22. 58.73.37 + 42. +54.6 +32 + 87.43 + 98.27? 23. $8.75$9.72 $4.83+$27. +$8.07+ $47.43 +

$91.24?

24. $87.50 $647. +$8.54 + $.73 +$.025+ $87.631 +$42.968?

25. $3976.43 $18.275+ $867. + $4.04 + $.07 + $87894.325?

26. 7698 +43279+86372 +48563+ 19048 +25407? 27. 104376298543724187 +436794 +827632 + 549731+286423 +379485 +2176369 +453642+815437? 28. 8067.134+538.0076 +91.0789 +4736.89 +25.9843 +5813.0076+4257.321879.5207+6007.006 ?

29. 7386.275 +42.78 +64.83 +2.719+84.6796.81 +37.94814.946.244.376.821 +474.3 86.27

+ 47.09 ?

30. 4.763.27+48.+ 29.3 +2.17+ 217. +48.3+ 625.2.8 37.964.83+5.27+.691 +478+27.3

+4.8197.06 ?

31. 5£, 8s. 7d. 3qr. + 12£, 8s. 9d. 1qr. + 4£, 18s. 11d. 2qr. +7£, 14s. 6d. 1qr. + 5£, 19s. 7d. 1qr. + 13£, 4s. 2d. 2qr. ?

32. 47 gal. 3 qt. 1 pt. 2 gi. +37 gal. 1 qt. 1 pt. 1 gi. +85 gal. 2 qt. 2 gi.+25 gal. 2 qt. 1 pt. 3 gi. + 54 gal. 2 qt. 1 pt. 3 gi.? 33. 15 yd. 2 qr. 2 na. + 18 yd. 3 qr. 1 na. + 27 yd. 3 qr. 3 na. + 42 yd. 1 qr. + 87 yd. 3 na. + 3 qr. 3 na. + 26 yd. 1 qr. 1 na.?

34. 18 H, 63,5 3, 2 Ɖ, 5 gr. + 7 H, 83, 7 3, 1, 18 gr. +4b, 11 3,4 3, 2 Ɖ, 13 gr. + 25 H, 93, 19, 4 gr. † 11 3, 19?

35. 17 T. 18 cwt. 3 qr. 25 lb. + 19 T. 13 cwt. 2 qr. 14 lb. +7 T. 9 cwt. 23 lb. + 16 cwt. 17 lb. +8 T. 3 qr. 14 lb. ?

36. 2 m. 7 fur. 28 rd. 4 yd. 1 ft. 3 in. + 6 m. 5 fur. 19 rd. 2 yd. 2 ft. 11 in. + 25 m. 4 fur. 37 rd. 5 yd. 8 in. + 94 m. 1 fur. 24 rd. 4 yd. 2 ft. 8 in.?

37. 19 m. 5 fur. 37 rd. 2 yd. 2 ft. 2 in. + 16 m. 4 fur. 18 rd. 5 yd. 1 ft. 7 in. +37 m. 15 rd. 2 yd. 2 ft. 8 in. + 17 rd. 5 yd. 7 in. +3 m. 7 fur. 18 rd. 4 yd. 2ft. 9 in. ?

38. 14 A. 3 R. 28 sq. rd. 27 sq. yd. 8 sq. ft. 12 sq. in. -† 27 A. 2 R. 31 sq. rd. 17 sq. yd. 5 sq. ft. 137 sq. in. + 35 A. 1 R. 31 sq. rd. 18 sq. yd. 5 sq. ft. 116 sq. in. + 21 A. 26 sq. rd. 25 sq. yd. 5 sq. ft. 107 sq. in. + 43 A. 2 R. 14 sq. rd. 19 sq. yd. + 1 R. 15 sq. rd. 37 sq. in.?

39. 18 w. 4 da. 21 h. 37 m. 5 sec. + 37 w. 5 da. 16 h. 43 m. 57 sec. +19 w. 3 da. 14 h. 46 m. 38 sec. + 19 w. 6 da. 28 h. 56 m. 27 sec.?

