carriage for 150 dollars, and a harness for 87 dollars. How much did he give for the whole ?

25. A man bought 268 bushels of wheat for 287 dollars, 187 bushels of corn for 98 dollars, and 156 bushels of oats for 128 dollars. How much did he give for the whole ?

36. A farmer, wishing to stock his farm, paid 197 dollars for a span of horses, 86 dollars for a yoke of oxen, 175 dollars for cows, and 169 dollars for sheep. How much did he give for the whole ?

37. A butcher sold to one customer 157 pounds of meat, to another 159, to another 149, to another 97, and to another 68. How much did he sell in all?

38. A carpenter received for one job 879 dollars, for another 786, for another 693, for another 587, for another 476, and for another 368 dollars. How much did he receive in all ?

39. A grocer bought 375 dollars worth of sugar, 287 dollars worth of molasses, 168 dollars worth of tea, 158 dollars worth of coffee, and 137 dollars worth of spices. What was the amount of his bill?

40. A merchant bought calico to the amount of 568 dollars, silks to the amount of 479 dollars, and broadcloths to the amount of 784 dollars. He sold them so as to gain 134 dollars on the calico, 178 dollars on the silks, and 242 dollars on the broadcloths. How much did he sell them for? What was the amount of his gains?

41. A merchant pays 560 dollars a year for store rent, 386 dollars to one clerk, 267 to another, and 369 dollars for various other expenses. What does it cost him a year to carry on his business?

42. A man receives 568 dollars rent for one store, 479 for another, and 276 for another. How much does he receive for them all?

43. The distance from Boston to Springfield is 98 miles, from Springfield to Pittsfield is 53 miles, from Pittsfield to Albany is 49 miles, from Albany to Auburn is 173 miles, and from Auburn to Buffalo is 152 miles. How far is it from Boston to Buffalo ?

44. A man bought a quantity of oil for 2649 dollars, and candles for 1367 dollars: he afterwards sold them so as to gain 568 dollars on the oil, and 346 dollars on the candles. How much did he receive for the whole?

45. In 1840 the state of Maine contained 501793 inhabitants; New Hampshire, 284574; Vermont, 291948; Massachusetts, 737699; Connecticut, 309978; and Rhode Island, 108830. What was the population of New England?

46. In 1840, the state of New York contained 2428921 inhabitants; New Jersey, 373306; Pennsylvania, 1724033; and Delaware, 78085. What was the population

of the Middle States?

47. In 1840, the state of Maryland contained 470019* inhabitants; Virginia, 1239797; North Carolina, 753419; South Carolina, 594398; Georgia, 691392; Alabama, 590756; Mississippi, 375651; and Louisiana, 352411. What was the population of the Southern States?

48. In 1840, the state of Tennessee contained 829210 inhabitants; Kentucky, 779828; Ohio, 1519467; Michigan, 212267; Indiana, 685866; Illinois, 476183; Missouri, 383702; and Arkansas, 97574. What was the population of the Western States?

49. In 1840, the territory of Florida contained 54477 inhabitants; Wisconsin, 30945; Iowa, 43112; and the District of Columbia, 43712: on board vessels of war, 6100. What was the population of the Territories and naval service of the United States?

50. What was the whole population of the United States in 1840 ?

* According to the Official Revision.

SECTION III.

SUBTRACTION.

MENTAL EXERCISES.

ART. 30. Ex. 1. Henry having 7 peaches, gave 4 to his sister how many had he left?

OBS. To solve this question, think what number added to 4 makes 7. Now, from addition we know that 4 and 3 make 7; that is, 7 is composed of the numbers 4 and 3. It is evident, therefore, if one of these numbers be taken from 7, the other number will be left. Hence 4 peaches from 7 peaches leave 3 peaches. Ans. 3 peaches.

