PROOF I. Add cach 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. 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, 318. 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. 876205 + 918 + 468 + 207 + 948 + 572 + 618 +861594872+206 +48 +500+918+1331=what? on; if th med to only the of saying ing, I t tens, sa 16. 361965384 + 2963 + 1200 + 100200 + 2560 + 74 +36 + 5 + 4786 + 186 + 544 + 396486 = what? 17. Find the sum of the last five answers. Ans. 587,294. PROOF II. Separate the example into two or more parts by horizontal lines; add the parts separately, and then add their amounts; if the same result be obtained as before, the work may be presumed to be correct. See Example 18. 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 8 2 1 8 A-9 8 7 4 490 25 9 8 7 9 1 5 3 1 7 1 8 4- A 7 4 4 4 7 J 6 22 06-K 5 2 6 3 5 4 4 1 7- L 4 6 4 9 4 7 1 8 8 8- I 680 71 K-6 6 7 8 7 16 6 8 3 1 820 68 L-7 2 8 4 3 1 6 6 9 4 1 9 M-8 4 5 2 1 9 2 4 8 1 8 7 8 4 9 5 3 4 6 2 1-M 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 P-1 9 9 5 9 8 9 8 2 2 Q-9 4 1 5 2 9 5 5 5 2 R-7 9 5 7 2 1 8 2 3 8 9 6 5 9 49 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 40 63 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 7 5 4 5 4 1 9 7 2 9 0-0 8 4 5 7 5 4 9 0 9 4 0- P 9 4 1 8 0 8 7 6 7 0 0-Q 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 socks; 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. men; 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 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 regiments, 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 furnished army shoes, 16649 + 4480 + 713932282022+2336+2220+1000+1200+1236 +1013240 pairs; cavalry boots, 336 +1008 +336+192 +160+168 +150 pairs. Required the number of pairs of boots; of shoes; of both. 40. She furnished hats, 12000 +4704; caps, 121302934 +2069450 +251 +98 +160. Required the number of hats; of caps. 41. On commencing business a merchant had $7752 in cash, $7719 in real estate, goods valued at $9728, a lot of cattle valued at $6930, a ship valued at $16834; during the first year he was in trade he gained above all his expenses $3195. What was he worth at the end of the year? 42. What is the number of square miles in the British Isles, there being in Scotland 30000, in England 31200, in Wales 7200, and in Ireland 32500? 43. The United States contain 3284100 square miles more than the British Isles; required the area of the United States? 44. What is the length of the Grand Trunk Railway from Detroit to Portland, the distance from Detroit to Stratford being 143 miles; from Stratford to Georgetown, 59 miles; from Georgetown to Toronto, 30 miles; from Toronto to Coburg, 69 miles; from Coburg to Belleville, 44 miles; from Belleville to Kingston, 48 miles; from Kingston to Brockville, 47 miles; from Brockville to Prescott, 12 miles; from Prescott to Cornwall, 46 miles; from Cornwall to Montreal, 67 miles; from Montreal to Richmond, 73 miles; from Richmond to Island Pond, 71 miles; from Island Pond to Gorham, 58 miles; from Gorham to Bethel, 21 miles; from Bethel to Danville, 42 miles; from Danville to Portland, 28 miles? 45. How far is it from Detroit to Toronto ? 46. How far from Toronto to Montreal? 47. How far from Kingston to Montreal? 48. How far from Montreal to Portland? 49. How far from Portland to Gorham? 50. From Boston to Portland is 111 miles; how far is it from Boston to Montreal? For Dictation Exercises, see Key. |
