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.
For the first he

52. A merchant bought five pieces of cloth. 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 583,034, 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?

OPERATION.

Years.

68

91

83

85

Amount 3 27

Ans. 327.

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.

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

§ 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.

will make 7.

We first inquire what number added to 4 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.

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

2. Thomas had five oranges, and gave two of them to John; how many had he left?

3. Peter had six marbles, and gave two of them to Samuel · how many had he left?

4. Lydia had four cakes; having lost one, how many had she left?

5. Daniel, having eight cents, gives three to Mary; how many has he left?

6. Benjamin had ten nuts; he gave four to Jane, and three to Emily; how many had he left?

7. Moses gives eleven oranges to John, and eight to Enoch: how many more has John than Enoch?

8. Paid seven dollars for a pair of boots, and two dollars for shoes; how much did the boots cost more than the shoes?

4 less 4?

10. How many are 4 less 3?

5 less 1?

5 less 5?

11. How many are 5 less 2?

5 less 3?

5 less 4?

12. How many are 6 less 1?

6 less 2?

6 less 4?

6 less 5?

26. How many are 20 less 5? 20 less 8? 20 less 9? 20 less 12? 20 less 15? 20 less 19?

27. Bought a horse for 60 dollars, and sold him for 90 dollars; how much did I gain?

ILLUSTRATION.

We may divide the two prices of the horse into tens, and subtract the greater from the less. Thus 60 equals 6 tens, and 90 equals 9 tens; 6 tens from 9 tens leave 3 tens, or 30. Therefore I gained 30 dollars.

28. Sold a wagon for 70 dollars, which cost me 100 dollars; how much did I lose?

29. John travels 30 miles a day, and Samuel 90 miles; what is the difference?

30. I have 100 dollars, and after I shall have given 20 to Benjamin, and paid a debt of 30 dollars to J. Smith, how many dollars have I left?

31. John Smith, Jr., had 170 dollars; he gave his oldest daughter, Angeline, 40 dollars, his youngest daughter, Mary, 50 dollars, his oldest son, James, 30, and his youngest son, William, 20 dollars; he also paid 20 dollars for his taxes; how many dollars had he remaining?

ART. 26. The pupil, having solved the preceding questions, will perceive, that

SUBTRACTION is the taking of one number from another to find the difference.

When the two numbers are unequal, the larger is called the Minuend, and the less number the Subtrahend. The answer, or number found by the operation, is called the Difference, or Remainder.

NOTE. The words minuend and subtrahend are derived from two Latin words; the former from minuendum, which signifies to be diminished or made less, and the latter from subtrahendum, which means to be subtracted or taken away.

ART. 27. SIGNS. Subtraction is denoted by a short horizontal line, thus, signifying minus, or less. It indicates that the number following is to be taken from the one that precedes it. The expression 6 — 2 = 4 is read, 6 minus, or less, 2 is equal to 4.

QUESTIONS. Art. 26. What is subtraction? What is the greater number called? What is the less number called? What the answer? - Art. 27. What is the sign of subtraction? What does it signify and indicate?