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2. Miles. 151 2 12 321

EXAMPLES FOR PRACTICE.
3.

4.
Furlongs.

Days. 234

472 423

315 321

102

5. Weeks. 121 5 16 361

Ans. 684 6. What is the sum of 231, 114, and 324 ? Ans. 669. 7. Required the sum of 235, 321, and 142. Ans. 698. 8. What is the sum of 11, 22, 505, and 461 ? Ans. 999.

9. Sold twelve ploughs for 104 dollars, two wagons for 214 dollars, and one chaise for 121 dollars ; what was the amount of the whole ?

Ans. 439 dollars. 10. A drover bought 125 sheep of one man, 432 of another, and of a third 311; how many did he buy? Ans. 868 sheep.

ART. 22. Method of operation, when the sum of any column is equal to, or exceeds, 10.

Ex. 1. I have three lots of wild land; the first contains 246 acres, the second 764 acres, and the third 918 acres; I wish to know how many acres are in the three lots.

Ans. 1928 acres. Having arranged the numbers as in the preceding examples, we first add

the units; thus, 8 and 4 are 12, and 246

6 are 18. In 18 units there are 1 ten 764

and 8 units; we write the 8 units un918

der the column of units, and, reserving

the 1 ten in the mind, we carry or add Amount 1928

it to the column of tens; thus, 1 car

ried to 1 makes 2, and 6 are 8, and 4 are 12 (tens), equal to 1 hundred and 2 tens. We write the 2 tens under the column of tens, and, reserving the 1 hundred in the mind, carry it to the column of hundreds ; thus, 1 carried to 9 makes 10, and 7 are 17, and 2 are 19 (hundreds), equal to 1 thousand and 9 hundreds. We write the 9 under the column of hundreds; and there being no other column to be added, we set down the 1 thousand in thousands? place, and find the amount of the several numbers to be 1928.

OPERATION.

Acres.

QUESTIONS. - Art. 22. When the sum of any column exceeds ten, where are the units written ? What is done with the tens? What is meant by car. rying the tens? Why do you carry one for every 10 ? Why not for every 12? How is the sum of the last column written ?

Art. 23. From the preceding examples and illustrations in addition, we deduce the following general

Rule. – 1. Write down the numbers to be added, units under units, tens under tens, &c., and draw a line underneath.

2. Then, beginning at the right hand, add, upward, all the figures in the column of units, and, if the amount be less than ten, set it down under the column added. But, if the amount be ten or more, write down the unit figure only, and carry the figure denoting the ten or tens in the mind, and add it to the next column.

3. Proceed in this way with each column, until they are all added, ohserving to write down the whole amount of the last column.

Art. 24. Second Method of Proof.-Separate the numbers to be added into two parts by drawing a horizontal line between them. Add the numbers below the line and set down their sum.

Then add this sum and the number or numbers above the line together; and, if their sum is equal to the first amount, the work is presumed to be right.

The reason of this proof depends on the obvious principle, That the sum of all the parts into which any number is divided is equal to the whole.

EXAMPLES FOR PRACTICE.
2.

2.
3.

3.

OPERATION.
526

5 26
241

241 317

532 317

532 529

207 529

207 132

913 132

913 Ans. 1 504

Ans. 1893
First am't 1504

First am't 1893 978

1652

OPERATION.

OPERATION AND PROOF.

OPERATION AND PROOF.

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Questions. — Art. 23. What is the general rule for addition ? - Art. 24. What is the second method of proving addition? What is the reason of this method of proof ?

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23. Add 1001, 76, 10078, 15, 8761, 7, and 1678.

Ans. 21616.
24. Add 49, 761, 3756, 8, 150, 761761, and 18.

Ans. 766503.
25. Required the sum of 3717, 8, 7, 10001, 58, 18, and 5.

Ans. 13814.
26. Add 19, 181, 5, 897156, 81, 800, and 71512.

Ans. 969754.
27. What is the sum of 999, 8081, 9, 1567, 88, 91, 7,
and 878 ?

Ans. 11720.
28. Add 71, 18765, 9111, 1471, 678, 9, 1446, and 71.

Ans. 31622.
29. Add 51, 1, 7671, 89, 871787, 61, and 70001.

Ans. 949661.

30. What is the sum of 71, 8956, 1, 785, 587, and 76178 ?

Ans. 86578. 31. Add 9999, 8008, 8, 81, 4777, and 516785.

Ans. 539658. 32. Add 5, 7, 8911, 467, 47895, and 87. Ans. 57372. 33. Add 123456, 71, 8005, 21, and 716787.

