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?

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 cach 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, 154 ÷ 7, 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 7)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?

5. If a mason built 3 rods of walk per day, how long did it take him to build 21 rods?

6. B paid 96 cents for glass at 8 cents a pane. How many panes did he buy?

7. At $9 a cord, how many cords of wood can be bought for $45?

8. If a man earns $11 a week, how many weeks will he require to earn $66?

9. How many lots of 11 acres each can be made from a farm containing 132 acres?

10. If a farmer exchanges 6 firkins of butter worth $20 a firkin for cloth at $4 a yard, how many yards will he receive? 11. My coal cost me $35 at the rate of $7 a ton. many tons did I purchase?

How

12. How many engravings must an artist sell for $12 apiece to realize $84?

13. When sugar is worth 9 cents a pound, how many pounds can be bought for 45 cents?

14. At the rate of $7 a rod, how many rods of fence can be built for $63?

15. I hired a man for $45 to do a piece of work at the rate of $5 a day. How many days did it take him?

16. A lady bought some silk worth $3 a yard, paying $36 for it. How many yards did she buy?

17. How many barrels of flour at $8 a barrel can be bought for $48?

18. How many pounds of nails can be bought for 75 cents at the rate of 4 pounds for 20 cents?

19. I bought 6 sheep for $30.

head?

How much did I pay per

20. At $5 per head, how many head of sheep can be bought for $37? Ans. 7 sheep and $2 left. 21. A man whose wages were $4 a day earned in a certain time $33. How many days did he work?

Ans. 8 days.