2. James had 7 cents and spent three of them: how many had he left?

3. Jack has 6 marbles: how many more must he get to make 10?

4. A farmer having 9 cows, sold 5 of them: how many had he left?

5. A pound of raisins costs 11 cents and a pound of sugar 8 cents: what is the difference in their prices ?

6. In a stage coach there were 10 passengers, 6 of them got out at a hotel: how many remained in the coach?

7. Dick bought a knife for 12 cents, and having but 7 cents in his pocket, agreed to pay the rest to-morrow: how much does he owe for it?

8. John gathered 8 quarts of chestnuts: how many more must he gather to make 14 quarts?

9. The cost of a cap is 13 shillings, and the cost of a comforter is 3 shillings; what is the difference in their cost?

10. Susan is 15 years old, and Harriet is only 9: what is the difference in their ages?

OBS. This Table is the reverse of Addition Table. Hence if the pupil has thoroughly learned that, it will cost him but little time or trouble to learn this. (See observations under Addition Table, p. 20.)

11. 4 from 7 leaves how many? 4 from 9? 4 from 12? 4 from 8? 4 from 11? 4 from 13 ?

12. 6 from 8 leaves how many? 6 from 10? 6 from 13? 6 from 11? 6 from 15? 6 from 12? 6 from 16?

13. 7 from 9 leaves how many? 7 from 11? 7 from 14 7 from 15? 7 from 16? 7 from 13? 7 from 15? 7 from 17?

14. 8 from 11? 8 from 13? 8 from 16? 8 from 12? 8 from 15? 8 from 17? 8 from 14? 8 from 18?

15. 9 from 12? 9 from 14? 9 from 11? 9 from 13? 9 from 17? 9 from 15? 9 from 18? 9 from 19?

16. 2 from 4 leaves how many? 2 from 14? 2 from 24? 2 from 34? 2 from 44? 2 from 54? 2 from 64? 2 from 74? 2 from 84? 2 from 94 ?

17. 3 from 6? 3 from 16? 3 from 26? 3 from 36? 3 from 46 3 from 56? 3 from 66? 3 from 76? 3 from 86? 3 from 96 ?

18. 4 from 9? 4 from 29? 4 from 39? 4 from 49? 4 from 59? 4 from 69? 4 from 79? 4 from 89? 4 from 99?

19. 6 from 15? 6 from 25? 6 from 35? 6 from 45?

6 from 55? 6 from 65? 6 from 75? 6 from 95?

20. 8 from 14? 8 from 24? 8 from 34? 8 from 44? 8 from 54 8 from 64? 8 from 74? 8 from 84? 8 from 94 ? 21. A gentleman bought a coat for 15 dollars and a hat for 6 dollars: how much more did his coat cost than his hat?

28. PROOF.-Beginning at the top, add each column, downwards, and if the second result is the same as the first, the work is supposed to be right.

OBS. The object of beginning at the top and adding downwards, is, that the figures may be taken in a different order from that in which they were added before; otherwise, if a mistake has been made the first time adding, we should be liable to fall into the same again. But the order being reversed, the presumption is, that any mistake which may have been made will thus be detected; for it can hardly be supposed that two mistakes exactly equal will occur.

20. Find the sum of 256, 763, and 894, and prove the operation.

21. Find the sum of 8054, 5730, and 3056, and prove the operation.

22. Find the sum of 74502, 83000, and 62581, and prove the operation.

23. Find the sum of 68056, 31067, 680, and 200, and prove the operation.

24. Find the sum of 50563, 8276, 75009, 31, and 856, and prove the operation.

25. Find the sum of 65031, 2900, 35221, and 870, and prove the operation.

29. From the preceding illustrations and principles we derive the following

GENERAL RULE FOR ADDITION.

I. Write the numbers to be added under each other; so that units may stand under units, tens under tens, &c. (Art. 21.)

II. Begin at the right hand, and add each column separately. When the sum of a column does not exceed 9, write it under the column; but if the sum of a column exceeds 9, write the units' figure under the column added, and carry the tens to the next column. (Arts. 23, 25.)

QUEST.-28. How is addition proved? Obs. Why add the columns downwards, instead of upwards? 29. What is the general rule for addition?