7. A gentleman owns a store worth 4695 dollars, and a grist-mill worth 2135 dollars; how much more is the store worth than the grist-mill? 8. A gentleman gave for a house and lot- 9899 dollars, for a cotton factory 8495 dollars; how much more did he give for the one than the other? 9. A speculator bought some land for 12897 dollars, a tannery for 10444 dollars; how much more did the land cost than the tannery? 10. A merchant, having 9847 yards of cloth, sold 5844 yards of it; how many yards had he remaining? 11. A drover bought cattle to the amount of 9647 dollars, and sheep to the amount of 5434 dollars; how much more did he give for the cattle than for the sheep? 12. A merchant sold a quantity of goods for 8697 dollars, and by so doing gained 1495 dollars; how much did the goods cost him? 13. A gentleman sold an estate for 7499 dollars, and by so doing gained 1084 dollars; how much did the estate cost him? 14. A farm was sold for 3495 dollars, which was 1032 dollars more than it was worth; how much was it worth? 15. A farmer had 4295 sheep, and 2145 lambs; how many more sheep had he than lambs?. 16. A farmer, having 1346 bushels of wheat, sold 1042 bushels of it; how many bushels had he remaining? 17. A merchant, during one year, sold 1247 barrels of molasses, and 2489 barrels of sugar; how many more barrels of sugar did he sell than molasses? 18. A gentleman willed to his son 49865 dollars, and to his daughter 34534 dollars; how much more did he will to his son than to his daughter? 19. A man, driving 1565 sheep to market, on his way sold 435 of them; how many had he remaining? 20. A ship is valued at 69847 dollars, and its cargo at 45837 dollars; how much more is the ship valued at than the cargo ? CASE II. ART. 34. Subtraction of Abstract numbers in ger eral. 1. From 728 subtract 364. OPERATION. Minuend, Hundreds. Tens. ∞ Units. Hundreds. Tens. ∞ Units. 72 8: Subtrahend, 364 EXPLANATION. -The numbers being properly written down, we proceed thus: 4 units taken from 8 units leave 4 units, which write in unit's place. I cannot take 6 tens from 2 tens; therefore, from (12) 8 the 7 hundreds I take 1 hundred 10 TENS, and add it to the 2 tens, making 12 tens, 6 tens from 12 tens leave 6 tens, which I write in tens' place. I have taken 1 hundred from the seven hundreds, which leaves 6 hundreds; 3 hundreds from 6 hundreds leave 3 hundreds. But for convenience, it is customary to add the 1 hundred to the 3 hundreds, (the next figure in the subtrahend,) and take the sum from the figure in the minuend under which it is placed, which is the same in effect as the above. Remainder, 364 NOTE.-The minuend 7 hundreds, 2 tens and 8 units, is = 6 hundreds, 12 tens and 8 units, which form it, absolutely assumes in the mind while giving the above explanation; still it is not necessary to be written except to render the explanation more plain. PROOF by the excess of 9's.-Find the excess of 9's in the sum of the digits of the remainder,-also of the subtrahend. Then find the excess of 9's in the excesses just found,if this excess equals the excess of 9's in the minucnd, the work is right. Take for illustration the above example : remainder, which is the same as the excess in the minuend, therefore the work is right. EXPLANATION.-The numbers being properly arranged, com mence at the right and proceed thus: we cannot take 4 units from 1 unit; therefore I seek 1 from the tens' place, but finding no tens there, I proceed to the hundreds' place, and finding no hundreds there, I take 1 thousand from the 4 thousands and set it in the next place towards the right, which causes the minuend to take the 2nd form. Then take 1 hundred from the 10 hundreds, and set it in the next place towards the right, causes the minuend to take the 3rd form. Now taking 1 ten from the 10 tens, and adding it to the 1 unit causes the minuend to assume the 4th form,--from which we are now prepared to take the subtrahend. 4 units from 11 units leave 7 units; 4 tens from 9 tens leave 5 tens; 3 hundreds from 9 hundreds leave 6 hundreds; and 1 thousand from 3 thousands leave 2 thousands. Hence the difference of these two numbers is 2657. REMARK.-The 2nd, 3rd and 4th forms of the minuend serve merely to explain the method of subtracting more clearly, and should, therefore, in practice, be performed in the mind and not be written down. The same result will be obtained by simply adding 10 to the upper figure when it is smaller than the one below it, and carrying, or adding, i to the next figure of the subtrahend. 17 From 41007 subtract 34138 ? 29. How many are 909090-1 ? 30. How many are 9080706050-16070809 ? PRACTICAL QUESTIONS. 1. A gentleman willed to his son 3862 dollars, and to his daughter 5324 dollars; how much more did he will to his daughter than to his son? 2. In a certain orchard there are 425 apple-trees and 297 plum-trees; how many more apple-trees than plumtrees? 3. A man traveled 14637 miles during one year, and 9843 miles the next year; how much farther did he travel the first year than the second ? 4. A merchant had 25694 pounds of pork, and sold 19832 pounds of it; how many pounds remained unsold? 5. A speculator bought a quantity of cotton for 294682 dollars, and sold it for 516390 dollars; how much did he gain? 6. Gunpowder was invented by Schwartz, in the year 1330; how long was it before the birth of Bonaparte, 1769? 7. George Washington died in the year 1799, at the age of 67; in what year was he born? 8. The mariner's compass was invented at Naples in the year 1302; how long before the discovery of America 1492? 9. Joseph Addison, the poet, was born 1672, and died, 1719; how old was he when he died? 10. Sir William Blackstone, the lawyer, was born 1723, and died, 1780; at what age did he die ? 11. Francis Bacon, a universal genius, died in the year 1626, at the age of 65; in what year was he born? 12. Robert Burns, the poet, was born 1759, and died 1796; Lord Byron, the poet, was born 1788, and died 1824. What was the age of each, and how long after the birth of Burns was Byron born? 13. George Edwards, the ornithologist, was born 1694; how long was this before the birth of Harvey, the discoverer of the circulation of the blood, who was born 1578? 14. Massachusetts was settled in 1620, at Plymouth; how many years before the declaration of our National Independence 1776 ? 15. The Independence of the United States was acknowledged in Europe in 1783; how long was that after the battle of Bunker's Hill, 1775? 16. The first newspaper published in America, at Boston, was in 1704, which was 183 years after Mexico was conquered by the Spaniards; in what year was Mexico conquered? 17. Michael Angelo, an Italian painter, died 1563, at the age of 89; in what year was he born? 18. Benjamin Franklin, the philosopher and statesman, died 1790, at the age of 84; in what year was he born? 19. Galileo, an Italian astronomer, died 1642, at the age of 78; in what year was he born? 20. Luther, the reformer, died 1546, at the age of 63, in what year was he born? |