26. A farmer having $3264, paid $3 a head for 536 sheep, and $27 a head for 26 cows. How much money had he left? 27. Bought 84 hogs, each weighing 386 lb., at 9 cts. a pound, and sold the same at 12 cts. a pound. What was gained?

28. What is the difference in the cost of 48 horses at $184 each, and 130 sheep at $5 a head?

29 A man bought 350 head of cattle at $30 a head, and 450 sheep at $5 a head. He sold the whole for $13000. he gain or lose, and how much?

30. If a steamer sail 265

in 16 days? In 18 days? 31. A man bought 136

sold the whole for $1248.

Did

miles a day, how far will she sail In 24 days?

barrels of flour at $8 a barrel, and What was his gain?

32. Find the cost of the following articles: 25 pounds of sugar, at 12 cents a pound; 16 pounds of tea, at 75 cents a pound; and 38 pounds of ham, at 14 cents a pound.

33. A man earns $9 a week, and his son $5. What will both earn in 3 weeks? In 5 weeks?

34. If a clerk earn a salary of $950 a year, and his expenses are $525 a year, how much can he save in 6 years?

35. A man bought a farm containing 175 acres, at $24 an What did the farm cost him?

acre.

36. A farmer sold 15 tons of hay at $18 a ton, and 36 cords of wood at $4 a cord. What was the value of both ?

37. Bought 13 yards of cloth, at $3 a yard; 6 cords of wood at $5 a cord; and 3 tons of coal, at $9 a ton; gave in payment 2 twenty-dollar bills, 5 ten-dollar bills, and a two-dollar bill. How much more ought I to pay?

38. There are 36 tubs of butter, each weighing 108 pounds, and the tubs which contain the butter each weigh 19 pounds. What is the weight of the butter without the tubs?

DIVISION.

INDUCTIVE EXERCISES.

40. 1. How many dollars are $12 less $6, less $6?

$12 $4 $4 $4? $12

$3

$3

$3

2. How many times can $6 be taken from $12?

$12 $3 from $12? $2 from $12 ?

$3? $4 from

2's?

3. How many 6's in 12? How many 4's? 3's? 4. What is of $12? of $12? of $12 ? of $12 ? 5. How many times can 4 pounds of honey be taken from a box containing 20 pounds? How many 4's in 20? 4 in 20, how many times? 20÷4=?

6. If 6 men earn $24, what part of $24 does 1 man earn? How many dollars?

7. At 9 cents a quart, how many quarts of milk can be bought for 63 cents?

8. When the divisor and dividend are of the same name or kind, what do we do? Ans. Find how many times the dividend contains the divisor.

9. What is the quotient?

Ans. Times.

10. When the divisor and dividend are not of the same name or kind, what do we do?

Ans. Find a certain part of the dividend. 11. What is the quotient? Ans. A part of the dividend. 12. How many yards of cloth, at $7 a yard, can be bought for $70? For $63? For $84?

13. If you divide 84 cents among 7 children, what part of the whole do you give to each? How many cents?

The teacher should make plain the two forms of division, and require the proper solution for each kind of example.

ORAL AND SLATE

EXERCISES.

41. 1. When lemons are 4 cents each, how many can be bought for 48 cents?

No. of lemons bought.

WRITTEN SOLUTION. 48 cts. 4 cts. = ORAL SOLUTION. As many lemons as 4 cents are contained times in 48 cents, which are 12 times, or 12 lemons.

2. If a man travel 6 miles an hour, how long will it take him to travel 54 miles?

3. How many kegs containing 9 gallons each can be filled. from a hogshead containing 63 gallons ?

4. If a man drive 8 miles an hour, in what time will he drive 56 miles ?

5. A farmer bought some sheep for $60, paying $5 a head. How many sheep did he buy?

6. At $9 a week, in what time will a man earn $36? $54 ? $72 ? $81 ? $108?

7. If 7 barrels of flour cost $63, what is the cost of 1 bbl. ?

WRITTEN SOLUTION.

ORAL SOLUTION.

$63, or $9.

$63
7

or of $63 = cost of 1 barrel.

Since 7 barrels cost $63, 1 barrel costs 1 seventh of

8. If 9 tons of coal cost $72, what is the cost of 1 ton?

9. If a man travel 48 miles in 4 hours, how far does he travel in 1 hour?

10. What is the cost of 1 ton of hay, if 8 tons cost $64 ? 11. If you divide 90 cents equally among 9 children, what part of the whole do you give to each? How many cents?

12. If a man can build 72 rods of fence in 8 days, how many rods can he build in 1 day?

13. If 9 doz. eggs cost 108 cents, what is the cost of 1 dozen?

14. Divide and prove, reading rapidly, thus, 4 in 24 six

15. And the following, thus: 1 sixth of 72 is 12; 12 times

In proving division, multiply the divisor by the quotient, not the quo tient by the divisor.

16. What is 1 half of 12? Of 16? Of (18+6)?

*These examples may be expressed on the slate or paper in the form

WRITTEN EXERCISES.

42. 1. Divide 447 by 3.

Divisor. Dividend. Quotient.

3) 447 (149

3

14

12

27

27

In this example, write the divisor at the left, and the quotient at the right of the dividend, and begin at the left to divide, thus: 3 is contained in 4, 1 time and a remainder; write 1 for the first figure of the quotient and multiply the divisor 3 by it, and subtract the product 3 from 4 hundreds, and the remainder is 1 hundred, equal to 10 tens, to which add the 4 tens of the dividend, making 14 tens, expressed by bringing down the 4 to the right of the 1 hundred. Then 3 is contained in 14, 4 times and a remainder. multiply the divisor by it, and subtract the remainder is 2 tens or 20 units, to which add the 7 units of the dividend making 27. 3 is contained in 27, 9 times. Multiplying and subtracting as before, nothing remains. PROOF: 149 × 3 = 447.

0

Write the 4 in the quotient, product 12 from 14, and the

The work may be shortened very much by what is termed Short Division, as follows:

3 is contained in 4, once and 1 remainder; 1 prefixed or placed before 4, makes 14; 3 in 14, 4 times and 2 remainder; 2 prefixed to 7 makes 27; 3 in 27, 9 times. Hence the quotient is 149.

3) 447

149