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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.

ins.

:57. 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.

ox?

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

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 1850 there were in Maine 583,169, in New Hampshire 317,976, in Massachusetts 994,514, in Rhode Island 147,545, in Connecticut 370,792, and in Vermont 314,120.

Ans. 2,728,116. 56. Required the number of inhabitants in the Middle States, including the District of Columbia. In 1850 there were in New York 3,097,394, in New Jersey 489,555, in Pennsylvania 2,311,786, in Delaware 91,532, in Maryland 583,031, and in the District of Columbia 51,687.

Ans. 6,624,988. 57. Required the number of inhabitants in the Southern States. In 1850 there were in Virginia 1,421,661, in North Carolina 869,039, in South Carolina 668,507, in Georgia 906,185, and in Florida 87,445.

Ans. 3,952,837. 58. Required the number of inhabitants in the South-Western States. In 1850 there were in Alabama 771,623, in Mississippi 606,526, in Louisiana 517,762, in Texas 212,592, in Arkansas 209,897, and in Tennessee 1,002,917. Ans. 3,321,317.

59. Required the number of inhabitants in the North-Western States and Territories. In 1850 there were in Missouri 682,044, in Kentucky 982,405, in Ohio 1,980,329, in Indiana 988,416, in Illinois 851,470, in Michigan 397,654, in Wisconsin 305,391,

in Iowa 192,214, in California 92,597, and in the Territories 92,298.

Ans. 6,564,818. Art. 24. Method of adding two or more columns at a single operation.

Ex. 1. Washington lived 68 years ; John Adams, 91 years Jefferson, 83 years; Madison, 85 years. What is the sum of the years they all lived ?

Ans. 327.

OPERATION.
Years.
68
91
83
85

Beginning with the number last written down, we add the units and tens, thus : 85 and 3 equal 88, and 80 equal 168, and 1 equal 169, and 90 equal 259, and 8 equal 267, and 60 equal 327, the sum sought. In like manner may be added more than two columns at one operation.

Amount 3 27

NOTE. — The examples that follow can be performed as the above, or hy the common method, or by both, as the teacher may advise.

2. Ounces. 1 2 3 4 5 6 7 8 9012 3 4 5 6 7890 1 3 4 5 6 7 8 9 3216 7 8 9 0 1030 70 5 5 5 6 7 8 1234 5 6 7 8 9001 2 3 4 5 6 7 8 9 1030 7 816 1781

3.
Yards.
2 3 4 5
6789
1023
4 4 5 6
7890
1 2 3 4
5 6 7 8
9012
3 4 5 6
7890
1345
6 7 8 9
3 4 5 6
7890
5 6 7 8
9012
3 4 5 6
7 8 9 0
1234
5 6 7 8

4. Feet. 3456 7891 3 4 5 6 7891 3 4 5 6 7 8 9 0 1378 8123 4 5 6 7 8912 3 4 5 6 7 8 9 1 3 4 5 6 7 891 3783 1237 7891 1007 5 6 70 1234

5. Inches. 7 8 9 1 1 3 5 6 7 891 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9123 4 5 6 7 8912 3 4 5 6 7 812 3 4 5 6 7812 3713 7891 1 3 5 7 9009 8 7 6 5 4 3 2 1

6. Chaldrons. 5 6 7 8 3215 6 7 8 9 3214 1234 3 789 1379 9008 1071 7163 6781 1780 3007 5617 44 5 6 3 4 5 6 7891 3070 4 5 6 7 3 4 5 6

III. SUBTRACTION.

MENTAL EXERCISES.

ART. 25. WHEN it is required to find the difference between two numbers, the process is called Subtraction. The operation is the reverse of addition.

Ex. 1. John has 7 oranges, and his sister but 4; how many more has John than his sister ?

ILLUSTRATION. We first inquire what number added to 4 will make 7. From addition we learn that 4 and 3 are 7; consequently, if 4 oranges be taken from 7 oranges, 3 will remain Hence John has 3 oranges more than his sister.

SUBTRACTION TABLE.

