PROOF I. Add each column in a reverse direction; if the same result be obtained as before, the work may be presumed to be correct. NOTE. Greater readiness will be attained by mentioning only the results in adding columns. Thus, in the above example, instead of saying 7 and 5 are 12, and 1 are 13, say 7, 12, 13; and instead of saying, 1 ten and 3 tens are 4 tens, and 8 tens are 12 tens, and 2 tens are 14 tens, say 1, 4, 12, 14 tens. 35. EXAMPLES FOR PRACTICE. 1. What is the sum of twenty-one, sixty-seven, eighty-nine, thirty-two, forty-five, thirteen, ninety, and seventy-eight? Ans. 435. 2. What is the sum of six hundred four, nine hundred ninetynine, seven hundred ten, six thousand nine hundred eighty-two, eleven thousand eight hundred seven? Ans. 21,102. 3. What is the sum of 326, 981, 362, 707, 889, and 864? Ans. 4129. 4. What is the sum of 246, 368, 909, 896, 763, and 892? Ans. 4074. 5. What is the sum of 32689, 86543, 94861, 18325, and 90026? Ans. 322,444. 6. What is the sum of all the numbers from one to thirty, inclusive? Ans. 465. 7. What is the sum of all the numbers from one hundred fifty to one hundred seventy-five, inclusive? 8. Add 99, 364, 77, 86, 912, 32678, 96542, and 32684. 9. Add 987, 5, 679, 369, 153, 888, 806, 17, 27, and 5654. 10. Add 915, 875, 617, 868, 575, 387, 694, 946, and 6377. 11. Find the sum of the last four answers. Ans. 189,506. 12. Add 987, 425, 672, 307, 216, 321, 111, 872, 564, 876, 818. 419, 187, 160, and 3453. 13. 875 +466 + 327 + 942 + 286 + 424 + 309 + 429 + 482 + 317 + 406 + 466 + 111 + 171 + 1618 = what? 14. 324868 + 522 + 297 + 789 + 524 + 286 + 361 + 472 + 884 + 472 + 287 + 649 + 592 +1788 what? 15. 876 +205 +918 + 468 + 207 + 948 + 572 + 618 +861 +594 +872+206 +48 +500 +918+1331=what? 16. 361965384 +2963 + 1200+100200 + 2560 + PROOF II. Separate the example into two or more parts by 36, TABLE FOR PRACTICE IN THE FUNDAMENTAL OPERATIONS. 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 A-9 8 7 4 4 90 2 5 9 8 7 9 1 5 3 1 7 1 8 4- A B-9 0 5 7 8 8 8 8 4 4 2 5 8 7 5 9 9 5 3 3 7- B C-6 7 9 4 3 5 5 6 8 6 7 2 6 1 7 8 7 2 6 9 2- C D-3 6 9 6 6 3 5 3 6 3 0 7 8 6 8 3 2 7 4 7 6-D E-1 5 3 9 6 7 8 5 6 2 1 6 5 7 5 4 3 6 2 0 8- E F-8 8 8 4 5 5 5 5 0 3 2 13 8 7 2 1 6 3 5 6- F G-8 0 63 9 9 5 1 6 1 1 1 6 9 4 5 0 3 5 7 5– G H-9 1 7 5 1 7 2 4 4 8 7 29 4 6 8 4 2 9 9 3-H I -9 2 7 9 3 1 3 3 0 5 6 4 6 4 9 4 7 1 8 8 8- I J -9 5 3 2 0 5 6 4 9 8 7 6 8 0 71 7 4 4 4 7~ J K-6 6 7 8 7 16 6 8 3 1 820 6 8 6 2 2 0 6- K L-7 2 8 4 3 1 6 6 9 4 1 9 5 2 6 3 5 4 4 1 7- L M-8 4 5 2 1 9 2 4 8 1 8 7 8 4 9 5 3 4 6 2 1-M 81 78 N-1 4 4 8 6 8 1 5 2 1 6 0 2 1 6 1 1 1 5 8 4- N O-2 2 5 1 8 9 3 9 3 8 7 5 4 5 4 1 9 7 2 9 0-0 P-1 9 9 5 9 8 9 8 2 2 8 