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2058 2079 2112 2156 2178 2187 2205 2268 2304 2352 2376 2401 2464 2475 2541 2592 2625 2646 2662 2673 2688 2695 2744 2772 2816 2835 2904 2916 3024 3025 3072 3087 3125 3136 3168 3234 3267 3375 3388 3402 3456 3465 3528 3564 3584 3645 3675 3696 3773

7776 3872 11 11 8 6468 12 11 7 7 11 9 7 3 3888

99 8 6 6534 11 11 9 6 11 8 8 3 3969 9 9 7 7 6561 9 9 9 9 11 7 7 3993 11 11 11 3 6615 97

7 5 31 11 11 9 2 4032 9 8 8 7 6655 11 11 11 5 9 9 9 3 4096 8 8 8 8 6776 11 11 8 7 9 7 7 5 4116 12 7 7 7

6804 12 9 9 7 9 9 7 4 4125 11 5 5 5 3 6860 10 7 7 7 2 9 8 8 4 4158 11 9 7 6 6875 11 5 5 5 5 8 7 6 4224 11 8 8 6 6912 12 9 8 8 11 9 8 3 4235 11 1175 7056 9 8 7 7 7 ay 7 7 4312 11 8 7 7

11 9 9 11 8 7 4 4356 11 11 9 4 7168 8 8 8 7 11 9 5 5 4374 9 996 7203 7 7 7 7 3 11 11 7 3 4375 7 5 5 5 5 7392 12 11 8 7

9 9 8 4 4455 11 9 9 5 7425 11 9 5 5 3 7 5 5 5 3 4536 9 9 8 7 7546 11 7 7 7 2

9 7 7 6 4608 9 8 8 8 7560 12 10 9 7 11 11 11 2 4704

12 8 7 7 7623 11 11 97 11 9 9 3 4725 9 7 5 5 3 7744 11 11 8 8

8 8 7 6 4752 11 9 8 6 7776 12 9 9 8 11 7 7 5 4802 7 7 7 7 2 7875 97 5 5 5

8 777 4851 11 9 77 7938 97 7 2
11 9 7 4 4928 11 8 8 7 7986 11 11 11 6
11 8 8 4 5082 11 11 7 6 8019 11 9 9 9

9 9 7 5 5103 9 9 9 7 8064 9 8 8 7 2
11 11 8 3 5145 7 7 7 5 3 8085 11 7 7 5 3
9 9 9 4 5184 9 9 8 8 8192 8 8 8 4 4
9 8 7 6 5292 12 9 7 7 8232 8 7 7 7 3
11 11 5 5 5324 11 11 11 4 8316 12 11 97
8 8 8 6 5346 11 996

8448 12 11 8 8 9 7 7 7 5376 12 8 8 7 8505 9 9 7 5 3 5 5 5 5 5 5445 1111 95 8575 7 7 7 5 5

8 8 7 7 5488 8 7 7 7 2 8624 11 88772 11 9 8 4 5544 11 9 8 7 8712 11 11 98 11 7 7 6 5625 9 5 5 5 58748 12 9 9 9 11 11 9 3 5632 11 8 8 9072 9 9 8 7 2 9 5 5 5 3 5775 11 7 5 5 3 9075 11 11 5 5 3 11 11 7 4 5808 11 11 8 6 9216 9 8 8 4 4

9 9 6 5832 9 99 8 9261 9 7 773 9 8 8 6 5929 11 11 77 9317 11 11 11 7 11 9 7 5 6048 12 9 8 7 9375 5 5 5 5 5 3

9 8 7 7 6075 9 9 5 5 3|| 9408 8 8 7 7 3 11 9 9 4 6125 7 7 5 5 5| 9504 12 11 9 8

8 8 7 6144 12 8 8 8 9604 7777 4 9 9 9 5 6174 97772 9625 11 7 5 5 5 77 5 5 3 6237 11 997 9702 11 977 21 11 8 7 6 6272 8 8 7 7 2 9801 11 11 99 11 7 7 7 6336 11 98 8 9856 11 8 7 4 4

181

ANSWERS TO THE EXERCISES.

