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108. A gardener has 3476 apple-trees, 8476 pear-trees, 5684 peach-trees, 1845 plum-trees, 4680 quince-trees, and 9487 ornamental trees; how many trees are there in his nursery?

109. The first of three numbers is 4768, the second 8942, and the third is as much as the other two; what is the sum of the three numbers ?

110. I have $ 376.25 in one bank, $ 4678.85 in another, and in another as much as in both of these ; how much money have I in the three banks ?

111. An army consists of 276450 infantry, 14875 cavalry, and 27846 artillery men ; what is the number of men in the army?

112. A carpenter engaged to build 4 houses, the first for $ 3462, the second for $ 6875, the third for $ 8963, and the fourth for $ 12462; what shall he receive for the four houses ?

113. During the year ending June 30, 1878, the value of the issue of ordinary postage stamps by the Post-Office Department amounted to $ 19468618; of newspaper stamps, to $ 1093845 ; of stamped envelopes and wrappers, to $ 4905774; and of postal cards, to $ 2000630. Find the total value of these items.

41. QUESTIONS. 30. What is meant by the Sum, or Amount ? 31. Only what kind of numbers can be added ? 32. What is Addition ? 33. A Sign ? 34. Write the sign for dollars. 35. What does the sign of Equality mean? Write it. 36. Write the sign for Addition. 38. How are numbers arranged for addition? Which column is added first ? Its sum, where placed ? Is it desirable to name the figures as we add them ? If the amount of any column is ten or more, where is the right-hand figure of the amount written ? What is done with the left-hand figure ? 39. Repeat the rule for Addition. 40. How is Addition proved ? Why do we add in the opposite direction ? In United States money what places do cents occupy ? Mills ?

SUBTRACTION.

42. 1. Arthur had 7 peaches, but he has given 3 of them to John; how many peaches has he left ?

2. James had 9 cents, and spent 5 cents ; how many cents did he have left ?

43. Only numbers of the same kind can be subtracted from each other; thus, we can take 5 books from 8 books; but we cannot take 5 books from 8 marbles.

44. Subtraction is the process of finding the difference between two numbers of the same kind.

45. The greater number is called the Minuend; the less number is called the Subtrahend; and the result is called the Difference or Remainder.

46. The sign of subtraction, – , called minus, signifies that the number after it is to be taken from the number before it; thus, 7 4= 3, that is, seven minus four, or seven diminished by four, equals three.

47. Oral Exercises. 3. If I give away 5 oranges from 9 which I have, how many shall I have left ?

4. If my father gives me 10 cents and I lose 6 of them, how many shall I have left ?

5. If Mr. Russell buys 7 liters of peas and sells from these 4 liters, how many liters will he have left ?

6. A merchant has 19 meters of cloth and sold 8 meters ; how many meters had he left ?

7. John had 27 cents, but gave 8 to James, and then 6 to Arthur; how many cents did he have left ?

8. Subtract by twos from 50 to 0; from 49 to 1.

9. Subtract by threes from 50 to 2 ; from 49 to 1 ; from 48 to 0.

10. Subtract by fours from 50 to 2; from 49 to 1; from 48 to 0; from 47 to 3.

11. Subtract by fives from 50 to 0; from 49 to 4; from 48 to 3 ; from 47 to 2; from 46 to 1.

12. Subtract by sixes from 50 to 2 ; from 49 to 1; from 48 to 0; from 47 to 5 ; from 46 to 4 ; from 45 to 3.

13. Subtract by sevens from 50 to 1; from 49 to 0; from 48 to 6; from 47 to 5 ; from 46 to 4; from 45 to 3 ; from 44 to 2.

14. Subtract by eights from 50 to 2; from 49 to 1 ; from 48 to 0; from 47 to 7; from 46 to 6 ; from 45 to 5; from 44 to 4 ; from 43 to 3.

15. Subtract by nines from 50 to 5 ; from 49 to 4 ; from 48 to 3.; from 47 to 2 ; from 46 to 1; from 45 to 0; from 44 to 8; from 43 to 7 ; from 42 to 6.

16. If I buy 17 cents' worth of sugar, 33 cents' worth of tea, and 42 cents' worth of flour, and hand to the vender two fiftycent pieces, how much change ought he to give me?

17. Mr. B. owes me 47 cents and I owe him 73 cents ; how shall we settle ?

18. If a horse is bought for $ 250, and sold for $ 325, what is the gain ?

19. If of 76 chickens 27 are caught by foxes, how many are left ?

20. From a piece of sheeting containing 44 yards, there are

sold to one man 8, to another 9, to another 7; how many yards are left ?

21. Mr. Ames owed his neighbor $57 ; Mr. Ames brought to pay the bill $ 4 worth of eggs, $ 6 worth of butter, $ 8 worth of potatoes, $ 21 worth of wood, and a twenty-dollar bill; how did the account stand then ?

48.

Exercises for Written Work.

22. From 796 take 582.

OPERATION.

Write units under units, tens under tens, Minuend, 796 etc., as in addition. Then 2 units from 6 Subtrahend, 582 units leave 4 units, which we write under Remainder, 214

the units' column ; 8 tens from 9 tens

leave 1 ten, which we write under the tens' column ; 5 hundreds from 7 hundreds leave 2 hundreds, which we write under the hundreds' column. The remainder then is 2 hundreds, 1 ten, 4 units, or 214.

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31. A farmer bought a farm for $ 4875 and sold it again for $ 3463 ; how much did he lose by the transactions ?

32. By the census of 1870 the population of Maine was 628915, and that of New Hampshire was 318300; how many more people were there in Maine than in New Hampshire ?

33. If I borrow $ 4687 and afterwards pay $ 2423, how much do I still owe?

34. From 483 take 257.

OPERATION.

As we cannot take 7 units from 3 units, Minuend, 483 one of the 8 tens is put with the 3 units, Subtrahend, 257 making 13 units, and then, 7 units from 13

units leave 6 units. Now as one of the 8 Remainder, 226

o tens has been put with the 3 units, only 7 tens remain in the minuend, and 5 tens from 7 tens leave 2 tens, and, finally, 2 hundreds from 4 hundreds leave 2 hundreds ; hence, the entire remainder is 2 hundreds, 2 tens, 6 units, or 226.

35. From 256.17 take 187.245.

OPERATION. Writing units of the same order in the same

256.17 column, as there are no thousandths in the 187.245 minuend, we take of the 7 hundredths 1 hun

dredth,= 10 thousandths; then, 5 thousandths Ans. 68.925

from 10 thousandths leave 5 thousandths ; 4 Proof, 256.17 from (7--1, or) 6 leave 2; and so on, exactly as in Ex. 34, remembering also to place the decimal point directly under the points in the minuend and subtrahend.

49. Hence, to perform subtraction,

Rule. 1. Write the less number under the greater, units under units, tenths under tenths, etc., and draw a line beneath.

2. Beginning at the right hand, take each figure of the subtrahend from the figure above it, and place the remainder under the line, with the decimal point directly under the decimal points in the minuend and subtrahend.

3. If any figure in the subtrahend is greater than the figure above it, add ten to the upper figure and take the lower figure from the sum ; write down the remainder and, considering the next figure in the minuend one less, proceed as before.

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