22. A farmer having sold 6 cords of wood for 18 dollars, took a barrel of flour at 6 dollars towards his pay and the rest in cash: how much money did he receive?

23. A lady bought a shawl for 15 dollars, and handed the shopkeeper a 20 dollar bill: how much change ought she to receive back?

24. A man having 25 watermelons in his garden, some wicked boys stole 9 of them: how many had he left?

25. James is 14 years old, and his sister is 19: what is the difference in their ages?

26. A merchant had a piece of calico which contained 33 yards; on measuring the remnant he finds he has but 7 yards left: how many yards has he sold?

27. A hogshead of cider contains 63 gallons: after drawing out 9 gallons, how many will be left?

28. Henry had 48 silver dollars, and gave 8 to the orphan asylum: how many dollars did he have left?

29. A man bought a piece of cloth containing 39 yards, and sold 6 yards of it: how many yards had he left? 30. George gave 75 cents for a pair of skates, and sold them for 9 cents less than he gave: how much did he get for his skates?

31. William had 67 cents; he spent 5 for chestnuts and 2 for apples: how many cents has he left?

32. A man sold a load of wood for 18 shillings; he laid out 4 shillings for tea and 6 for sugar: how many shillings had he to carry home?

33. Sarah having 85 cents, gave 10 cents to the Sabbath School Society, 8 to the Bible Society, and spent 6 for candy: how many cents had she left?

34. If I pay 27 dollars for a cow and sell it for 18 dollars, how much do I lose by the bargain?

35. Richard had 45 marbles; he lost 7 and gave away 5: how many had he left?

36. A man having 56 dollars in his pocket, bought a hat for 5 dollars, a coat for 10, and a pair of boots for 4: how much money had he left?

37. If I owe a merchant 50 dollars and pay him 20 dollars, how many dollars shall I then owe him? Ans. 30 dollars.

Suggestion. It is advisable for beginners to analyze the numbers in this question, as in Art. 16, Ex. 31, and then take 2 tens from 5 tens.

38. A farmer having 80 sheep, sold all but 30: how many did he sell?

39. A man having 90 acres of land, gave 50 acres to his son how many acres has he left?

40. George had 70 cents and spent 30: how many had he left?

41. In a certain orchard there are 100 trees, 60 of them are apple-trees and the rest are peach-trees: how many peach-trees are there?

42. A grocer bought 150 eggs, and afterwards found that 20 of them were rotten: how many sound ones were there?

43. In the Center School there are 150 scholars, 60 of whom are girls how many boys are there?

44. A man bought a horse for 90 dollars, and sold it immediately for 130 dollars: how much did he make by his bargain?

45. A man owing me 200 dollars, turned me out a horse worth 80 dollars, and is to pay the balance in cash: how much money must he pay me?

46. A boy going to market with 80 cents, bought 20 cents worth of cheese, and 30 cents worth of butter: how much change had he left?

47. 35 from 42 leaves how many? 63 from 75? 48. 26 from 40 leaves how many? 35 from 45? 49. 65 from 85, how many? 82 from 94, how many? 50. 8 from 17, how many? 13 from 26, how many ? 6 from 25, how many? 8 from 94, how many? 5 from 68, how many? 17 from 34, how many? 7 from 43, how many? 6 from 72, how many? 9 from 75, how many? 7 from 86, how many?

31. It will be observed that all the preceding examples of this section, though expressed in a variety of ways, involve the same principle; that the object aimed at in each of them, is to find the difference between two numbers; consequently, they are all performed in the

same manner. The operation consists in taking a less number from a greater, and is called subtraction. Hence, 32. SUBTRACTION is the process of finding the difference between two numbers.

The difference, or the answer to the question, is called

the remainder.

OBS. 1. The number to be subtracted is often called the subtrahend, and the number from which it is subtracted, the minuend. These terms, however, are calculated to embarrass, rather than assist the learner, and are properly falling into disuse.

2. Subtraction, it will be perceived, is the reverse of addition. Addition unites two or more numbers into one single number; subtraction, on the other hand, separates a number into two parts.

3. When the given numbers are of the same denomination, the operation is called Simple Subtraction. (Art. 18. Obs.)

33. Subtraction is often represented by a short horizontal line (—), which is called minus. When placed between two numbers, this sign shows that the number after it is to be subtracted from the one before it. the expression 8-5, signifies that 5 is to be subtracted from 8; and is read, "8 minus 5," or "8 less 5."

