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39. Proof.—Add the remainder to the smaller number; and if the sum is equal to the larger number, the work is right.

19. A man bought a horse for 175 dollars, and sold it for 127 dollars: how much did he lose by his bargain?

Operation. Paid 175 dolls. Rec'd 127 dolls. Lost 48 dolls.

Proof.

127 Smaller No.

48 Remainder. 175 Larger No.

Since the sum of the smaller number and remainder is equal to the larger number, the operation is correct.

OBS. This method of proof depends upon the obvious principle, that if the difference between two numbers be added to the less, the sum must be equal to the greater.

20. From 8796 subtract 2675, and prove the operation. 21. From 6210896 subtract 3456809, and prove the operation.

22. From 1000000 subtract 67583, and prove the ope

ration.

23. From 7834501 subtract 1000000, and prove the operation.

24. From 68436907 subtract 59476012, and prove the operation.

25. From 8006754231 subtract 7975663417, and prove the operation.

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

GENERAL RULE FOR SUBTRACTION.

I. Write the less number under the greater, so that units may stand under units, tens under tens, &c.

II. Beginning at the right hand, subtract each figure in the lower number from the figure above it, and set the remainder directly under the figure subtracted. (Art. 35.)

QUEST.-38. How then do you proceed, when a figure in the lower number is larger than the one over it? Why do you add 1 to the next figure in the lower line? 39. How is subtraction proved? Obs. Upon what principle does the proof of subtraction depend? 40. What is the general rule for subtraction?

III. When a figure in the lower number is larger than that above it, add 10 to the upper figure; then subtract as before, and add 1 to the next figure in the lower number. (Arts. 37, 38.)

EXAMPLES FOR PRACTICE.

1. A man bought a piece of cloth containing 37 yards, and sold 24 yards of it. How much had he left?

2. A merchant had on hand a quantity of flour for which he asked 245 dollars; but for ready money he made a deduction of 24 dollars. How much did he receive for his flour?

3. In a certain Academy there were 357 scholars, 168 of whom were young ladies. How many young gentlemen were there?

4. A farmer raised 4879 bushels of wheat, and sold 3876 bushels. How much had he left?

5. A man purchased a farm for 4687 dollars, but the times becoming hard he was obliged to sell it for 896 dollars less than he gave for it. How much did he sell it for?

6. A merchant bought 2268 dollars worth of goods, which, in consequence of getting damaged, he sold for 848 dollars less than cost. How much did he sell them for?

7. A merchant sold a lot of silks for 561 dollars, which was 179 dollars more than the cost of them. How much did he give for them?

8. A man bought an estate for 8796 dollars, and sold it again for 9875 dollars. How much did he gain by his bargain?

9. A farmer raised 1389 bushels of wheat one year, and 1763 the next. How much more did he raise the second year than the first?

10. A man bought a house and lot for 5687 dollars. The house was worth 3698 dollars, how much was the lot worth?

11. Suppose a gentleman's income is 3268 dollars a year, and his expenses are 2789 dollars. How much does he save in a year?

12. The United States declared their independence in 1776; how many years is it since ?

13. Two brothers commenced business at the same time; one gained 3678 dollars in five years, the other gained 2387 dollars in the same time. How much more did one gain than the other?

14. The distance from Boston to

Springfield is 98

miles, and from Boston to Pittsfield is 151 miles.

far is it from Springfield to Pittsfield?

How

15. From New York to Utica it is 243 miles, and from

New York to Albany it is 150 miles.

from Albany to Utica?

How far is it

16. America was discovered by Columbus in 1492; how many years is it since ?

17. Dr. Franklin died A. D. 1790, and was 84 years old when he died; in what year was he born?

18. General Washington was born A. D. 1732, and died in 1799; how old was he when he died?

19. The first settlement in New England was made at Plymouth in the year 1620. How many years is it since ?

20. A ship sailed having on board a cargo valued at 100000 dollars, but being overtaken by a storm, 27680 dollars worth of goods were thrown overboard. How much of the cargo was saved?

21. The population of Massachusetts in 1840 was 737699, and that of Connecticut was 309978. How many more inhabitants were there in Massachusetts than in Connecticut?

