CASE II. 48. When any figure in the subtrahend is greater than the corresponding figure in the minuend. 1. From 846 take 359. OPERATION. ∞hunds. tens. units. 359 487 ANALYSIS. Since we cannot take 9 units from 6 units, we add 10 units to 6 units, making 16 units; and 9 units from 16 units leave 7 units. But as we have added 10 units, or 1 ten to the minuend, we shall have a remainder 1 ten too large, to avoid which, we add 1 ten to the 5 tens in the subtrahend, making 6 tens. We can not take 6 tens from 4 tens; so we add 10 tens to 4, making 14 tens; 6 tens from 14 tens leaves 8 tens. Now, having added 10 tens, or 1 hundred, to the minuend, we shall have a remainder 1 hundred too large, unless we add 1 hundred to the 3 hundreds in the subtrahend, making 4 hundreds; 4 hundreds from 8 hundreds leave 4 hundreds, and we have for the total remainder, 487. The process of adding 10 to the minuend is sometimes called borrowing 10; and that of adding 1 to the next figure of the subtrahend, carrying one. 49. From the preceding example and illustration we have the following general RULE. I. Write the less number under the greater, placing units of the same order in the same column. II. Beginning at the right hand, take each figure of the subtrahend from the figure above it, and write the result underneath. III. If any figure in the subtrahend be greater than the corresponding figure above it, add 10 to that upper figure before subtracting, and then add 1 to the next left-hand figure of the subtrahend. PROOF. 1st. Add the remainder to the subtrahend; the sum will be equal to the minuend. Or, 2d. Subtract the remainder from the minuend; the difference will be equal to the subtrahend. 23. 234100-9970-how many? (22.) 103810040 91300397 12509643 Ans. 224130. Ans. 1975645. Ans. 4918889. 35. Subtract 432986702100 from 539864298670. 36. Subtract 29176807982 from 86543298765. 37. A speculator bought wild lands for 10580 dollars, and sold them for 7642 dollars; how much did he lose? Ans. 2938 dollars. 38. Napoleon the Great was born in 1769, and died in 1821; how old was he at his death? Ans. 52 years. 39. Gunpowder was invented in 1330, and printing in 1440; how many years between the two? Ans. 110. 40. George Washington was born in 1732, and died in 1799; how old was he at his death? Ans. 67 years. 41. The first newspaper published in America was issued at Boston in 1704; how long was that before the death of Benjamin Franklin, which occurred in 1790 ? Ans. 86 years. 42. The first steamboat in the United States, built by Robert Fulton, in 1807, made a trip from New York to Albany in 33 hours; how many years from that time to the visit of the Great Eastern to this country in 1860? Ans. 53 years. 43. Queen Victoria was born in 1819; what was her age in 1862 ? Ans. 43 years. 44. The United States contain 2983153 square miles, and the British North American Provinces 3125401 square miles; how many square miles does the latter country exceed the former ? Ans. 142248. EXAMPLES COMBINING ADDITION AND SUBTRACTION. 1. A farmer having 450 sheep, sold 124 at one time, and 96 at another; how many had he left? Ans. 230. 2. If a man's income is 175 dollars a month, and he pays 25 dollars for rent, 44 dollars for provisions, and 18 dollars for other expenses, how much will he have left? Ans. 88 dollars. 3. A man gave his note for 3245 dollars. He paid at one time 780 dollars, and at another 484 dollars; how much remained unpaid? Ans. 1981 dollars. 4. A man paid 140 dollars for a horse and 165 dollars for a carriage. He afterward sold them both for 300 dollars; did he gain or lose, and how much? Ans. Lost 5 dollars. 5. A flour merchant having 700 barrels of flour on hand, sold 278 barrels to one man, and 142 to another; how many barrels had he left? Ans. 280 barrels. 6. Three men bought a farm for 9840 dollars. The first paid 2672 dollars, the second paid 3089 dollars, and the third, the remainder; what did the third pay? Ans. 4079 dollars. 7. A man bought a house for 1500 dollars, and having expended 315 dollars for repairs, sold it for 2000 dollars; what was his gain? Ans. 185 dollars. 8. Henry Jones owns property to the amount of 36748 dollars, of which he has invested in real estate 12850 dollars, in personal property 9086 dollars, and the remainder he has in bank; how much has he in bank? Ans. 14812 dollars. 9. A grocer bought 275 pounds of butter of one farmer, and 318 pounds of another; he afterward sold 210 pounds to one customer, and 97 to another; how many pounds had he left ? Ans. 286 pounds. 10. A man deposited in bank 10476 dollars; he drew out at one time 2356 dollars, at another 1242, and at another 737 dollars; how much had he remaining in bank? Ans. 6141 dollars. 11. Borrowed of my neighbor at one time 680 dollars, at another time 910 dollars, and at another time 218 dollars. Having paid him 1309 dollars, how much do I still owe him? Ans. 499 dollars. 12. A man bought 3 lots; for the first he paid 2480 dollars, for the second 3137 dollars, and for the third as much as for the other two; he afterward sold them for 15000 dollars; what was his gain? Ans. 3766 dollars. 13. A farmer raised 1864 bushels of wheat, and 1129 bushels of corn. Having sold 1340 bushels of wheat, and 1000 bushels of corn, how many bushels of each has he remaining? Ans. 524 bushels, and 129 bushels. 14. A gentleman worth 25800 dollars, bequeathed his estate so that each of his two sons should have 9400 dollars, and his daughter the remainder; what was the daughter's portion? |