rel. He sold the whole of it at $8 per barrel. Did he gain or lose, and how much? 8. How much will a house lot, 137 feet long and 89 feet wide, cost, at 2 cents per square foot? 9. Which is the larger 13 × 17 × 28 × 43, or 28 × 13 × 43 × 17, and how much? 10. A man who had $4376 invested it in flour at $8 per barrel. He sold 238 barrels of the flour at $9 per barrel, and the rest for enough to make up $5232. For how much did he sell the last lot per barrel? 11. A man bought a horse for $237; he kept him 19 weeks at an expense of $2.50 per week, and then exchanged him for another horse, receiving $48. for their difference in value. After keeping the second horse 4 weeks, at an expense of $2.25 per week, he sold him for $225. Now, allow ing that the use of each horse was worth $1.75 per week, did he gain or lose by the transaction, and how much? 12. To 12 times 487 add 8 times 683, multiply the sum by 7, and subtract 4279 from the product. 13. James Smith bought of John Brown 7 hogsheads of molasses, each containing 147 gallons, at $.27 per gallon, and gave in payment $100 in money, and the rest in nails at 5 cents per pound. How many pounds of nails did it take? 14. How many cords of wood at $4 per cord can be bought for 82 barrels of apples at $2 per barrel? 15. John earns $4 per week, and William earns $7. How many weeks will it take John to earn as much as William can earn in 48 weeks? 16. Gave 3 hogsheads of oil, each containing 167 gallons, worth $1.68 per gallon, and $200 in money, for 4 acres of land. How much ought the land to be worth per acre, that I may neither gain nor lose? 17. George had 378 oranges, which sold at 2 cents apiece. With the money thus received he bought a box of oranges, which he found contained 427. He ate 9 of these, gave away 7, had 4 stolen from him, sold 294 at 3 cents apiece, and the rest at 2 cents apiece. Did he gain or lose on the box, and how much? 18. How many times will a carriage wheel. 12 feet 6 inches in circumference, revolve in going 5 miles, 4 fur., 18 rd., 2 yd., 7 ft., 1 in.? 19. A boy, riding with his father, ascertained that the hinder wheel of the carriage, which was 10 feet 4 inches in circumference, revolved 1297 times in passing from one village to another. How far apart were the villages, reckoning the distance in miles, furlongs, rods, &c.? 20. Mr. Clarke's house lot is 83 feet wide, and contains 8051 square feet. How long is it? 21. Mr. Angell says that his house lot is 97 feet long, but that if it were 100 feet long, it would contain 168 square feet more than it now does. How many feet does it now contain ? 22. Multiply 837 by 5, add 247 to the result, divide this by 4, and calling the result dollars, find how many yards of cloth at $2 per yard you could buy with it. 23. By buying a cargo of coal at $6 per ton, and selling it at $8 per ton, I gained $198. How much did I pay for it? 24. A silversmith bought 13 lb., 4 oz., 2 dwt., 5 gr. of silver, and after mixing with it 1 lb., 5 oz., 15 dwt., 19 gr. of alloy, made it into spoons, each weighing 1 oz., 4 dwt., 17 gr. How many spoons did he make? 25. I bought the wood standing on 9 acres of land, paying for it at the rate of $67.25 per acre. I paid $.625 per cord for having it cut, and $.75 per cord to have it carted to a railroad depot, where I sold it for $4.50 per cord. If there was an average of 30 cords to the acre, how much did I gain by the transaction? 26. A trader mixed 536 lb. of sugar, worth 9 cents per pound, with 52 lb., worth 6 cents per pound, and 432 lb., worth 7 cents per pound. For how much per pound ought he to sell the mixture so as neither to gain nor lose? 27. A trader bought 597 gallons of vinegar at 14 cents per gallon, and after mixing with it 24 gallons of water, sold it for 15 cents per gallon. How much did he gain by the transaction? 28. I bought a pile of wood, 144 feet long, 4 feet wide, and 6 feet high, at $3.92 per cord. What did it cost me? 29. How many square feet in the walls of a room 18 feet long, 16 feet wide, and 12 feet high? 30. If William walks at the rate of 16 rods per minute, and Joseph at the rate of 19 rods per minute, how long will it take Joseph to overtake William, when William has 12 minutes the start. 99. Bills of Goods. (a.) When a man sells goods, he usually gives the purchaser a written statement of the articles bought, and the prices he is to pay for them. Such a statement is called a "Bill of the Goods," or simply a "Bill.” (b.) A bill, like every other business paper, should contain the date, i. e., the time and place of the transaction, and also the names of the parties, and an account of the transaction. If the goods are paid for, the bill should be receipted; i. e., the words Received Payment being written at the bottom, the seller should affix his name. (c.) The following example will illustrate this : Mr. George W. Dodge is a trader, residing in Lancaster. On the 1st of January, 1855, he sold to Mr. Humphrey Barrett, for cash, 3 yards of broadcloth at $3.75 per yard, 6 yards of doeskin at $1.87 per yard, 32 yards of sheeting at 11 cents per yard, 9 yards of black silk at 97 cents per yard, and 6 linen handkerchiefs at 34 cents apiece. Mr. Dodge made out the bill as follows: |