NUMERATION (pp. 4 and 5). 1. Two thousand, seven hundred and sixty-three. Thirty

five thousand, one hundred and sixty-two. Forty

five thousand, two hundred and eighty. 2. Fifty-six thousand, one hundred and six. Eighty-two

thousand, and thirty. Nine hundred and ten thou

sand, two hundred and fifty-seven. 3. One hundred and seventy-three thousand, and four. Six

million, seven hundred and eighty-nine thousand, five hundred and twenty-three. Three million, four hun

dred and eighty-six thousand, and twenty-five. 4. One million, one hundred and forty-two thousand, and

sixty. One million, one hundred and ten thousand, one hundred and eleven. Four million, three hundred

and sixty-two thousand, eight hundred. 5. Sixty-four million, three hundred and seventy thousand,

two hundred and fifty-three. Ninety-nine million, eight hundred and seventy-four thousand, and sixty

two. Thirty-five million, six thousand, two hundred. 6. Seventy-three million, eight hundred and ninety-two

thousand, five hundred and thirty-one. Eight hundred and seventy-five million, sixty-two thousand, and thirty-five. One hundred and seven million, nine

bundred and twenty-six thousand, five hundred. 7. Seven thousand five hundred and thirty-nine million,

three hundred and thirty-six thousand, two hundred and ten. Three hundred and twenty-six thousand nine hundred and seventy-two million, five hundred and seventy-three thousand, nine hundred and seventy

Four hundred and fifteen thousand, eight hundred and sixty-two million, three hundred and fourteen

thousand, two hundred and three. 8. Seven hundred and thirty thousand two hundred and

fifty-four million, sixty-two thousand, eight hundred and ten. One hundred and seventy-three thousand and four million, two hundred and two thousand, six hundred and four. Five hundred and two thousand one hundred and thirty million, sixty-five thousand, and eighty.

one.

1. 1760. 2. 546000. 3. 2000000. 4. 621865.

(Pages 4, 5.)
5. 312500.
6. 1177580.
7. 109915.
8. 505107.

9. 1155240. 10. 1314176. 11. 6007944. 12. 20936468.

ADDITION (pp. 7, 8, 9). 1. 541. 2. 409.

3. 4641.

4. 12485. 5. 47115. 6. 797527. 7. 7581522. 8. 127297. 9. 11812. 10. In 1841, 18664761 ; in 1851, 20936468. 11. 518277. 12. 144 days; 6169016 visits. 13. 580347. 14. Newspapers, 593; advertisements, 2252550.

SUBTRACTION (pp. 12, 13, 14). 1. 471 and 1628. 2. 35891. 3. 10105 and 701208. 4. 4049.

5. 8888. 6. 1698069. 7. 82.

8. 1659330. 9. 965574. 10. 2271707.

11. 10892.

12. 877744. 13. 803899 pounds. 14. 9321416. 15. 203 pounds. 16. 2870784. 17. 21811085 pounds. 18. Born, 283001; died, 219052. 19. 10131. 20. Nothing.

21. 415539.

MULTIPLICATION (pp. 18, 19). 1. 1026. 2. 19044. 3. 35325. 4. 484344. 5. 7976563. 6. 3276.

7. 601604512. 8. 101904804408. 9. 7801178441640. 10. 49906. 11. 535914.* 12. 365000.

13. 269195. 14. 2250 and 7875. 15. 12375.

16. 86879544. (Pages 24, 25.) 1. 114361. 2. 531786. 3. 2101120. 4. 471854788. 5. 478491860. 6. 2288575200. 7. 51947970000. 8. 16064348846.

9. 153787670242500. 10. 34141125200427.

11. 56604636. 12. 3024.

13. 759746144. 14. 94902500 miles. 15. 1238525174. 16. 427816 pounds. 17. 3486. 18. Gross earnings, 1177414 pounds; net earnings, 442157

pounds. * The daily average stated in the question is taken from “The Com. panion to the Almanac for 1852;" but it is too great : the true daily average was 86379. See Ex. 11, p. 8.

DIVISION (pp. 29, 30). 1. 744 2. 1 2013

3. 156049 4. 250797} 5. 5788233

6. 103460241 7. 8993361 8. 664591

9. 1246247 10. 7048.

11. 30651705 12. 86379. 13. 1628948. 14. 124353 pounds. 15. 1034280. 16. 1556441 pounds.

(Pages 35, 36.) 1. 5217.

2. 4709 3. 4. 14348578 5. 112221

1498016 25. 7. 2602 708 8. 203_1 5 6 7

12. 3143431300 13. 1662 pounds. 14. 3846.

15. 13209. 16. 7727. 17. 781, nearly. 18. 62 times, nearly.

3. 3500-342

64

111
8 4 3

9. 22478910

14 3 9 4

4 0 2 600

3 0 4 6 61907 8

11. 2272-246083•

REDUCTION (pp. 47, 48). 1. 207809d.

2. 381907 f. 3. 525600. 4. 662. 5. 35459.

6. 8550. 7. 838724. 8. 33880.

9. 8254. 10. 6624 qts.

11. 3411520 lbs. 12. 11474 lbs. 13. 432000 lbs. 14. 1254400 oz., 6272000s.* 15. 288. 16. 38016.

17. 91476. 18. 1728000 qts.

19. 23rd June. 20. 81998.

(Pages 51, 52.) 1. £27 118. 11 d.

