ner: Suppose a man have 252 bushels of grain in 3 boxes; in the first, 200 bushels; in the second, 50; in the third, 2. He sells to A. 100 bushels; to B. 60; to C. 1. he left? 252 161 200+50+2 100+60+1 How many has He may take one bushel from the smallest box, but the 60 bushels cannot be taken from the 50 in the second box; he therefore takes 100 bushels from the largest box, and adds it to the 50, in the smaller. Thus: 100+150+2=252 He can now take 60 from 100+ 60+1=161 90+1 91 Ans. 150, or 6 tens from 15 tens, and 9 tens remain. Then, because he has taken 100 bushels from the largest box, there remains but 100; therefore, 100 from 100, or 1 from 1, and nothing remains. Whenever, therefore, the lower figure exceeds the upper, we take 1 from the next left-hand column of the upper line, calling it 10, because 1 in the left-hand column is equal to 10 in the right, and add it to the upper figure. OBS.-We take from the left-hand place, because the right can never contain enough. We take but 1, because 1 is always sufficient. 2. From seven thousand and five, take six thousand seven hundred and forty-six. row, or rather make another division of the minuend; but as the second and third places contain ciphers, we must go to the thousand's place. From the one thousand, which we borrow, we take ten units, and add them to the 5 units of the minuend. The remainder, nine hundred and nine tens, now occupy the second and third places, instead of the ciphers, and we say 4 from 9, and 5 remain; 7 from 9, and 2 remain. From the foregoing we derive the following RULE. Place the numbers, the less under the greater; units under units, tens under tens, hundreds under hundreds, etc. Begin at the right hand, or unit's place, and take each figure in the lower line from the one above it, and set down the remainder. If either of the lower figures be greater than the one above it, suppose ten to be added to the upper figure, subtract the lower figure from it, and set down the difference, observing to carry one to the next left-hand figure of the subtrahend,- —or suppose the next left-hand figure of the minuend to be diminished by one. If the next figure of the minuend be a cipher, call it 9. Proof.-Add the remainder and lower line together. If the work be right, the amount will correspond with the upper line. Art. 21.-1. From four hundred and seventy-nine, take three hundred and seventy-five. 2. Take twenty-five thousand nine hundred and twentythree, from forty-four thousand five hundred and twenty. 3. What number must be subtracted from 2081 that the remainder may be 1104? Ans. 977. 4. From thirty-four thousand, take seventeen thousand and ninety-one. 5. John's uncle gave him 20 cents. He lost 5 of them; how many had he left? 6. A western hunter met with 45 buffaloes in one drove, and killed all but 18; how many did he kill? 7. The Arabian, or Indian method of known in England about the year 1150. since to the present year, 1849 ? Ans. 27. notation, was first How long is it Ans. 699. about the year Arabian method Ans. 152 years. 8. The mariner's compass was invented 1302. How long before that period was the of notation known in England? 9. The first settlement in New England was made at Plymouth, by the Puritans, in the year 1620. that time to the year 1837? How long is it since QUESTIONS.-11. What is the rule for Simple Subtraction? 12. How do you prove Subtraction? 13. When the lower figure exceeds the upper, what is to be done? 14. What do you call it? 15, Why? 16. Suppose the next left-hand figure be a cipher, what is to be done? 10. Gunpowder was invented in the year 1320. How long was it after the invention of the mariner's compass? Ans. 18 years. How 11. Virginia contains 64000 square miles; New York contains 46000. What is the difference? Ans. 18000. 12. The library of Dartmouth College contains 12,800 volumes; Harvard University contains 34,600 volumes. many does one contain more than the other? Ans. 21,800. 13. Dartmouth College was incorporated in the year 1769; Harvard University in the year 1638. What is the difference Ans. 131 years. in time? 14. The population of the state of New York in 1820 was 1,372,812; in the year 1835 it was 1,616,482. How many years between these two periods, and how much was the increase? 15 years. 243,670 increase. Ans. 15. An officer, with a company of 102 soldiers, was met by a party of Indians, who killed all his army but 17 men. How many were killed ? Ans. 85. 