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11. Solve by Long Division, explain, aird prove the following: (1.) (2.) (3.)

(4.)
3) 849 5) 940 ( 7) 497 ( 8) 992

(7.) 11) 103,961 (

Process.

(5.)

(6.) 5) 7506 ( 1501 | 9) 7506 ( 10) 41,690 (

5 25

(8.)

(9.) 25

12) 113,820 ( 11 ) 57,893 (
06
5
(11.)

(12.)
1 rem. 8)38,496 ( 9) 43,281 (

(10.) 12) 74,856 (

(13.) 12) 2964 (

[blocks in formation]

12. Solve by Short Division the following: (1.)

(2.)

(3.)
6)
1698 10 ) 1980

7) 994

(4.) 8) 1984

(5.)
9)
15,012

(6.)
(7.)

(8.)
10 ) 41,690 11 ) 103,961 12)

113,820

[blocks in formation]

Pounds.

Bushels.

Rods.

360,723

? 94,000 = 8=? 760,344 - 12 = ?

:-8 11 In (24), (25), (26), are your quotients abstract or concrete ? Give the principle.

th. h.t.u. th.hut.u.

The Divisor exceeding 12, but less than 100. 1. Divide 34,028 by 13. Process.

Explanation.

34,028 34 thousands 0 hundreds 2 tens 8 13) 34,028 ( 2617 units. 34 thousands : 13 - 2 thousands, with 26

8 thousands remaining; 8 thousands + 0 hun

dreds 80 hundreds ; 80 hundreds : 13 = 6 78

hundreds, with 2 hundreds remaining; 2 hun

dreds + 2 tens - 22 tens; 22 tens • 13 = 1 22 t

ten, with 9 tens remaining; 9 tens +8 units = 13

98 units; 98 units = 13 = 7 units, with 7 units

remaining 91

2. Divide 5684 by 14. 7

3. Divide 6480 by 15.

80 h.

.

98 u.

4. Divide 2672 by 16. 5. Divide 2928 by 17. 6. Divide 4147 by 18. 7. Divide 8797 by 19. 8. Divide 6872 by 24. 9. Divide 8519 by 27. 10. Divide 9672 by 31. 11. Divide 28,490 by 15. 12. Divide 18,476 by 42.

13. 1504 ; 47 = ?
14. 5289 : 43 ?
15. 9464 ; 52 = ?
16. 5612 : 61 ?
17. 6336 ; 72 ?
18. 4557 ; 21 ?
19. 3264 ; 24 ?
20. 2664 : 37 ?
21. 3465 : 99 ?

PROBLEMS.

feet.

feet.

1. 3 feet = 1 yard. How many yards in 927 feet ? Process.

Explanation. LONG DIVISION. Since 3 feet = 1 yard, 927 feet equal as many

yards as 3 is contained times in 927. 927 = 3 3) 927 (309 309. Therefore 927 feet equal 309 yards. 9

How is the 0 in the quotient obtained ? 27

In the process, is 309 an abstract or a 27

concrete number? State the principle. 0

Is the process long or short division ? Write the process in short division and explain the steps.

2. I paid 285 cents for a railroad ticket at 3 cents a mile. How many miles did I ride?

3. If you buy 12 pounds of soap for 96 cents, how much do you pay for a pound?

4. If the circumference of a wheel is 12 inches, how many times will it revolve in moving 1728 inches ?

5. If it takes 5 bushels of wheat to make a barrel of flour, how many barrels can be made from 65,890 bushels ?

6. A merchant has 1620 yards of calico, which he wishes to cut into 15-yard patterns. How many patterns will he have ?

a

a

7. How many times must you take 7 dollars to make 567 dollars ?

8. A boat sails 1872 miles, going at the rate of 18 miles an hour. How many hours does it sail ?

9. How many sacks, each containing 55 pounds, can be filled from 2035 pounds of flour ?

10. If I divided $576 equally among some men, giving to each man $8.00, how many men were there?

11. If 4 weeks make a month, how many months are there in 264 weeks ?

12. Into how many lots of 39 acres each can a tract of land containing 6318 acres be divided ?

13. The circumference of a wheel of a bicycle is 7 feet. How many revolutions will it make in going 18,480 feet ?

14. How many sheep at $9 a head can be bought for $1377 ?

15. A man bought land at $87 an acre, paying $31,755 for it. How many acres did he buy? 16. How

many feet are there in a mile, if 42 miles contain 221,760 feet?

17. Divide four hundred eighteen thousand six hundred forty-eight by twenty-four.

18. If the post-office sends 13,125 pounds of mail-matter in bags, each holding 75 pounds, how many bags will it require ?

19. An estate worth 2943 dollars is to be divided equally among a father, mother, 3 daughters, and 4 sons. What will be the portion of each ? 20. Solve the following equation :

1728 (5280 — 1760 + 144) X

: 12

?

72 21. I bought 15 horses at $75 a head; at how much per head must I sell them to gain $210?

:

EXERCISES.

The Divisor exceeding 100.

1. Divide 145,260 by 108.

Process.

Explanation. 108 ) 145,260 ( 1345

145 thousand : 108 1 thousand, with 108

37 thousand remaining; 37 thousand + 2

hundred 372 hundred ; 372 hundred : 372

108 3 hundred, with 48 hundred remain324

ing; 48 hundred + 6 tens 486 tens ; 486 486

tens • 108 = 4 tens, with 54 tens remain432

ing; 54 tens + 0 units 540 units; 540

units : 108 : 5, with O remaining.
540
540

2. Divide :
1. 1,874,774 by 162. 6. 503,652 by 564.
2. 1,206,528 by 192. 7. 705,776 by 728.
3. 815,898 by 421. 8. 892,696 by 839.
4. 199,864 by 301. 9. 902,260 by 916.

5. 315,008 by 428. 10. 683,537 by 987. 3. Find the value of:

1. 395,630 = 750. 8. 1,056,566 – 326.
2. 683,537 - 987. 9. 10,365,051 - 3021.
3. 900,503 ; 173. 10. 2,159,450 ; 2465.
4. 456,007 ; 560. 11. 496,839,715 1047.
5. 881,881 - 700. 12. 9,325,814 - 2042.
6. 311,517 - 529, 13. 27,227,704 : 6472.

7. 237,607 ; 837. 14. 47,251,149 · 4674. 4. Find the value of:

1. 352,107,193,214 - 210,472.
2. 558,001,172,606,176,724 ; 2,708,630,425.
3. 123,456,789,102,345,678 : 1,234,567,890.
4. 987,654,321,000,000,000 = 9,876,543,210.
5. 2,016,722,783,975,663,729 - 41,927,081.

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