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2 1 2 1 4 1 7 9 Illustration. When the sum of the figures in any column, exceeds 9, we add the tens contained in that sum with the sum of the next column, because. each 1 in the tens is equal to 10 in that column, and set the number above an exact number of tens, under the column last added; so that the sum of all the columns equal the given numbers; that is, the sum of all the columns contains as many units as all the given numbers. In the first operation of the last question, the sum of the right hand column is 29, and we place the 9 under that column, and set the 2 tens under the column of tens. The sum in the column of tens, is 15 tens, or 150 ; as to tens make 1 hundred, we place 1 for the 10 tens under the column of hundreds, and set 5, the remaining tens, under the column of tens. There being just 20, (or 20 hundred, which make 2 thousand,) in the column of hundreds, we have nothing to set in the place of hundreds, but carry the 2 tens of hundreds into the next place. The 2 in the 12 thousands contained in the column of thousands, is set under that column and the ten, which is 10 thousand, is carried into the column of tens of thousands. By adding up these several sums, we obtain 14179 dollars, which is the total value of all the farms. In the second operation, 9 is set under the right hand column, and the 2 tens added to the 5 tens, and 7, their sum, set down under the column of tens; the 10 tens being equal to 1 hundred, 1 hundred is added to the next column. Lastly the 2 tens contained in the column of hundreds, or 2 thousand, we add to 12,
the sum of the thousands, and obtain the same answer as before. 24. Four men bought a piece of land in company ; the first gave one hundred and seventeen dollars; the second, two hundred ; the third, one hundred and sixty-two ; and the fourth, one thousand and one ; what did the land cost 7 Ans. 1480 dollars. 25. Add together the following numbers ; one thousand, six thousand and sixty, thirteen thousand and eight, four hundred and twenty. - - Sum 20488. 26. How many feet of boards will it take to cover a building, if it require twenty-five hundred to board the sides ; eighteen hundred and sixty-seven the ends; twenty-four hundred and thirteen feet to board the roof? Ans. 6780. 27. A gentleman paid four hundred and twentysix dollars for lumber for the purpose of erecting a house ; one hundred and three oil. for brick; thirty-five dollars for glass: forty-one for nails; for work, three hundred and fifteen ; for boarding workmen, one hundred and eight; for lime, twenty-five ; for the cellar, ninety-one ; for paints, thirty-six. What was the cost of his house, if he pays one hundred and one dollars for other articles that have not been mentioned ? Ans. 1281 dollars. 28. How many square miles on the surface of the earth, estimating Europe to contain 3387,09; Asia, 16728002; Africa, 1165.2442; America, 16504254; and the islands, 4164420 ! Ans. 52436227. This sign or character--, one line being horizontal, the other perpendicular, implies addition; or that the number before it is to be added to the number after it. It is sometimes called plus, because the word plus signifies more. Two horizontal parallel lines = are used as a sign of equality, implying that the numbers before it are equal to the numbers after it. It is generally read is, or are, equal to ; Thus, 6-1-9–15; or 6 plus 9=15, and the ex* pression is read, 6 added to 9 are equal to 15, or 6 plus 9 equals 15. The scholar is required to work the following examples as directed by the signs: 29. 6724-1-1 1971 = 18695. 30. 269-H 109-1-210=588. 31. 245690-H.44444-H 555=290689. 32. 101 + 1010+10101 +900830=912042. 33. 66 plus 83=149. 34. 400 plus 527 plus 601 = 1528. 35. 70000 plus 8008 plus 606 plus 55=78669. 36. 9 plus 99 plus 888 plus. 7777 plus 66666= 75439. 37. Seventeen thousand, one hundred and six-i-six hundred thousand, nine hundred and one-Hsive milHion, five hundred and five thousand, five hundred and fifty–6 123557. 38. A gentleman gave his estate to his three sons in the following order: to the youngest, four thousand and fifty dollars; to the second, one thousand and seventy-five dollars more than to the third; and to the first, as much as to the second and third; what did the eldest son receive, and what was the amount of the estate. Ans. The cláest son received 94.75 dollars. The whole estate was 18350 dollars.
