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With divisors of two places, the trial quotient figure obtained as indicated in 1 and 3 will be found to be the true quotient figure. Often with divisors of more than two places, the trial quotient figure will be found to be one more than the true quotient figure.

261. Written Exercises.
Examine the divisors used in these exercises.
Divide :
1. 51,913 by 54.

12. 86,734 by 85
2. 65,760 by 87.

13. 67,863 b 75. 3. 51,596 by 92.

14. 54,326 by 64. 4. 61,640 by 76.

15. 92,147 by 53. 5. 51,594 by 96.

16. 92,147 by 534. 6. 83,756 by 43. 17. 54,326 by 647. 7. : 98,765 by. 21.

18. 94,245 by 736. 8. 45,637 by 86. 19. 67,863 by 754. 9. 94,245 by 73. 20. 67,321 by 959. 10. 87,653 by 54. 21. 51,504 by 967. 11. 67,321 by 95. 22. 45,637 by 865.

262. Written Exercises.
Examine each divisor before using it.

Divide each of the following by 87, 94, 63, 72, 55, 22, 31, 44, 33, 652, 773, 940: 1. 93,456. 3. 54,943. 5. 19,831. 7. 40,572. 2. 67,342. 4. 86,425. 6. 24,753. 8. 98,345.

263. Written Problems.

He

1. There are 52 weeks in one year. How many years are there in 468 weeks?

2. A man bought a carload of cattle at $32 each.

paid $ 800 for the carload. Find the number of cattle in the car.

3. A train travels at an average speed of 42 mi. an hour. How many hours will it take it to travel 1000 mi.?

4. A hardware merchant paid $ 21 each for stoves. The amount of his bill was $315. How

How many stoves did he buy?

5. A dealer bought a carload of horses at $ 95 each. He paid $2565 for them. How many horses

. did he buy?

6. A merchant paid $3570 for some carriages at $210 each. How many carriages did he buy?

7. At $65 a month, in how many months will a clerk earn $ 975 ?

8. At 55¢ a yard, how many yards of cloth can be bought for $ 8.25? (Change to cents.)

9. At 75$ each, how many tickets must be sold to amount to $15?

10. There were 42 children at a school picnic. The expenses of the picnic were $10.50. Find each one's share of the expenses.

CASE TWO

264. When the second figure of the divisor is greater than the first figure, as in 37, 28, 287, 596, etc. Divide 1734 by 47.

When the divisor is 47, 48, or 49, 3

use 5 as the divisor to find the trial MODEL : 47)1734

quotient figure. 5 is contained in 17 three times. Use 3 as the trial quotient figure. Complete the division.

When the second - figure of the divisor is 7, 8, or 9, the number to be used as a divisor to find the trial quotient figure is determined as follows:

When the divisor is 47, 48, 49, 475, etc., use 5 as divisor. When the divisor is 57, 58, 59, 584, etc., use 6 as a divisor.

The trial quotient figure thus obtained is sometimes one more or one less than the true quotient figure.

a

265. Written Exercises.

Before dividing, state what divisor will be used to find the trial quotient figure in each of the following:

Divide: 1. 54,321 by 19. 7. 71,067 by 38. 13. 43,907 by 275. 2. 54,796 by 38. 8. 30,402 by 49. 14. 69,087 by 594. 3. 12,345 by 69. 9. 42,796 by 59. 15. 87,906 by 178. 4. 43,697 by 28. 10. 74,908 by 67. 16. 38,690 by 576. 5. 43,345 by 18. 11. 43,768 by 57. 17. 43,234 by 374. 6. 54,678 by 57. 12. 67,098 by 19. 18. 41,908 by 490.

266. Divide 1085 by 25.

.

2 is contained in 10 five times.

4 MODEL: 25)1065

Use one less than this quotient as a

trial quotient figure. 4 is the trial quotient figure. Complete the division.

When 23-26, 34-36, 45, 46, and 56 are used as divisors, or as the first two figures of divisors, use as a trial quotient figure one less than the quotient obtained by dividing the first figure, or figures, of the dividend by the first figure of the divisor.

The trial quotient figure thus obtained is sometimes one more or one less than the true quotient figure.

267.

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Written Exercises. Divide each by 25, 35, 46, 56, 243, 462, and 358: 1. 9875. 7. 9356. 13. 6532.

19. 9530. 2. 2675. 8. 3640. 14. 3256.

20. 4780. 3. 3650. 9. 1884. 15. 7890.

21. 8020. 4. 4563. 10. 3657. 16. 5231.

22. 6510. 5. 1895. 11. 7627. 17. 6423.

23. 1560. 6. 2750. 12. 1840. 18. 5768.

24. 7090.

5

268. Written Exercises.

Divide each by 65, 49, 36, 245, and 684: 1. 547,659. 5. 634,237.

9. 120,500. 2. 134,652. 6. 845,178.

10. 387,945. 3. 347,865. 7. 342,156.

11. 674,109. 4. 937,311. 8. 240,100. 12. 832,674. 269. When such numbers as 13, 14, 15, 16, 134, 149, 157, etc., are used as divisors, the trial quotient figure can not be determined by any definite rule; but by the following method a trial quotient figure may be found that will seldom vary more than one from the true quotient figure. Divide 1067 by 14.

Use 2 as a divisor.

2 is con7

tained in 10 five times. Add 2 to MODEL: 14)1067

this quotient for a trial quotient fig7 is the trial quotient figure. Complete the division. When 13, 14, 15, 16, 138, etc., are used as divisors, divide the first figure, or the first two figures, of the dividend by 2, and add 2 to the quotient thus obtained for a trial quotient figure, unless the quotient figure can be determined readily by inspection

ure.

270. Written Exercises.

Divide : 1. 95,478 by 15. 6. 13,468 by 16. 11. 84,675 by 138. 2. 87,345 by 14. 7. 23,410 by 15. 12. 12,432 by 146. 3. 11,745 by 16. 8. 46,098 by 13. 13. 90,543 by 164. 4. 10,000 by 13. 9. 10,710 by 14. 14. 14,500 by 159. 5. 20,348 by 14. 10. 12,000 by 15. 15. 15,234 by 163.

271. Written Exercises.

Divide each by 95, 79, 36, 16, 425, 386, and 145: 1. 548,674. 3. 240,575. 5. 450,100. 2. 427,658. 4. 318,925. 6. 987,689.

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