2. 225 m. 4 fur. 26 per. 1 yd. 3. 7 h. 57 m. 15 sec.

4. 2 lb. 2 oz. 16 dwt. 11 gr. 5. 78 t. 15 cwt. 1

qr.

4 lb. 6. 1539 yds. 1 qr. 3 na. 7. 266 ac. 2 roo. 17 po. 8. 21 sq. yds. 2 ft. 64 in. 9. 12500 gal.

10. 36° 48' 50". 11. 2 c. yds. 3 ft. 1504 in. 12. 44 t. 12 cwt. 3 qrs. 12 lb. 13. £650.

14. £30166 10s. 2d. 15. 13 d. 31ho.

16. 39 d. 191; ho. 17. 200 t. O cwt. 3 qrs. 7 lbs. 18. £132546 18. 6d. 19. 3 ho. 3 min. 20 sec. 20. 1961 t. 5 cwt. 20 lb. 21. 2603 c. yds. 10ft. 22. 10 d. 4 h. 4m. 48., the gal. imp. 23. 4240.

24. 10s.

* The reported weight was stated to be " about 35 tons ;' but this estimate was too great. See the answer to Ex. 24, p. 107.

ADDITION OF COMPOUND QUANTITIES (pp. 54, 55). 1. £38 11s. 7 d.

2. £568 16s. 11d. 3. £1571 11s. 61d.

4. 100 d. 7 h. 19 m. 5. 140 d. 19 h, 34 m.

6. 485 d. 3 h. 14 m. 29 s. 7. 69 lb. 3 oz. 9 dr.

8. 71 cwt. 1

qr.

22 lb. 9. 112 cwt. 1 qr. 26 lb. 13 oz. 10. 44 oz. 1 dwt. 5 gr. 11. 37 oz. 6 dwt.

12. 62 lb. 4 oz. 8 dwt. 16 gr. 13. 23 dr. 0 sc. 8 gr.

14. 38 oz. O dr. 1 sc. 15. 34 lb. O oz. 3 dr. O sc. 17 gr. 16. 548 yd. 1 ft. 2 in. 17. 23 fur. 25 po. ż yd. 18. 425 m. 3 fur. 34 po. 4 yd. 19. 405 ac. 2 roo. O per. 12 yds. 20. 918 ac. 1 roo. 16 per. 99 yds.

SUBTRACTION OF COMPOUND QUANTITIES (pp. 56, 57, 58). 1. £15 14s. 81d.

2. £206 128. 81d. 3. £2283 10s. 81d.

4. 6 d. 19 h. 58 m. 5. 67 d. 21 h. 46 m.

6. 16 h. 32 m. 32 s. 7. 74 yd. 1 ft. 5 in.

8. 188 yd. 1 ft. 9 in. 9. 12 per. 5 yds. O ft. 2 in. 10. 5° 33' 54". 11. 8° 36' 49".

12. 23° 54' 47". 13. 3 d. 22 h. 43 m. 34 sec. 14. 3 t. 16 cwt. 1 qr. 20 lb. 15. 6 t. 1 cwt. 1 qr. 13 lbs. 16. lt. 3 cwt. 2 qrs. 3 lb. 17. 75 m. O fur. 15 per. 2ų yds. 18. 15 m. 2 fur. 34 per. 21 yds. 19. 101 m. 1 fur. 27 per. 4 yds. 20. 53 ac. 2 roo. 22 per. 254 yds. 21. 6 ac. O roo. 29 per. 29. yds. 22. 2 roo. 33 per. 151 yds. 23. 10 oz. 18 dwt. 6 gr. 24. i lb. 5 oz. 14 dwts. 16 gr. 25. 5 lb. O oz. 7 dwts. 13 g

gr. 26. 38 c. yds. 26 ft. 1697 in. 27. 63 c. yds. 20 ft. 1591 in. 28. 315 c. yds. 4 ft. 1547 in. 29. 85 sq. yds. 3 ft. 32 in. 30. 201 sq. yds. 8 ft. 122 in. 31. 806 sq. yds. 4 ft. 83 in. 32. 8 gal. 1 qt. 1 pt.

33. 1708 gal. 1 qt. 34. 684 gal. 2 qts. 1 pt.

35. 1 bu. O pk. 1 gal. 36. 5 bu. O pk. O gal. 2 qt. 37. 15 bu. lpk. O gal. 3 qt.

MULTIPLICATION OF COMPOUND QUANTITIES (pp. 60, 61). 1. £162 28. 8£d.

2. £348 11s. 2d. 3. £1507 16s. 3d.

4. £2397 68. 5 d. 5. £6614 16s. 9 d.

6. £550 16s. 3d. 7. £7372 78. 12d.

8. £16560 1s. 6d.

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