22. In 1840 the population of Massachusetts was 737699, and in 1820 it was 523287. How much did the population increase during this period?

23. In 1840 the population of the State of New York was 2428921, and in 1820 it was 1372812.

How much

did the population increase during that period?

24. In 1840 the population of the New England States was 2234822, and that of the State of New York was 2428921. How many more inhabitants were there in the State of New York than in New England?

25. In 1800 the population of the United States was 5305925, and in 1840 it was 17069453. How much did it increase in forty years?

26. A farmer having 389 acres of land, sold to one man 126 acres, and to another 163. How many acres had he left?

27. A gentleman had 1768 dollars deposited in the bank; he gave to one man a check for 175 dollars, to another for 238 dollars, and to another for 369 dollars. How much remained on deposit?

28. A man bought a horse for 87 dollars, a carriage for 75 dollars, and a harness for 16 dollars, and sold them all together for 200 dollars. How much did he gain by the bargain?

29. A man bought a quantity of sugar for 25 dollars, a quantity of molasses for 27 dollars, and a quantity of raisins for 29 dollars, for which he paid a hundred dollarbill. How much change ought he to receive back?

30. An orchard contained 120 apple-trees, 47 peachtrees, and 28 pear-trees. Of the apple-trees 26 were cut down for a Railroad to pass through, 18 of the peach-trees died, and 5 of the pear-trees were blown down. How many trees were left in the orchard?

31. A gentleman had 2700 dollars which he wished to distribute among his three sons. To the oldest he gave 825 dollars, to the second 785 dollars, and the remainder to the youngest. How much did the youngest son receive?

32. A man owed 5648 dollars: he paid at one time 536 dollars, at another 378 dollars, and at another 896 dollars. How much did he then owe?

33. A man having 7689 dollars, invested 689 dollars in Railroad stock, 500 dollars in a woolen factory, and 1250 dollars in bank stock. How much had he left?

34. A man bought a quantity of oil for 1763 dollars, and a lot of candles for 598 dollars. He afterwards sold them both for 2684 dollars. How much did he gain by

the bargain?

35. A man owned 3789 acres of land: he gave to one son 869 acres, and to another 987 acres. How much had he left?

36. A ship of war sailing with 650 men, lost in one battle 29 men, in another 37, and by sickness 19 more. How many were still living?

37. A merchant owes to one man 2684 dollars, to another 1786 dollars, to another 987 dollars. amount of his property is 4684 dollars. more does he owe than he is worth?

The whole How much

38. A man owned three farms: for the first he gave 4673 dollars, for the second 5674 dollars, and for the third 9287 dollars. He sold them all for 37687 dollars. How much did he gain by the bargain?

39. A man bought 86 dollars worth of wheat, 48 dollars worth of butter, and a fine horse worth 148 dollars. He gave his note for 128 dollars and paid the rest in cash. How much money did he pay?

40. A gentleman left a fortune of 18864 dollars to be divided between his two sons and one daughter; to one son he gave 6389 dollars, to the other 6984 dollars. How much did the daughter receive?

41. A man owing 8648 dollars, paid at one time 486, at another 684, at another 729 dollars. How much did he still owe?

42. Suppose a man gains by one speculation 867 dollars, by another 687; another time he gains 563 dollars and then loses 479; still another time he gains 435 dollars and loses 378. How much more has he gained than

lost?

43. A man borrowed of a friend 684 dollars at one time, 786 at another, 874 at another, and 976 at another. He has paid 568 dollars. How much does he still owe?

44. If a man's income is 4586 dollars a year, and he spends 384 dollars for clothing, 568 for house rent, 784 for provisions, 568 for servants, and 369 for traveling, how much will he have left at the end of the year?

45. A merchant bought a quantity of sugar for 8978 dollars, paid 374 dollars freight, and then sold it for 9684 dollars. How much did he gain by the trade?

46. A merchant had in his storehouse 6384 bushels of wheat, 3752 bushels of corn, 4564 bushels of oats, and 1384 bushels of rye: it was broken open and 3564 bushels of grain taken out. How many bushels remained?

47. A man bought a quantity of beef for 5493 dollars,

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