4 5 7 5 4 9 0 9 4 0- P Q-9 4 1 5 2 9 5 5 5 2 9 4 1 8 0 8 7 6 7 0 0-Q R-7 9 5 7 2 1 8 2 3 8 9 6 5 9 4 9 0 2 2 9 8-R S-7 3 4 2 5 6 3 2 1 5 1 7 8 0 6 3 9 6 4 7 5- S T-3 2 3 5 8 3 5 3 0 8 9 4 5 1 6 4 8 4 6 2 7- T U-8 2 4 1 7 4 7 7 4 2 8 7 4 9 9 2 3 5 5 8 6-U V -7 6 9 4 1 6 2 6 8 4 0 6 3 6 4 3 8 7 2 1 9- V W-1 0 8 8 2 4 8 2 4 7 1 6 7 6 2 8 9 7 9 8 4-W X-8 7 2 8 9 29 8 2 8 7 2 8 9 8 6 2 4 7 6 8-X Y-4 4 4 7 6 4 4 2 5 5 7 4 4 5 7 4 7 6 5 1 1-Y Add in the above Table (as units, tens, and hundreds) columns, 34. Paid $2400 (dollars) for my farm, $155 for my horse and cart, $26 for garden utensils, $86 for a mowing-machine, $10 for a horse-rake, and $108 for a pair of oxen. Required the amount. 35. A body of troops were furnished with 3622 Springfield rifled muskets, 7690 smooth-bores, and 13185 Enfield rifles. Required the amount. 36. J. R. bought of the Seneca Knitting Mills, 39600 pairs of Bocks; of Whitten, Hopkins & Co., 9782 pairs; of Pierce Brothers & Co., 9353 pairs; of Allen, Lane & Washburn, 5664 pairs; of George C. Bosson, 4296 pairs; of Cushing, Pierce & Co., 1315 pairs; of Samuel Dennis, 276 pairs. Required the amount. 37. Required the average number of pupils attending the Grammar Schools of Boston during the year 1859-60, the average number attending the Adams School being 493; the Bigelow School, 469; Bowdoin School, 538; Boylston, 941; Brimmer, 575; Chapman, 626; Dwight, for boys, 622; Dwight, for girls, 489; Eliot, 708; Franklin, 559; Hancock, 719; Lawrence, 761; Lincoln, 466; Lyman, 370; Mayhew, 367; Phillips, 549; Quincy, 720; Wells, 494; Winthrop, 933. 38. In the year 1861, Massachusetts furnished for the U. S. army, from her several counties, as follows: From Barnstable, 3 commissioned officers and 108 enlisted men; Berkshire, 21 officers, 614 men; Bristol, 59 officers, 1681 men; Dukes, 0 officers, 1 man; Essex, 148 officers, 4134 men; Franklin, 12 officers, 482 men; Hampden, 35 officers, 845 men; Hampshire, 15 officers, 575 men; Middlesex, 141 officers, 4200 men; Nantucket, 1 officer, 7 men; Norfolk, 70 officers, 2031 men; Plymouth, 44 officers, 1363 men; Suffolk, 278 officers, 4111 men; Worcester, 110 officers, 3464 men. Besides these, there joined her regi ments, 647 men whose residences were not given, and 20 officers and 955 men from other States. Required the whole number of enlisted men in her regiments; of commissioned officers; of both. 39. Massachusetts Cariched army shoes, 16649 + 4480 + 36, TABLE FOR PRACTICE IN THE FUNDAMENTAL 21 20 19 18 17 16 J-9 5 3 2 2 5 9 8 7 9 1 5 3 1 7 1 8 4- A 8 4 4 2 5 8 7 5 9 9 5 3 3 7- B 8 6 7 2 6 1 7 8 7 2 6 9 2- C A-9 8 7 4 490 Add in the above Table (as units, tens, and hundreds) colurans, |