40. 40 lb. 7 oz. 5 dwt. 6 gr. + 9 lb. 8 oz. 19 dwt. 22 gr. + 2 lb. 11 oz. 19 dwt. 23 gr. + 7 lb. 8 dwt. 19 gr. + 11 oz. 6 dwt. +3 lb. 1 oz. 15 gr. + 8 lb. 17 dwt. + 3 lb. 23 gr. + 18 dwt. 7 gr.9 oz. 15 gr. + 7 lb. 3 oz. 13 dwt. 15 gr. ?

41. A stable-keeper bought 4 loads of hay. The first load weighed 1 T. 17 cwt. 2 qr. 15 lb., the second 18 cwt. 3 qr. 34 lb., the third 1 T. 8 cwt. 1 qr. 19 lb., and the fourth 1 T. 4 cwt. 2 qr. 21 lb. How much did they all weigh?

42. He paid $21.57 for the first load, $14.98 for the second, $22.19 for the third, $19.73 for the fourth. How much did he pay for all?

3 da.,

43. The first load lasted him 2 w. 5 da., the second 2 w. the third 3 w. 1 da., and the fourth 3 w. 6 da. How long did all last him?

44. An apothecary in mixing medicine used 13,3 3, 29, 5 gr. of one kind, 3 3, 5 3, 1 9, 15 gr. of another, 7 3, 2 9, 17 gr. of another, 4 3, 29, of another, and 5 3, 29, 17 gr. of another. What was the weight of the mixture?

45. A trader sold 9 lb. 6 oz. of sugar to one man, 8 lb. 10 oz. to another, 5 lb. 8 oz. to another, 6 lb. 10 oz. to another, 3 lb. 4 oz. to another, 2 lb. 2 oz. to another, 1 lb. 5 oz. to another, and 8 lb. 6 oz. to another. How much did he sell in all?

46. He received $.755 for the first lot, $.605 for the second, $.40 for the third, $.485 for the fourth, $.23 for the fifth, $.15 for the sixth, $.095 for the seventh, $.585 for the eighth. How much did he receive in all ?

SECTION XXI.

A. All arithmetical questions in which we are required to find the difference between two numbers, or the excess of one number over another, are questions in subtraction, and the process by which we determine the answers to them is called the process of Subtraction. The following are questions in Subtraction: 1. Henry found 27 apples and gave away 9 of them. How many had he left?

2. How many are 8-5?

3. 7 from 12 leaves how many?

Subtraction, then, may be defined to be a process by which we find how many units there are in one given number more than in another.

It may also be defined to be a process by which we find a number equal in value to the difference between two given numbers.

The larger given number, or one from which we subtract, is called the Minuend, the smaller given number, or one subtracted, is called the Subtrahend, and the result obtained is called the Difference or Remainder. In example 1, 27 is the minuend, 9 is the subtrahend, and 18 is the difference or remainder.

The minuend and subtrahend must represent things of the same kind, otherwise the subtraction cannot be performed. 5 apples from 7 apples leave 2 apples, and 5 pears from 7 pears leave 2 pears; but it would be absurd to talk of taking 5 pears from 7 apples, or 5 apples from 7 pears. We cannot subtract 5 cents from 7 dimes, but if we should exchange one of the dimes for its value in cents, we should have 6 dimes and 10 cents, from which if we should subtract 5 cents, there would be 6 dimes and 5 cents left.

We cannot subtract units from tens, but we can find how many units a given number of tens is equal to, and then subtract from that number of units.

B. The following examples will illustrate some of the principles to be kept in view in subtracting large numbers:

-

1. Mr. Morse has in his possession 4697 dollars, and he owes 3265 dollars. How many dollars would he have left if he should pay his debts?

Solution. If he has 4697 dollars, and owes 3265, he would have as many dollars left as there are units in the difference between 4697 and 3265. We can best find this difference by considering the denominations separately. 5 units from 7 units

leave 2 units; 6 tens from 9 tens leave 3 tens; 2 hundreds from 6 hundreds leave 4 hundreds; 3 thousands from 4 thousands leave 1 thousand. Having thus subtracted the numbers in all the denominations, we know that the remainder must be 1 thousand, 4 hundred, 3 tens, and 2 units, or that Mr. Morse would have 1432 dollars after paying his debts.

