Perform subtraction in the following examples. (2). 1853 (3). 5264 1370 (4). 2657 (5). 6807 4096 6. Subtract 1268 from 1503. 1503 235 In subtracting the 8 units, we use a ten, that we obtain by supposing 1 of the 5 hun dreds, (which is 10 tens,) to be where the 0 is. Then, having used 1 of the 10 tens, we presently subtract 6 tens from 9 tens. 7. Subtract 1146 from 2601. 8. Subtract 5428 from 8019. 9. Subtract 258 from 34307. RULE FOR SUBTRACTION. Write the smaller number under the greater, placing units under units, &c. Begin with the units, and subtract each figure in the lower number from the figure over it. When a figure in the upper number is smaller than the figure under it, consider the upper figure to be 10 more than it is, and the next upper figure on the left hand, to be 1 less than it is. PROOF. Add together the remainder and the smaller number: their sum will be equal to the greater number, if the work he right. 10. Find the difference between 39 and 64, by sub tracting the smaller number from the greater. 11. What is the difference between 464 and 502? 12. What is the difference between 99 and 200? 13. What is the difference between 35720 and 9100? 14. Subtract 44 from 10000. 15. I deposited 1450 dollars in the bank, and I have since drawn out 835 dollars. How many dollars have I remaining in the bank? 16. Suppose a man owes 1634 dollars, and possesses property to the amount of 8150 dollars; how much wil he have left, after paying his debts? 17. Subtract sixty-two thousand five hundred and seven. from one million eighty thousand and forty-four 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 m 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 45 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 1492. How many years is it since the discovery? 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 1652 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 mucn 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 vears 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 2; that is, by finding 3 times 72. Multiplicand 72 216 We write 72, and write 3 under it. Then we multiply the 2 units and the 7 tens separately, thus, 3 times 2 are 6; 3 times 7 are 21. 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 4 2 (5). 420121 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 1.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 (5). 3640 I* 6 What will 3 books cost, at 31 cents apiece? What will 4 slates cost, at 24 cents apiece? 8. What will 5 baskets cost, at 17 cents apiece? 9. What will 6 cows cost, at 25 dollars apiece? 10. What will 7 horses cost, at 115 dollars apiece? 11. How many are 8 times 9? 12. How many are 9 times 16? 17. Multiply 251 by 8,-that is, find 8 times 251. 18. Multiply 475 by 4. 19. Multiply 3086 by 6. 25. Suppose 8 to be a multiplicand, and 6 the multiplier; 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 mul tiplier; how much will be the product? SECTION 3. 1. Multiply 657 by 24. 657 2628 1314 15768 We first multiply by the 4 units. Then we multiply by the 2 tens, and since this product must be ten times greater than it would be if the 2 were 2 units, we set the product one place to the left. At last, we add the two products together, and the sum is the whole product of 657 by 24. 2. Multiply 75 by 16. |