9. In a mile there are 5280 feet. How many feet are there in 500 miles?

10. In an acre there are 160 square rods. How many square rods are there in a farm of 300 acres?

11. A farmer sold a flock of 260 sheep at $3.20 per head. How much did he get for them?

12. A drover sold 1120 hogs at an average price of $16.30 per head. How much did he receive for them?

EXAMPLES.

81. 1. What will be the cost of 896 chests of tea, each chest containing 58 pounds, at 63 cents a pound?

2. An agent sold 3923 Lyman's Historical Charts at $3.50 each. How much did he receive for them?

3. I have 6 bins that hold 119 bushels each. They are full of grain and I have already sold 515 bushels. It was all raised on my farm this year. How much grain was raised?

4. A. J. Newton & Co. bought 113 cases of calico, each case containing 64 pieces, and each piece 47 yards. How many yards did they buy?

5. A drover bought 25 oxen at $85 a head; 316 sheep at $4.50 a head, and 94 calves at $8 a head. What was the whole amount paid?

6. A man insured 2 houses valued at $3750 and $4650, respectively, at the rate of $2 per hundred dollars. How much did the insurance cost him?

7. If I have 219 acres of land, and each acre produces 47 bushels of corn, how many bushels do I receive?

8. How many quills can be obtained from 398 geese, if each wing furnishes 6 quills?

9. A grocer sold in one month 81 dozen eggs at 26 cents per dozen; in the next, 53 dozen at 28 cents per dozen. How much money did he receive for the eggs?

10. It requires 1716 pickets to fence one side of a square lot. How many pickets will be required to fence 13 lots of the same size and shape?

11. A sold 13 firkins of butter, each firkin containing 56 pounds, at $.34 a pound. How much did he receive for it?

12. A coal dealer bought 13 car loads of coal, each load containing 10 tons, at $6.85 a ton. He retailed 48 tons of this at $7 per ton, 28 tons at $8.25 per ton, 27 tons at $8.75 per ton, and the remainder at $9.50 per ton. How much did he make by the transaction?

13. An army lost in battle 315 killed, 417 wounded; the enemy lost in killed and wounded, together, 13 times as many. How many soldiers were killed and wounded in this battle?

14. If two steamers should leave New York at the same time, and should sail in the same direction, the first at the rate of 18 miles an hour, the second at the rate of 15 miles an hour, how far apart would they be in 36 hours?

15. Mr. Hudson bought 350 bushels of corn at 65 cents a bushel, 215 bushels of wheat at $1.35 per bushel, and 273 bushels of oats at 43 cents a bushel. What did the whole cost him?

16. Mr. Henderson sold a farm of 325 acres at $65.50 per acre, and received in payment 345 sheep at $3.25 per head, a note for $2684.95 and the rest in cash. How much cash did he receive?

17. A cloth merchant sold two lots of cassimeres, the first containing 17 pieces of 28 yards each, at $1.75 per yard, the second containing 23 pieces averaging 29 yards each, at $1.85 per yard. What was the value of the whole?

18. An excursion train composed of 13 passenger coaches, each containing 37 persons, went from Syracuse to Niagara Falls and back. If the fare to Niagara Falls and return to Syracuse, was $3.25 per ticket, how much did the railroad company receive?

INDUCTIVE EXERCISES.

82. 1. How many groups of 2 birds each can be formed from 6 birds? How many 2's are there in 6?

2. How many groups of 3 sheep each can be formed from 9 sheep? How many 3's are there in 9?

3. How many groups of 2 chickens each can be formed from 10 chickens? How many 2's are there in 10?

4. At 5 cents apiece, how many pencils can be bought for 10 cents? How many 5's are there in 10?

5. When milk is worth 7 cents a quart, how many quarts can be bought for 28 cents? How many 7's are there in 28?

6. There are 20 panes of glass in the front of a block of stores. If each window contains 4 panes, how many windows are there? How many 4's are there in 20?

7. At 8 cents a dozen, how many peaches can be bought for 24 cents? How many times 8 cents are 24 cents? How many 8's are there in 24?

8. How many groups of 4 things each can be formed from 16 things? How many 4's are there in 16?

9. A merchant had 30 yards of calico which he cut into pieces 5 yards long. How many pieces did it make? How many 5's are there in 30? How many times is 5 contained in 30?

10. How many 9's are there in 18? How many times is 9 contained in 18?

11. How many 5's are there in 10? In 15? In 20? In 25? In 30?

12. If 15 cents are divided equally among 3 boys, how many cents will each receive? When 15 cents are divided into 3 equal parts, how many cents will each part contain?

13. If 12 peaches are arranged in 3 rows, how many will there be in each row?

14. What is one of the 4 equal parts of 8? Of 12? Of 16? 15. How many 3's are there in 30? How many are 10 threes, or 10 times 3?

16. How many 4's are there in 40? How many times is 4 contained in 40? How many are 10 fours?

DEFINITIONS.

83. Division is the process of finding how many times one number is contained in another; or,

The process of separating a number into equal parts.

84. The Dividend is the number to be divided.

85. The Divisor is the number by which we divide. It shows into how many equal parts the dividend is to be divided.

86. The Quotient is the result obtained by division. It shows how many times the divisor is contained in the dividend.

87. The part of the dividend remaining when the division is not exact is called the Remainder.

88. The Sign of Division is. It is read divided by. When placed between two numbers it shows that the one at the left is to be divided by the one at the right.

Thus, 1547, is read 154 divided by 7.

Division is also indicated by placing the dividend above. the divisor with a line between them, and by writing the divisor at the left of the dividend with a curved line between them. Thus, 154 divided by 7, may also be written 154, and 154.

89. PRINCIPLES.-1. The dividend and divisor must be like numbers.

2. The quotient must be an abstract number.

3. The product of the divisor by the quotient, plus the remainder, is equal to the dividend.

9

3

6

3

3

3

1. In problems where it is required to separate a number into equal parts, it is customary to regard the dividend and quotient as like numbers, and the divisor as an abstract number.

2. The example "How many 3's are there in 9" may be solved, as in the margin, by subtraction. All examples in division may be solved in the same manner. Hence, division may

be regarded as a short method of subtracting equal numbers.

3. In multiplication two numbers are given to find their product. In division the product is given and one of the factors to find the other. Hence, division is the converse of multiplication.

CASE I.

90. When the divisor is expressed by one figure.

1. At $8 each, how many plows can be bought for $24? ANALYSIS. Since each plow costs $8, as many plows can be bought for $24 as $8 is contained times in $24, which is 3 times. Therefore 3 plows can be bought for $24.

2. If a man can earn $7 in a day, how long will it take him to earn $28?

3. At $4 each, how many hats can be bought for $24? 4. When flour is selling at $6 a hundred-weight, how many hundred-weight can be bought for $36?