13. What is the sum of 85046+90045+412260+125781+ 4060+273048 ?

14. What is the sum of 1500267+45085+4652+4780400+ 90276+89760841?

15. What is the sum of 45702125+67070420+670856+ 4230825+750642+8790845?

16. What is the sum of 825760842+35620476+7800490+ 467243+98371+6425+740 ?

17. What is the sum of 2503+37621+475290+1223729+ 10671840-275600312?

18. What is the sum of 463270+2500+7200342+10271+ 426345+6200705 ?

19. What is the sum of 80429+7562345+700100+85261798 +-4000101+3007002 ?

20. What is the sum of 756+849+934+680+720+843 1 657?

21. What is the sum of 6457+29301+82406+7589+63489 +101364+46745 ?

22. Add together 786, 840, 910, 403, 783, 650, 809, 670, 408, 310, and 652.

23. Add together 16075, 250763, 7561, 830654, 293106, 2537104, and 316725.

24. Add together 256, 40, 751, 302, 75, 831, 26, 43, 621, 340, and 510.

25. Add together 493742, 56710607, 23461, 400072, 6811004, 8999003, and 26501.

26. Add together 629405, 7629, 31000401, 263012, 1300512, 390217, and 13268.

27. Add together 286013, 4016702, 1971342, 6894680, 28945, and 2624302.

28. Add together 460167, 296345, 84634123, 64205, 9673108 and 1931456.

29. Add together 432678902, 310046734, 2167005, 327861. and 293000428.

COUNTING-ROOM EXERCISES.

60. To the accountant as well as the mathematician, accuracy and expertness in adding, are indispensable. These attainments can be acquired only by frequent exercises in footing up long columns of figures.

Note.-1. Instead of saying 4 and 8 are 12, and 2 are 14, and 7 are 21, and 4 are 25, &c., a skilful accountant, performing the addition at a glance, simply pronounces the results. Thus, four, twelve, twenty-one, thirty-one, (4+6 =10,) thirty-seven, forty-seven, (7+3=10,) fifty-two.

2. When two or three figures taken together make 10, as 6 and 4, or 2, 3, and 5, &c., it accelerates the process to add their sum at once. A little practice will enable the student to run up a long column of figures with as much facility almost as he can count.

30.

86015

25163

85057

12236

43026

67084

21167

54042

42158

24034

459982 Ans.

3045 Car.

3. When the columns are long, accountants sometimes set the figure to be carried below the other figure under the column added. Thus, the sum of the first column in the example above being 52, set the 5 (the figure carried) below the 2. The sum of the second column being 48, set the 4 below the 8, &c. This method saves much time in reviewing an operation, and also enables us, when interrupted, to resume the process where we left off.

Required the amount of each of the following examples:

61. Accountants often acquire the habit of adding two columns of figures at a time. The power of rapid addition is easily acquired, and is well worthy the attention of the student. The following examples will illustrate the principle.

39. What is the sum of 312817+527236+141625+462415 +251818+234112?

Taking the two right hand columns, we say, 12 and 18 are 30, and 15 are 45, and 25 are 70, and 36 are 106, and 17 are 123. Set down the 23 under the columns added, and carry the 1 or left hand figure to the column of hundreds. Proceed in the same manner with the other columns.

Operation.

312817

527236

141625

462415

251818

234112

Ans. 1930023

What was the amount of exports and imports of the United States in 1840, and of shipping in 1842 ?

50. The appropriations of the Government of the United States, for 1847, were as follows: for the Civil and Diplomatic expenses 4,442,790 dolls.; for the Army and Volunteers 32,178,461 dolls.; for the Navy 9,307,958 dolls.; for the Post Office Department 4,145,400 dolls.; for the Indian Department 1,364,204 dolls.; for the Military Academy 124,906 dolls.; for building Steam Ships 1,000,000 dolls. ; for Revolutionary and other Pensions 1,358,700 dolls.; for concluding Peace with Mexico 3,000, 000 dolls.; for Light Houses 518,830 dolls.; Miscellaneous 540,243 dolls. What was the amount of all the appropriations?

62. It may sometimes be convenient for the learner, as well as gratifying to his curiosity, to be able to add numbers expressed by the Roman Notation.

51. A man paid MDCCCLXXXIII dollars for a farm, DCCXXIIII dollars for stock, and CCCLXVIIII dollars for tools: how much did he pay for all?

Operation. MDCCCLXXXIII dolls.

DCCXXIIII dolls. CCCLXVIIII dolls.

MMDCCCCLXXVI dolls.

Beginning at the right hand, we proceed thus: four Is and four Is are eight, and three Is make eleven, which is equal to two Vs and I. We set down the I, and adding the two Vs to one V makes fifteen, which is equal to X and V. Setting down the V, we count in the X with the other Xs, and find they make seven Xs or seventy, which is expressed by L and XX. We set down the two Xs, and adding the L to the other Ls, it makes three Ls, or one hundred and fifty, which is expressed by C and L. Setting down the L, and counting the C with the other Cs, we have nine Cs or nine hundred, which is expressed by D and CCCC. We set down the four Cs, and counting the D with the other Ds, it makes three Ds or fifteen hundred, which is expressed by M and D. We set down the D, and adding the M to the other M, we have two Ms, which we set down on the left of the other letters. Hence,

63. To add numbers expressed by the Roman Notation.

Beginning at the right hand, count all the letters of each kind together; set down the result, and carry on the principle that five Is make one V; two Vs, one X; five Xs, one L, &c.

OBS. The teacher can extend the exercises in the Roman Notation as far as he may deem it expedient. A single example is sufficient to illustrate the principle, and to show that the Roman is greatly inferior to the Arabic method in its adaptation to business calculations.