18. The number of inhabitants in the city of London is 1 250 000; the number in the city of Paris is 750 000. How many more are there in London, than in Paris? 19. The population of Great Britain and Ireland is 21 500 000; the population of France is 32 000 000. How many more inhabitants are there in France, than in Great Britain and Ireland? 20. The Rocky Mountains, in North America, rise 12 500 feet above the level of the ocean; the Andes, in South America, rise 21 440 feet. How many feet higher are the latter, than the former? 21. A merchant paid 13 745 dollars for a ship, and sold it for 15 150 dollars. What did he gain?" 22. A farmer sold a piece of wood-land for 396 dollars, which was 78 dollars more than he gave for it How much did he give for the land? 23. Columbus discovered America in the year 1 How many years is it since the discovery? 1492. 24. The United States declared Independence in the year 1776. How many years since the declaration? 25. A man bought 20 casks of wine, containing 2459 gallons, and sold 14 casks containing 1682 gallons. How many casks, and how many gallons were left? 26. There are two numbers, whose difference is 758; the greater number is 1524. What is the smaller number? Questions to be answered Orally. (1) How can you find what the difference is between two numbers? (2) When one number is to be subtracted from another, in what order must the numbers be written? (3) In what place do you begin to perform the subtraction? (4) When a figure in the upper number is smaller than the figure under it, what is to be done? (5) Where does the remainder appear, after the subtraction is performed? (6) Recite the rule for subtraction. (7) How can you prove that an operation in subtraction is performed correctly? SECTION 3. MISCELLANEOUS EXAMPLES. 1. A man owing 379 dollars, paid at one time 47 dollars, at another 23, at another 84, and at another, 143. How much did he still owe? 2. There are 1000 dollars in 4 bags; the first bag contains 230 dollars, the second 245, the third 270. What is contained in the fourth bag? 3. Suppose the world to have been created 4004 years before the Christian era, how old is it at this date? 4. A man having in his desk 2000 dollars, took out 120 dollars to pay a debt, and afterwards put in 75 dols. How much was there remaining in the desk? 5. A merchant bought a ship for 11 240 dollars, paid 305 dols. for repairing it, and sold it so that he lost 95 dols. For how much did he sell it? 6. What is the sum of 58, 45, and 70? Then, if you subtract 43 from this sum, what will be the remainder? 7. A merchant, who had 650 barrels of flour, sold 95 barrels to one man, 38 to another, and 225 to another. How many barrels had he left? 8. A jockey bought a horse for 115 dollars; he exchanged him for a better horse, paying 23 dollars, and then sold the better one for 137 dollars. Did he gain or lose? and how much? 9. If 654 be subtracted from 10000, and then 29 670 be added to the remainder, what will be the sum? 10. A gentleman gave 972 dollars for a carriage and two horses; the carriage was valued at 525 dollars. What was the value of the horses? 11. Dr. Franklin died in the year 1790, and he was 84 years old when he died. In what year was he born? 12. A clerk went out with 240 dollars, to settle some accounts: he paid 126 dollars to one man, received 37 dollars from another, and paid 94 dollars to another. How many dollars had he then? 13. Add together two hundred, sixteen thousand, thirteen million, and seven billion; and then subtract ten thousand from the sum. CHAP. IV. MULTIPLICATION. SECTION 1. 1. If a gunner shoot 72 pigeons every time he goes a gunning, how many will he shoot in going 3 times? We might here obtain the answer by adding together, 72 and 72 and 72; but we shall obtain it more readily by multiplying 72 by 3; that is, by finding 3 times 72. Multiplicand 72 Multiplier 3 Product 216 We write 72, and write 3 under it. Then we multiply the 2 units and the 7 tens separately, thus, times 2 are 6; 3 times 7 are 21. 3 Observe, that the number which we multiply is called the multiplicand; the number by which we multiply is called the multiplier; and the number which we obtain by multiplication is called the product. Find the product in each of the following examples. (2). 61 (3). 524 (4). 9132 (5). 420121 2 3 4 6. If a farm produce 230 bushels of wheat a year, how many bushels will it produce in 3 years? 7. Multiply 512 by 4; that is, find 4 times 512. SECTION 2. 1. Multiply 743 by 6;-that is, find 6 times 743. 743 6 4458 6 times 3 are 18, or I ten and 8 units; we write only the 8 units, (as in addition), and proceed; 6 times 4 are 24 and 1 we carry are 25; we write the 5 and proceed. Find the product in each of the following examples. (2). 5236 (3). 1908 (4). 6175 4 (5). 3640 6. What will 3 books cost, at 31 cents apiece? 12. How many are 9 times 16? 17. Multiply 251 by 8,-that is, find 8 times 251 19. Multiply 3086 by 6. 25. Suppose 8 to be a multiplicand, and 6 the multi plier; how much will be the product? 26. Suppose 35 to be a multiplicand, and 7 the multiplier; how much will be the product? 27. Suppose 491 to be a multiplicand, and 5 the multiplier; how much will be the product? SECTION 3. 1. Multiply 657 by 24. 657 2628 1314 15768 Then We first multiply by the 4 units. 2. Multiply 75 by 16. 5 RULE FOR MULTIPLICATION. Write the multiplier under the multiplicand, placing units under units, &c. When there is but one figure in the multiplier, begin with the units, multiply each figure in the multiplicand separately, and place each product under the figure in the multiplicand from which it arose; observing to carry the tens to the left as in addition. When there is more than one figure in the multiplier, multiply by each figure separately, and write its product in a separate line, placing the right hand figure of each line under the figure by which you multiply; and finalThe sum will be ly, add together the several products. the whole product. 7 Suppose 5 476 208 to be a multiplicand, and 3942 the multiplier; how much will be the product? 5476208 10952416 21904832 49285872 16428624 21587211936 8. Suppose 73 054 to be a multiplicand, and 548 the multiplier; how much will be the product? 9. Suppose 295 to be a multiplicand, and 486 the multiplier; what will be the product? 10. What is the product of 9351 by 765? 15. There is an orchard containing 9 rows of trees, and there are 5 trees in each row. are there in the orchard? How many trees 16. A merchant bought 75 pipes of wine, at 145 dollars a pipe. What did the whole cost? 17. A merchant bought 37 mules, for shipping, at 52 dollars per head. What d'd the whole cost? |