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10. If a boy earns 11 cents an hour, how long will it take him to earn 55 cents? 66 cents? - 88 cents ?

11. There are 20 hundred-weight in a ton. How many tons are there in 45 hundred-weight? How many in 55?

12. In one day there are 24 hours. How many days are there in 50 hours? In 60 hours? In 72 hours?

13. 12 articles make a dozen. How many dozen are there in 39 articles? In 48? In 51? In 60? In 65?

14. A farm of 60 acres was divided into 15 equal lots. How many acres were there in each lot?

15. At 18 cents a dozen, how many dozen of eggs can be bought for 36 cents? For 40 cents? For 54 cents ?

16. When butter is 30 cents a pound, how many pounds can be bought for 90 cents? For $1.20? For $1.50?

17. How many 20's are there in 40? In 50? In 60? 18. How

many

25's are there in 50? In 60? In 75? 19. By selling brooms at 25 cents each, I received $1.25. How many

brooms did I sell? 20. In 100 how many 10's are there?. How many 11's ? 12's? 13's? 15's? 16's? 20's? 23's? 25's?

WRITTEN

EXERCISES.

97. 1. Divide 7975 by 26.

PROCESS.

ANALYSIS.—26 is not contained in 7 Divisor. Dividend. Quotient.

thousands any thousands times; hence · 26)7975 (30648

we unite the thousands with the hun78

dreds, making 79 hundreds. 26 is con

tained in 79 hundreds 3 hundred times 175

and a remainder. We write the 3 hun156

dreds in the quotient and multiply the 19

divisor by it, obtaining for a product 78

hundreds, or 7 thousands and 8 hundreds, which we write under units of the same order in the dividend. Subtracting, there is a remainder of 1 hundred.

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We unite the 1 hundred with the 7 tens, making 17 tens. 26 is not contained in 17 tens any tens times; therefore there are no tens in the quotient, and we write a cipher there.

We unite the 17 tens with the 5 units, making 175 units. 26 is contained in 175 units 6 times and a remainder. We write the 6 in units' place in the quotient and multiply the divisor by it, obtaining for a product 156 units, or 1 hundred, 5 tens, and 6 units, which we write under units of same order in the partial dividend. Subtracting, there is a remainder of 19. We write the remainder over the divisor as a part of the quotient.

Hence the quotient is 306.18.
PROOF.—306 X 26 +19=7975. Hence the work is correct. (Prin. 3.)

98. When the steps in the solution of an example in division are written, the process is called Long Division.

RULE.— Write the divisor at the left of the dividend with a curved line between them.

Find how many times the divisor is contained in the fewest figures on the left hand of the dividend that will contain it, and write the quotient on the right.

Multiply the divisor by this quotient and place the product under the figures divided. Subtract the result from the partial dividend used, and to the remainder annex the next figure of the dividend.

Divide as before until all the figures of the dividend have been annexed to the remainder.

If any partial dividend will not contain the divisor, write a cipher in the quotient, then annex the next figure of the dividend and proceed as before.

If there is a remainder after the last division write it after the quotient, or with the divisor under it as part of the quotient.

PROOF.— Multiply the divisor by the quotient, and to the product add the remainder, if any. If the work is correct, the result will equal the dividend.

1. To find the quotient figure, see how many times the first figure of the divisor is contained in first figures of the partial dividend that will 6:01

tain it, making allowance for the addition of the tens from the product of the second figure of the divisor.

2. If the product of the divisor by the quotient figure be greater than the partial dividend from which it is to be subtracted, the quotient figure is too large.

3. Each remainder must be less than the divisor; otherwise the quotient figure is too small.

EXAMPLES

32.