Note.-The term minus, is a Latin word signifying less.

EXERCISES FOR THE SLATE.

Thus

34. When we wish to find the difference between two small numbers, it is the most convenient way to perform the subtraction in the mind. But when the numbers are large, it is difficult to retain them in the mind, and carry on the operation at the same time. By setting them down upon a slate or black-board, however, the process of subtracting large numbers is rendered short and simple. (Art. 21.)

QUEST.-31. What is the object aimed at in the preceding examples? In what does the operation consist? What is it called? 32. What then is subtraction? What is the difference or answer called? Obs. What is the number to be subtracted sometimes called? That from which it is subtracted? Of what is subtraction the reverse? When the given numbers are of the same denomination, what is the operation called? 33. What is the sign of subtraction called? Of what does it consist? What does it show? How is the expression 8-5, read? Note. What is the meaning of the term minus? 34. What is the most convenient way of finding the difference between two small numbers? What between two large ones?

Ex. 1. Suppose a man gave 475 dollars for a span of horses, and 352 dollars for a carriage: how much more did he pay for his horses than for his carriage?

Operation.

hund.

tens

units

Horses, 4 7 5 Dolls.
Carriage, 3 5 2 Dolls.
Rem. 1 2 3 Dolls.

Directions.-Write the less number under the greater, so that units may stand under units, tens under tens, &c. Now, beginning with the units, proceed thus: 2 units from 5 units leave 3 units; write the 3 in units' place, under the figure subtracted. 5 tens from 7 tens leave 2 tens; set the 2 in tens' place. 3 hundreds from 4 hundreds leave 1 hundred; write the 1 in hundreds' place. The remainder is 123 dollars.

OBS. It is important for the learner to observe, that we subtract units from units, tens from tens, &c.; that is, we subtract figures of the same order from each other. This is done for the same reason that we add figures of the same order to each other. (Art. 22.) Hence, in writing numbers for subtraction, great care should be taken to set units under units, &c., in order to prevent the mistake of subtracting different orders from each other.

2. A merchant bought 268 barrels of flour; and on examination, found that only 123 barrels were fit for use: how many were damaged? Ans. 145.

Suggestion.-Write the less number under the greater, &c., and proceed as above.

3. A traveler having 576 dollars, was robbed of 344 dollars: how many dollars had he left?

4. What is the difference between 648 and 235? 5. What is the difference between 876 and 523? 6. What is the difference between 759 and 341 ? 7. What is the difference between 4567 and 1235? 8. What is the difference between 8643 and 5412?

QUEST. In the 1st example how do you write the numbers for subtraction? Where begin to subtract? Obs. What orders do you subtract from each other? Why not subtract different orders from each other? Why place units under units, &c., in subtraction?

35. When the figures in the lower number are all smaller than those directly over them, each lower figure, as we have seen in the preceding examples, must be subtracted from that above it, and the remainder must be placed under the figure subtracted.

But it often happens that a figure in the lower number is larger than that above it, and consequently cannot be taken from it.

13. It is required to find the difference between 75 and 48.

Operation.

75

48

27 Rem.

It is plain that we cannot take 8 units from 5 units, for 8 is larger than 5. What then shall we do? Since 75 is composed of 7 tens and 5 units, we can take 1 ten from the 7 tens, and adding it mentally to the 5 units, it will make 15 units. Then subtracting the 8 units from 15 units, will leave 7 units; write the 7 under the units' column. As we took 1 ten from the 7 tens, we have but 6 tens left; and 4 tens from 6 tens leaves 2 tens: write the 2 under the tens' column. The whole remainder, therefore, is 2 tens and 7 units, or 27.

36. The process of taking one from a higher order in the upper number, and adding it to the figure from which the subtraction is to be made, is called borrowing ten, and is the reverse of carrying ten. (Art. 24.)

OBS. The 1 taken from a higher order, is always equal to 10 in the next lower order to which it is added. (Art. 8.)

37. The principle of borrowing may be illustrated by the following analytic solution of the last example.

QUEST.-35. When the figures in the lower number are each smaller than those over them, how proceed? Where do you place the remainder? Is a figure in the lower number ever larger than that above it? 36. What is meant by borrowing 10? What is the 1 taken from the higher order equal to?