1 from 1 leaves 0 1 from 2 leaves 1 1 from 3 leaves 2 1 from 4 leaves 3 1 from 5 leaves 4 1 from 6 leaves 5 1 from 7 leaves 6 1 from 8 leaves 7 1 from 9 leaves 8 1 from 10 leaves 9 1 from 11 leaves 10 1 from 12 leaves 11 1 from 13 leaves 12

2 from 2 leaves 0
2 from 3 leaves 1
2 from 4 leaves 2
2 from 5 leaves 3
2 from 6 leaves 4
2 from 7 leaves 5
2 from 8 leaves 6
2 from 9 leaves 7
2 from 10 leaves 8
2 from 11 leaves 9
2 from 12 leaves 10
2 from 13 leaves 11
2 from 14 leaves 12

3 from 3 leaves 0
3 from 4 leaves 1
3 from 5 leaves 2
3 from 6 leaves 3
3 from 7 leaves 4
3 from 8 leaves 5
3 from 9 leaves 6
3 from 10 leaves 7
3 from 11 leaves 8
3 from 12 leaves 9
3 from 13 leaves 10
3 from 14 leaves 11
3 from 15 leaves 12

4 from 4 leaves 0 4 from 5 leaves 1 4 from 6 leaves 2 4 from 7 leaves 3 4 from 8 leaves 4 4 from 9 leaves 5 4 from 10 leaves 6 4 from 11 leaves 7 4 from 12 leaves 8 4 from 13 leaves 9 4 from 14 leaves 10 4 from 15 leaves 11 4 from 16 leaves 12

5 from 5 leaves 0 5 from 6 leaves 1 5 from 7 leaves 2 5 from 8 leaves 3 5 from 9 leaves 4 5 from 10 leaves 5 5 from 11 leaves 6 5 from 12 leaves 7 5 from 13 leaves 8 5 from 14 leaves 9 5 from 15 leaves 10 5 from 16 leaves 11 5 from 17 leaves 12

6 from 6 leaves 0.7 from 7 leaves 0
6 from 7 leaves 1 7 from 8 leaves 1
6 from 8 leaves 2 7 from 9 leaves 2
6 from 9 leaves 3 7 from 10 leaves 3
6 from 10 leaves 4 7 from 11 leaves 4
6 from 11 leaves 5 7 from 12 leaves 5
6 from 12 leaves 6 7 from 13 leaves 6
6 from 13 leaves 7 7 from 14 leaves 7
6 from 14 leaves 8 7 from 15 leaves 8
6 from 15 leaves 9 7 from 16 leaves 9
6 from 16 leaves 10 7 from 17 leaves 10
6 from 17 leaves 11 from 18 leaves 11
6 from 18 leaves 12 7 from 19 leaves 12

8 from 8 leaves 0 8 from 9 leaves 1 8 from 10 leaves 2 8 from 11 leaves 3 8 from 12 leaves 4 8 from 13 leaves 5 8 from 14 leaves 6 8 from 15 leaves 7 8 from 16 leaves 8 8 from 17 leaves 9 8 from 18 leaves 10 8 from 19 leaves 11 8 from 20 leaves 12

9 from 9 leaves 0 10 from 10 leaves 0 11 from 11 leaves 0 12 from 12 leaves 0 9 from 10 leaves 1 10 from 11 leaves 1 11 from 12 leaves 1 12 from 13 leaves 1 9 from 11 leaves 2 10 from 12 leaves 2 11 from 13 leaves 2 12 from 14 leaves 2 9 from 12 leaves 3 10 from 13 leaves 3 11 from 14 leaves 3 12 from 15 leaves 3 9 from 13 leaves 4 10 from 14 leaves 4 11 from 15 leaves 4 12 from 16 leaves 4 9 from 14 leaves 5 10 from 15 leaves 5 11 from 16 leaves 5 12 from 17 leaves 5 9 from 15 leaves 6 10 from 16 leaves 611 from 17 leaves 6 12 from 18 leaves 6 9 from 16 leaves 7 | 10 from 17 leaves 711 from 18 leaves 712 from 19 leaves 7 9 from 17 leaves 8 10 from 18 leaves 8 11 from 19 leaves 8 12 from 20 leaves 8 9 from 18 leaves 9 | 10 from 19 leaves 9 11 from 20 leaves 9 12 from 21 leaves 9 9 from 19 leaves 10 10 from 20 leaves 10 11 from 21 leaves 10 12 from 22 leaves 10 9 from 20 leaves 11 10 from 21 leaves 11 | 11 from 22 ieaves 11 12 from 23 leaves 11 9 from 21 leaves 12 10 from 22 leaves 12 11 from 23 leaves 12 12 from 24 leaves 12

QUESTIONS. — Art. 25. What does subtraction teach? Of what is it the reverse ?

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