16. A merchant bought 40 tuns of gallons, which cost him 2410 dollars. taining 7056 gallons, for 1814 dollars. had he left, and how much money did the first cost? wine, containing 10080 ADDITION. Art. 22.-1. If a harness is worth 18 dollars, and the horse is worth 68 dollars more than the harness, what is the value of the horse? 3. If a merchant have 1734 yards of cloth, after selling 6588 yards, how many had he at first? 5. What is the amount of 2269+8625? 7. Dr. Franklin was born in 1706, 93 years before the death of Washington. In what year did Washington die? SUBTRACTION. Art. 23.-2. If a horse cost 86 dollars, and the harness 18 dollars, how much more than the harness did the horse cost? 4. A merchant having 8322 yards, sells 6588 yards; how many has he left? 6. What number must be added to 8625 to make 10894 ? 8. How many years before the death of Washington, in 1799, was the birth of Franklin ? 10. Sir Isaac Newton was born 9. The mariner's compass was invented in 1302; Sir Isaac New-in 1642; the mariner's compass ton was born 340 years after. In what year was he born? 11. If a piece of land be bought for 550 dollars, and sold for 250 more than it cost, for how much is it sold? 13. Peter the Great died in 1725, 112 years before the independence of Texas was acknowledged by the United States. In what year was the independence acknowledged? 15. Supposing a man to be born in the year 1738; lived 98 years; in what year did he die? 17. Columbus first sailed for America in the year 1492; the independence of America was declared 284 years after. In what year was it declared? 19. Washington was born in 1732; was 67 years old when he died; in what year did he die? 21. Noah's flood happened about the year of the world 1656; the birth of Christ was about 2348 years after; in what year was he born? was invented 340 years before. In what year was it invented? 12. If a piece of land sell for 800 dollars, which is 250 more than it cost, what was the first cost? 14. Peter the Great died in the year 1725. How many years from that period to the acknowledging of the independence of Texas, in 1837 ? PRACTICAL QUESTIONS IN ADDITION AND SUBTRACTION. Art. 24.-1. Add 900, 400, and 752; subtract from their sum 647. Ans. 1405. 2. Charles had 18 peaches. He gave his mother 6 and his sister 4. How many had he left? Ans. 8. 3. A man buys at one store 84 eggs, at another 4 dozen, at another 3 dozen. As he returns, he sells 5 dozen. How many did he purchase, and how many had he left when he arrived at home? Ans. { 168. 108. 4. James owes A. 20 cents; B. 30; C. 40; D. 50. John owes A. 18 cents; B. 23; C. 35; D. 47. How much do they both owe, and which owes the most? 5. A merchant owes A. 1300 dollars; B. 1900 dollars; C. 2500 dollars. He is worth 3500 dollars. How much does he owe, and how much more than he is worth? 6. A man borrowed of his friend, at one time 100 dollars; at another, 150 dollars; at another, 175 dollars. He paid 275 dollars. How much did he borrow, and how much does he still owe? Borrowed 425. Owes 150, Ans. 7. On a certain farm there are 750 apple-trees, 425 peartrees, 1000 peach-trees, and 389 plum-trees. What is the amount of the whole, and how many more apple-trees than pear-trees, and how many more peach than plum? 8. A man left to his wife 2500 dollars; to his four sons 900 dollars each; to his three daughters 450 each. What was the amount of property left, and how much more was left to the mother than to the daughters, and to the sons more than to the mother? 9. There were five important events in the course of 215 years, viz:-1. The invention of the mariner's compass. 2. The invention of gunpowder. 3. The art of printing. 4. The discovery of America. 5. The reformation. The last was accomplished A. D. 1517; the third, 77 years before; the second, 18 years after the first, and the fourth 148 years after the second. The question is, In what year did each happen? Mariner's compass in 1302; gunpowder in 1320; printing, 1440; discovery of America, 1492. Ans. { MULTIPLICATION. Art. 25.-1. If Mary give 4 cents for one picture-book, how much must she give for 2 books? how much for 4? how much for 5? 2. If one dozen of eggs cost 10 cents, how many cents will two dozen cost? how many will 4? 5? 6? 3. If one share in a library cost 5 dollars, how much will three shares cost? how much 4? how much 5? how much 6? 4. If a picture-frame cost 12 dollars, what will 4 cost? what will 6? what will 7? what will 8? what will 9? |