Ans. 848340. 34. Add 47, 911111, 717, 81, 88767, and 56.

Ans. 1000779. 35. What is the sum of 71, 8899, 4, 7111, and 678679 ?

Ans. 694764. 36. Add 81, 879, 41, 76789, 42, 1, and 78967.

Ans. 156800. 37. Add 917658, 75, 876789, 46, and 8222.

Ans. 1802790. 38. Add 91, 76756895, 76, 14, 3, and 76378.

Ans. 76833457. 39. Add 10, 100, 1000, 10000, 100000, and 1000000.

Ans. 1111110. 40. What is the sum of 9, 99, 99, 1111, 8000, and 5 ?

Ans. 9323. 41. Add 41, 7651, 7678956, 43, 15, and 6780.

Ans. 7693486. 42. Add 1234, 7891, 3146751, 27, 9, and 5.

Ans. 3155917. 43. What is the sum of 19, 91, 1, 1, 1478, 1007, and 46 ?

Ans. 2643. 44. Add four hundred seventy-six, seventy-one, one hundred five, and three hundred eighty-seven.

Ans. 1039. 45. Add fifty-six thousand seven hundred eighty-five, seven hundred five, thirty-six, one hundred seventy thousand and one, and four hundred seven.

Ans. 227934. 46. Add fifty-six thousand seven hundred eleven, three thousand seventy-one, four hundred seventy-one, sixty-one, and three thousand and one.

Ans. 63315. 47. What is the sum of the following numbers: seven hundred thousand seven hundred one, seventeen thousand nine, one million six hundred thousand seven hundred six, forty-seven thousand six hundred seventy-one, seven thousand forty-seven, four hundred one, and nine ?

Ans. 2373544. 48. Gave 73 dollars for a watch, 15 dollars for a cane, 119 dollars for a horse, 376 dollars for a carriage, and 7689 dollars for a house ; how much did they all cost ?

Ans. 8272 dollars.

49. In an orchard, 15 trees bear plums, 73 trees bear apples, 29 trees bear pears, and 14 trees bear cherries ; how many trees are there in the orchard ?

Ans. 131 trees. 50. The hind quarters of an ox weighed 375 pounds each, the fore quarters 315 pounds each ; the hide weighed 96 pounds, and the tallow 87 pounds. What was the whole weight of the ox?

Ans. 1563 pounds. 51. A man bought a farm for 1728 dollars, and sold it so as to gain 375 dollars; how much did he sell it for ?

Ans. 2103 dollars. 52. A merchant bought five pieces of cloth. For the first he gave 376 dollars, for the second 198 dollars, for the third 896 dollars, for the fourth 691 dollars, and for the fifth 96 dollars. How much did he give for the whole ? Ans. 2257 dollars.

53. A merchant bought five hogsheads of molasses for 375 dollars, and sold it so as to gain 25 dollars on each hogshead ; for how much did he sell it ?

Ans. 500 dollars. 54. John Smith's farm is worth 7896 dollars ; he has bank stock valued at 369 dollars, and he has in cash 850 dollars. How much is he worth?

Ans. 9115 dollars. 55. Required the number of inhabitants in the New England States by the census of 1840, there being in Maine 501,793, in New Hampshire 284,574, in Massachusetts 737,699, in Rhode Island 108,830, in Connecticut 309,978, and in Vermont 291,948.

Ans. 2,234,822. 56. Required the number of inhabitants in the Middle States in 1840, there being in New York 2,428,921, in New Jersey 373,306, in Pennsylvania 1,724,033, in Delaware 78,085, and in Maryland 469,232.

Ans. 5,073,577. 57. Required the number of persons in the Southern States in 1840, there being in Virginia 1,239,797, in North Carolina 753,419, in South Carolina 594,398, in Georgia 691,392, in Alabama 590,756, in Mississippi 375,651, and in Louisiana 352,411.

Ans. 4,597,824. 53. How many inhabitants in the Western States in 1840, there being in Tennessee 829,210, in Kentucky 779,828, in Ohio 1,519,467, in Indiana 685,866, in Illinois 476,183, in Missouri 383,702, in Arkansas 97,574, and in Michigan 212,267 ?

Ans. 4,984,097. 59. How many inhabitants in 1840 in the following Territories and the District of Columbia, there being in Florida 54,477, in Wisconsin 30,945, in Iowa 43,112, and in the District of Columbia 43,712 ?

Ans. 172,246.

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