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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.

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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. 2. 67,342.

7. 40,572.

4. 86,425. 6. 24,753. 8. 98,345.

263. Written Problems.

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

How many

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

3

MODEL: 47)1734

When the divisor is 47, 48, or 49, use 5 as the divisor to find the trial 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 a 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.

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. 2. 54,796 by 38. 3. 12,345 by 69. 4. 43,697 by 28. 5. 43,345 by 18. 6. 54,678 by 57.

7. 71,067 by 38. 8. 30,402 by 49. 9. 42,796 by 59. 10. 74,908 by 67. 11. 43,768 by 57. 12. 67,098 by 19.

13. 43,907 by 275. 14. 69,087 by 594. 15. 87,906 by 178. 16. 38,690 by 576. 17. 43,234 by 374. 18. 41,908 by 490.

266. Divide 1085 by 25.

4

MODEL: 25)1065

2 is contained in 10 five times. 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. Written Exercises.

Divide each by 25, 35, 46, 56, 243, 462, and 358:

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Divide each by 65, 49, 36, 245, and 684 :

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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.

7

2 is con

Add 2 to

Use 2 as a divisor. tained in 10 five times. this quotient for a trial quotient figure. 7 is the trial quotient figure. Complete the division.

MODEL: 14)1067

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.

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Divide each by 95, 79, 36, 16, 425, 386, and 145:

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