4. When there is no remainder the divisor is said to be exact.

99. Divide:

2. 1240 by 10. 3. 3443 by 11. 4. 2592 by 12. 5. 3978 by 13. 6. 5684 by 14. 7. 6480 by 15. 8. 8736 by 21. 9. 1472 by 32. 10. 9672 by 31. 11. 9724 by 22. 12. 2952 by 72. 13. 1188 by 54. 14. 4235 by 55. 15. 5356 by 52. 16. 8733 by 41. 17. 9639 by 81. 18. 7991 by 61. 19.2508 by 22. 20. 7332 by 52. 21. 4824 by 72. 22. 16665 by 33. 23. 13545 by 43. 24. 25578 by 63.

Divide:

25. 12456 by 24.
26. 28350 by 54.
27. 50854 by 94.
28. 58176 by 96.
29. 56394 by 78.
30. 54914 by 101,
31. 90992 by 121.

199864 by 301.
33. 475524 by 612.
34. 1445204 by 802.
35. 1760225 by 905.
36. 3156584 by 722.
37. 5173302 by 834.
38. 5926431 by 643.
39. 3214664 by 566.
40.

6923471 by 555. 41. 14293624 by 675. 42. 56243121 by 686. 43. 692348726 by 897. 44. 496839715 by 1047. 45. 786935846 by 3118. 46. 1234589640 by 96813. 47. 31964875932 by 37425.

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

49. Wm. Wallace has 17 horses, the aggregate value of which is $4386. What is the average worth of each horse?

50. A surveyor traveled 4160Q rods in one week. How many miles did he travel, there being 320 rods in a mile?

51. How many eggs at $.38 per dozen can be bought for $6.84?

52. In 24 hours the earth moves 1575000 miles. How far does it move in one minute, 60 minutes making an hour?

53. Mount Everest in Asia is 29100 feet high. There are 5280 feet in a mile. How many miles high is it?

54. It required 4375480 bricks to build an orphan asylum. How many days did it require 5 teams to draw the bricks, if they drew 5 loads per day and 1250 bricks at a load?

55. The earth is 91500000 miles from the sun. How many seconds does it take light to come from the sun to the earth, if it travels 185000 miles per second ?

56. A man bought a farm of 278 acres at $63 an acre. He paid $1275 down and agreed to pay the rest in 8 equal annual payments. How much was he required to pay yearly?

57. The earnings of a certain railroad were $3681452 during the year. The number of days in a year is 365. What was the average income per day?

58. How many feet are there in a mile, if 42 miles contain 221760 feet?

59. If the average wages of a laboring man are $500 per year,

how many men will it require to earn $50000 per year, the salary of the President?

60. The area of the State of North Carolina is 50704 square miles, and the population, according to the census of 1870, was 1071400. How many persons, on an average, were there living on a square mile?

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CASE III.

100. When the divisor has ciphers on the right.

1. How

many

10's and what remainder in 46? 84? 97? 2. When a number is divided by 10, what part is remainder? What part is quotient?

3. How many hundreds, and what remainder in 434? 516? 639? 758?

4. When a number is divided by 100 what part of it is remainder? What part is quotient?

5. When a number is divided by 1000, what part is remainder? What part is quotient?

101. PRINCIPLE.— In dividing by 10, 100, 1000, etc., the remainder will be as many of the figures at the right of the dividend as there are ciphers on the right of the divisor. The rest of the number is quotient. 102. 1. Divide 6374 by 1000.

ANALYSIS.—Since the divisor contains no 11000) 61374

order of units lower than thousands, in dividing we may omit or cut off from the dividend for a remainder, all orders of units lower

than thousands. (Prin.) Dividing 6 thousands by 1 thousand we obtain 6 for the quotient and 374 for the remainder; or 637. 2. Divide 39321 by 6000.

ANALYSIS.—Since the divisor con

tains no order of units lower than 61000) 391321

thousands, in dividing we may omit 6 Rem. 3000

or cut off from the dividend all or321 ders of units lower than thousands.

6 thousands are contained in 39 Entire remainder 3321

thousands 6 times and 3 thousand remainder. 3 thousand plus the other partial remainder equals the entire remainder. Hence the quotient is 6383).

PROCESS.

6 374

1000

PROCESS,

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