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27. Copy, complete, and recite the following:

9)8973 9)5346 9)4374 9)6102 9)7101 9)3547

997

594

394-1

MODEL FOR RECITATION.

(1) PROBLEM.-How many times are 9 contained in 8973?

(2) DIVISION.-9 in 89, 9 times and 8 over (hundreds); 9 in 87, 9 times and 6 over (tens); 9 in 63, 7 times (units). (3) RESULT.-Hence, 9 in 8973, 997 times.

(4) THE TERMS.-The dividend, or number to be divided, is 8973; the divisor is 9; the quotient, or number which shows how many times the divisor is contained in the dividend, is 997.

28. Divide 2520 by each of the nine digits. 29. Divide 5040 by each of the nine digits. 30. Divide 7560 by each of the nine digits. 31. Divide 10080 by each of the nine digits. 32. Divide 12600 by each of the nine digits. 33. Divide 15120 by each of the nine digits. 34. Divide 17640 by each of the nine digits. 35. Divide 20160 by each of the nine digits. 36. Divide 22680 by each of the nine digits. Find the value of the following expressions (34, ex. 32):

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61. There are 1095 days in 3 years. How many

days in a year?

62. A farm produced 1450 bushels of potatoes in 5 What was the average per year?

years.

63. In 92304 quarts how many gallons? 2316 quarts? 144 quarts? 36224 quarts? 20304 quarts? 4936 quarts? 64. In 61401 feet how many yards? 15840 feet? 9078 feet? 528 feet? 69 feet? 24 feet?

65. In 864197523 days how many weeks? 149007 days? 35049 days? 952 days? 189 days? 63 days?

66. In 1000608 quarts how many pecks? 32400 quarts? 1096 quarts? 200 quarts? 56 quarts?

LONG DIVISION.

41. To divide any number by any other number.

EXAMPLES.

1. Copy upon your slates and recite the following:

12)1476(123

13)11882(914

67)375803(5609

12

117

335

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RECITATION.

(1) PROBLEM.-What is the quotient of 1476 divided by 12?

(2) DIVISION.-12 in 14, once and 2 over (hundreds); 12 in 27, 2 times and 3 over (tens); 12 in 36, 3 times (units).

(3) RESULT.-Hence, the quotient is 123.

RULE.

(1.) Find how many times the whole divisor is containeȧ in the same number of figures on the left of the dividend considered as representing so many units; or, if this num ber is smaller than the divisor, find how many times the divisor is contained in a number of figures of the dividend greater by one than the number of figures in itself, and place the quotient on the right of the dividend.

(2.) Multiply the whole divisor by this quotient figure, and place the product under the figures of the dividend just compared with the divisor.

(3.) Subtract the product from the figures above it. (4.) To the right of the difference bring down the next figure of the dividend.

(5.) If the new dividend is now smaller than the divisor, place a cipher in the quotient, and bring down the next figure of the dividend; but if the dividend is equal to or larger than the divisor, proceed in obtaining the second figure of the quotient as with the first, and so on till all the figures are brought down.

REMARK 1.-Notice that no product can be greater than the figures of the dividend above it.

REMARK 2.-Notice that no difference can be equal to or greater than the divisor.

2. Divide 1488; 2808; 4140; 5472; 6804 by 12. 3. Divide 1599; 4042; 4485; 5928; 7371 by 13. 4. Divide 1722; 3276; 4830; 6384; 7938 by 14. 5. Divide 2010; 2175; 2340; 2505; 2715 by 15. 6. Divide 14576; 12976; 11376; 9776; 8176 by 16. 7. Divide 1887; 3774; 5661; 7548; 9435 by 17. 2. Divide 9990; 11988; 13986; 15984; 17982 by 18. 9. Divide 2357; 2508; 4047; 4389; 6099 by 19. 10. Divide 9639 by 7; 17; 21; 27; 51; 81.

11. Divide 24024 by 8; 11; 13; 22; 32; 52. 12. Divide 7161 by 3; 21; 31; 33; 63; 93. 13. Copy and recite the following exercises:

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(1) PROBLEM.-What is the quotient of 146795 divided by 935?

(2) DIVISION.-935 in 1467, once and 532 over (thousands); 935 in 5329, 5 times and 654 over (tens); 935. in 6545, 7 times (units).

(3) RESULT.-Hence, the quotient is 157.

14. Divide 15375; 27675; 39975; 52275 by 123. 15. Divide 29151; 52851; 76551; 100251 by 237. 16. Divide 76986; 109886; 142786; 175686 by 329. 17. Divide 168861; 216161; 263461; 310761 by 473. 18. Divide 198128; 295728; 393328; 490928 by 976. 19. Divide 232274; 302874; 373474; 444074 by 706. 20. Divide 161789; 192489; 223189; 253889 by 307. 21. Copy upon your slates and recite the following

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(1) PROBLEM.

in 4791?

RECITATION.

-How many times are 11 contained

(2) DIVISION.-11 in 47, 4 times and 3 over (hundreds); 11 in 39, 3 times and 6 over (tens); 11 in 61, 5 times and 6 over (units).

(3) RESULT.-Hence, 11 in 4791, 435 times and 6

REMAINDER.

Find the value of each of the following expressions:

22. 132652÷51. Rem. 1.

23. 140610÷52. Rem. 2.

24. 148880-53. Rem. 3.
25. 592710÷84. Rem. 6.
26. 357920-71. Rem. 9.
27. 912680-97. Rem. 7.

28. 132652-2601.

29. 140610÷÷2704. 30. 148880-2809. 31. 592710÷7056. 32. 357920-5041. 33. 912680-9409.

REMARK 3.—If there are ciphers on the right of the divisor, they may be neglected in the operation, together with a like number of figures on the right of the dividend.

34. Copy and recite the following exercises:

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9'0000)8100'0000 900

RECITATION.

(1) PROBLEM.-How many times are 500 contained in 126164?

(2) DIVISION.-5 in 12, 2 times and 2 over; 5 in 26, 5 times and 1 over; 5 in 11, 2 times and 1 over.

(3) RESULT.-Hence, 500 in 126164, 252 times, with a remainder of 164.

35. Divide 123456789 by 10; 100; 1000; 10000; 100000; 1000000. Last Ans. 123, with 456789 rem. 36. Divide 240000000 by 20; 200; 2000; 20000; 200000; 2000000. Last Ans. 120.

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