In performing the above subtraction the work could have been commenced as well at any other denomination as at the units. Example 2. A man who had 17£ 8s. 9d. paid away 3£ 4s 6d. How much had he remaining?

The usual reasoning process shows that he would have as many £, s., and d. left as there are in the difference between 17£ 8s. 9d. and 3£ 4s. 6d.

6d. from 9d. = 3d. 4s. from 8s. = 4s. 3£ from 17£- 14£. The answer is, therefore, 14£, 4s. 3d. Or, beginning at the left, 17£ 3£ 9d.

3d. 6d. Ans. 14£, 4s. 3d.

14. 8s. 4s. 4s.

C. From the nature of subtraction, it is evident, that if the minuend were divided into two parts, such that one should equal the subtrahend, the other would equal the remainder. We can, therefore, test the correctness of the work, by adding the subtrahend and remainder, observing whether the amount be equal to the minuend or not. If it be, the work is probably correct; but if it be not, there is an error either in the subtraction or addition, and possibly in both.

Another method of proof, depending upon the same principles as the last, is to subtract the remainder from the minuend;. the remainder thus obtained should equal the subtrahend.

Although the result is not affected by the manner of writing the numbers, it is convenient to place those of the same denomination near each other, or to write units under units, tens under tens, &c., in simple numbers, and pounds under pounds, shillings under shillings, yards under yards, feet under feet, &c., in compound.

For the sake of uniformity, we usually place the minuend above the subtrahend, and the remainder beneath; as in the following written work of examples 1 and 2:

4697. Minuend.

3265. Subtrahend.

1432. Remainder.

4697. Sum of Subtrahend and Remainder

3265. Difference of Rem. and Minuend

the Minuend.

the Subtrahend.

17, 8, 9. Sum of the Sub. and Rem. equal to the Minuend. 3, 4, 6. Difference of Rem. and Min. equal to Subtrahend.

2. How many are .0769.0316? 200.739 100.428?

What is the value of the following?

3. 27 bu. 3 pk. 7 qt. 1 pt. 14 bu. 2 pk. 3 qt. 1 pt. 4. 3 lb. 11 oz. 15 dwt. 18 gr. 1 lb. 8 oz. 13 dwt. 4 gr.

5. 6 T. 17 cwt. 2 qr. 26 lb. 13 oz. 11 dr.—2 T. 6 cwt. 15 lb. 8 oz. 3 dr.

6. 16 H, 83, 53, 2, 18 gr. - 5 b, 4 3, 23, 19, 6 gr. 7. 1757 gal. 3 qt. 1 pt. 3 gi.—1323 gal. 1 qt. 2 gi.

8. 18 rd. 4 yd. 2 ft. 11 in. - 6 rd. 2 yd. 1 ft. 5 in.

9. 4207.6539 yds. 3105.231 yds.

10. 9406 yds. 3 qr. 2 na. 2 in.

2103 yds. 1 qr. 1 na. 1 in.

11. .007639 Tons 007214 Tons.

12. A trader bought a box of sugar, weighing 3 cwt. 1 qr. 27 lb. How much did he have left after selling 1 cwt. 1 qr. 13 lb.?

13. A farmer bought a piece of land containing 38 A. 2 R. 35 rd., and afterwards sold 7 A. 1 R. 27 rd. How much did he have left?

14. Mr. Jackson spent 43£, 18s. 9d. 3qr. for travelling expenses in England, and 27£, 6s. 8d. 1qr. for travelling expenses in Scotland. How much more did he spend in England than in Scotland?

15. He travelled 2379.86 miles in England, and 1208.31 miles in Scotland. How many more miles did he travel in England than in Scotland?

16. A silver-smith bought 1 lb. 6 oz. 7 dwt. of silver of one man, 2 lb. 3 oz. 18 dwt. 23 gr. of another, and 3 lb. 11 oz. 13 dwt. 21 gr. of another. How much did he buy of all? How much will he have left, after manufacturing and selling 3 lb. 4 oz. 12 dwt. 16 gr. of it?