Explanation.—The last answer is found by adding the first to itself.
39. From the creation of the world to the flood was 1656 years; from the flood to the destruction of Sodom and Gomorrah, 451 years; from the destruction of Sodom and Gomorrah to the Christian Era, 1897 years;–how many years from the creation of the world to the Christian Era? also, how many ears from the creation of the world to the year 1826 of the Christian Era? Ans. To the Christian Era, four thousand and four years. To the year 1826 of the Christian Era, five thousand, eight hundred and thirty years. 40. A carpenter purchased shingles enough to lay 21 thousand upon a house, 14 thousand upon a barn,
7 thousand upon a shed, and he had 11 thousand left; how many shingles did he purchase. - Ans. Fifty-three thousand. 41. A truckman hauls 1 hogshead of molasses, weighing 1026 pounds; a hogshead of rum, weighing 907 pounds; and 656 pounds of iron, at one load. What is the weight of the load 2 Ans. 2589 pounds. 42. A butcher buys 4 droves of cattle numbering as follows: 1st. 106 head; 2d. 220; 3d. 85; 4th. 325; how many head of cattle does he purchase ? Ans. 736. 43. A gentleman's library contains 75 volumes upon Divinity; 119 upon Law; 13 on Medicine; 35 on History; and 100 on miscellaneous subjects 2 How many volumes in the library 2 Ans. 342. 44. A gentleman's yearly income is as follows: interest money, 60 dollars; compensation for services, 259 dollars; rent for a house, 73 dollars. What is his income f Ans. 392 dollars. 45. What number is equal to ten thousand, seven hundred and twenty, plus four thousand, five hundred and two, plus six hundred, twenty thousand and ninety, plus four hundred, four thousand, two hundred and one, plus one million, two thousand and seventeen 2 46. What number is equal to nine thousand, nine hundred and nine, plus four hundred thousand and four, plus seven hundred, ten thousand and nineteen, plus seventy thousand, seven hundred and seventy, plus eight million, twenty-four thousand, two hundred and forty, plus seventy million, seven hundred, seven thousand and seven 2 47. What number is equal to three hundred, three thousand, three hundred and thirty, plus four million and four, plus six million, six hundred thousand, seven hundred and seven, plus twenty-five million, twenty-five thousand and twenty-five, plus seven hundred and sixty-two million, ninety-four thousand and eighty-one, plus one hundred and one million; one hundred and ten thousand, one hundred and one 2
The sum of the answers to the three last questions is 98.1096727.
48. From the birth to the crucifixion of Christ was 33 years; to the commencement of the reign of Constantine 273 years more; to the cessation of speaking Latin in Italy, 275; to the flight of Mahomet from Mecca to Medina, 41; to the invention of glass in England, 42; to the founding of Cambridge University, (England,) 251; to the invention of musical notes, 155; to the invention of the mariner's compass, 232; to the engraving or etching on copper, 158; to the first knowledge of Algebra in Europe, 34; to the first making of knives in England, 69; to the first British Parliament, 144; to the birth of Washington, 25; to the battle of Bunker’s Hill, 43; to the Independence of the United States, 1 year; to proclaiming Washington first President of the United States, 13; to the battle of Waterloo, 26. In what year of the Christian Era was the
Battle of Waterloo 2 Y. 1815.
Explanation.—Each space of time in the last question, is the number of years between one event and that which next preceded it; consequently, by adding all the periods of time up to any particular event, we shall obtain the number of that year in which such an event took place.
MULTIPLICATION OF SIMPLE NUMBERs, OR A SHORT METHOD OF ADDING • EQUAL NUMBERS.
When two or more unequal numbers are to be added together, the operation is performed by addi"tion ; but when two or more equal numbers are to be added, the operation is performed by Multiplication. Multiplying is adding the same figure or number