45. A man bought 114 acres of land for 4104 dollars,

what was the average price per acre?

Ans. 36 dollars.

46. Nine thousand dollars was paid to 75 operatives:

how much did each receive?

Ans. 120 dollars.

47. There are 24 hours in a day; how many days in 11424 hours? Ans. 476.

48. In one hogshead are 63 gallons; how many hogsheads in 6615 gallons?

Ans. 105. 49. If a man travel 48 miles a day, how long will it take him to travel 1296 miles? Ans. 27 days. 50. If a person can count 8677 in an hour, how long will it take him to count 38369694? Ans. 4422 hours. 51. If it cost 5987520 dollars to construct a railroad 576 miles long, what will be the average cost per mile?

Ans. 10395 dollars.

52. The Memphis and Charleston railroad is 287 miles in length, and cost 5572470 dollars; what was the average cost per mile? Ans. 19416.78 dollars.

287

53. A garrison consumed 1712 barrels of flour in 107 days; how much was that per day? Ans. 16 barrels.

54. How long would it take a vessel to sail from New York to China, allowing the distance to be 9072 miles, and the ship to sail 144 miles a day? Ans. 63 days.

tle;

55. How long could 27 men subsist on a stock of provision, that would last I man 3456 days? Ans. 128 days. 56. A drover received 10362 dollars, for 314 head of cathow much was their average value per head? Ans. 33 dollars. 57. If 42864 pounds of cotton be packed in 94 bales, what is the average weight of each bale? Ans. 456 pounds. 58. If a field containing 42 acres produce 1659 bushels of wheat, what will be the number of bushels ?

per acre Ans. 392 bushels.

59. In what time will a reservoir containing 109440 gallons, be emptied by a pump discharging 608 gallons per Ans. 180 hours.

hour?

CONTRACTIONS.

CASE I.

72. When the divisor is 10, 100, 1000, &c.

1. Divide 374 by 10.

OPERATION.

1|0)37|4

Quotient, 37---4 Rem. or, 37, Ans.

ANALYSIS. Since we have shown, that to remove a figure one place toward the left by annexing a cipher increases its value tenfold, or multiplies it by 10, so, on the contrary, by cutting off or taking away the right hand figure of a number, each of the other figures is removed one place toward the right, and, consequently, the value of each is diminished tenfold, or divided by 10.

For similar reasons, if we cut off two figures, we divide by 100, if three, we divide by 1000, and so on. Hence the

RULE. From the right hand of the dividend cut off as many figures as there are ciphers in the divisor. Under the figures so cut off, place the divisor, and the whole will form the quotient.

6. Divide 9021300640 by 100000. 90213 640.

7. A man sold 100 acres of land for 3725 dollars; how much did he receive an acre? Ans. 37 dollars.

8. Bought 1000 barrels of flour for 6080 dollars; how much did it cost me a barrel? Ans. 67880 dollars.

9. Paid 12560 dollars for 10000 bushels of wheat; how much was the cost per bushel? Ans. 125 dollars.

CASE III.–

73. When there are ciphers on the right hand

of the divisor.

1. Divide 437661 by 800.

OPERATION.

800)437661

547---61 Rem.

ANALYSIS. In this example we resolve 800 into the factors 8 and 100, and divide first by 100, by cutting off two right hand figures of the

dividend, and we have a quotient of 4376, and a remainder of 61. We next divide by 8, and obtain 547 for a quotient; and the entire quotient is 547.

2. Divide 34716 by 900.

OPERATION.

9:00)347|16

ANALYSIS. Dividing as in the last example, we have a quotient of 38, and a remainder of 5 after dividing Quotient, 38--516 Rem. by 9, which we prefix to the figures or, 3818, Ans. cut off from the dividend, making a true remainder of 516, and the entire quotient 88518. Hence RULE. I. Cut off the ciphers from the right of the divisor, and the same number of figures from the right of the dividend.

900

II. Divide the remaining figures of the dividend by the remaining figures of the divisior, and the result will be the quotient. If there be a remainder after this division, prefix it to the figures cut off from the dividend, and this will form the true remainder.

175

EXAMPLES IN THE PRECEDING RULES.

1. A speculator bought at different times 320 acres, acres, 87 acres, and 32 acres of land, and afterward sold 467 acres; how many acres had he left? Ans. 147 acres.

2. Two men travel in opposite directions; one travels 31 miles a day, the other 43 miles a day; how far apart will they be in 12 days? Ans. 888 miles.

3. A tobacconist has 6324 pounds of tobacco, which he wishes to pack in boxes containing 62 pounds each; how many boxes must he procure to contain it? Ans. 102.

4. A farmer sold 15 tons of hay at 9 dollars a ton, and 25 cords of wood at 4 dollars a cord, and wished to divide the amount equally among 5 creditors; how much would each receive? Ans. 47 dollars.

5. If you deposit 216 cents each week in a savings bank, and take out 89 cents a week, how many cents will you have in bank at the end of 36 weeks? Ans. 4572 cents.

6. The product of two numbers is 8928, and one of the numbers is 72; what is the other number? Ans. 124. 7. The dividend is 7280, and the quotient is 208; what is the divisor? Ans. 35. 8. What is the remainder after dividing 876437 by 16900 ? Ans. 14537. 9. A man sold 6 horses at 125 dollars each, 25 head of cattle at 30 dollars each, and with the proceeds bought land at 25 dollars an acre; how many acres did he buy? Ans. 60 acres.