13. What is the sum of 85046 +90045+412260+125781+o 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 7.4000101+3007002 ?

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

21. What is the sum of 6457+29301 +82406+7589+68489 +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, 30. and 7 are 21, and 4 are 25, &c., a skilful accountant, per- 86015 forming the addition at a glance, simply pronounces the 25163 results. Thus, four, twelve, twenty-one, thirty-one, (4+6 85057 =10,) thirty-seven, forty-seven, (7+3=10,) fifty-two.

12236 2. When two or three figures taken together make 10, as 43026 6 and 4, or 2, 3, and 5, &c., it accelerates the process to

67084 add their sum at once. A little practice will enable the 21167 student to run up a long column of figures with as much 54042 facility almost as he can count.

42158 3. When the columns are long, accountants sometimes 24034 set the figure to be carried below the other figure under the 459982 Ans. column added. Thus, the sum of the first column in the 3045 Car. 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 :

35. 348,037 272,465 530,634 109,871 693,036 764,543 323,638 428,432 389,763 210,045 760,806 636,215 253,734 251,600 575,453 807,720 930,046 174,173 626,245 342,734

36. 460,375 841,681 239,724 763,256 437,891 825,432 285,678 310,720 403,521 687,489 324,061 530,724 623,452 487,638 290,731 803,256 731,463 379,574 823,156 928,348

37. 963,172 300,725 463,248 721,003 387,356 241,653 603,280 532,176 278,321 829,248 171,320 206,782 461,027 589,203 248,639 730,461 672,398 246,175 928,340 731,629

38. 349,652 361,728 412,381 635,403 872,545 406,223 294,867 811,236 576,037 213,744 764,368 305,216 436,720 823,284 217,436 592,301 243,762 731,445 429,374 684,569

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?

Operation. Taking the two right hand columns, we 312817 say, 12 and 18 are 30, and 15 are 45, and 527236 25 are 70, and 36 are 106, and 17 are 123.

141625 Set down the 23 under the columns added,

462415 and carry the 1 or left hand figure to the 251818 column of hundreds. Proceed in the same

234112 manner with the other columns.

Ans. 1930023

40

13

17

20

45

28

(41.) (42.) (43.) (44.) (45.) (46.) 21 22 44 1325 2610

344235 30 13 20 1510 1511

402321 11

25
1314
1021

141511
25
3141 1115

201250 14 50

1016
1513

154036 15 11 14 2233 4020

132212 34 33 16 1224 1316

181714 18

2415 1233

213025 12 12 11 1830 2515

111817 17 20 14 1814 1718

161518 23 78 37 1621 2142

432733 What was the amount of exports and imports of the United States in 1840, and of shipping in 1842 ?

(47.)

(48.)

(49.) States. Exports.

Imports. Shipping Maine, Dolls. 1,018,269

Dolls. 628,762 T. 281,930 N. Hampshire,

20,979

114,647 23,921 Vermont,

305,150
404,617

4,343 Massachusetts, 10,186,261 16,513,858 494,895 Rhode Island,

206,989

274,534 47,243 Connecticut,

518,210

277,072 67,749 New York,

34,264,080 60,440,750 518,133 New Jersey,

16,076

19,209

60,742 Pennsylvania, 6,820,145 8,464,882 113,569 Delaware,

37,001

802

10,396 Maryland,

5,768, 768 4,910,746 106,856 Dist. of Columbia, 753,923

119,852 17,711 Virginia, 4,778,220

545,085 47,536 North Carolina, 387,484

252,532 31,682 South Carolina,

10,036,769 2,058,870 23,469 Georgia, 6,862,959

491,428 16,536 Alabama, 12,854,694

574,651 14,577 Louisiana,

34,236,936 10,673,190 144,128 Ohio,

991,954

4,915

24,830 Michigan,

162,229

138,610 12,323 Florida,

1,858,850

190,728

7,288

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 ?

Beginning at the right hand, we proceed thus: Operation. four Is and four Is are eight, and three Is make MDCCCLXXXIII dolls. eleven, which is equal to two Vs and I. We set

DCCXXIIII dolls. down the I, and adding the two Vs to one V CCCLXVIIII dolls.. makes fifteen, which is equal to X and V. Set- MMDCCCCLXXVI dolls. ting 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.