5. At $5 a yard, how many yards of broadcloth can be bought for $355?

6. A man has 246 quarts of milk, and wishes to put it into 6-quart cans; how many cans must he use?

7. If a person saves $4 in a week, in how many weeks can he save $328?

Ill. Ex. IV. Divide 615 by 3.

Operation. 3)615

205

units by 3.

In this example, after dividing the 6 (hundreds) by 3, we have 1 ten to divide; as in 1 ten there are no tens of 3's, we put 0 in the tens' place of the quotient, and divide 15

8. If 8 gills make 1 quart, how many quarts are there in 832 gills?

Ill. Ex. V. In 1 week there are 7 days; how many weeks are there in 365 days?

Operation. 7) 365

52.1

Here 36 (tens) divided by 7, leaves a remainder of 1 (ten), which, with the 5 units, equals 15 units; again, 15 units divided by 7, leaves a remainder of 1; therefore, in 365 days there are 52 weeks

and 1 day remaining.

Proof. Multiply the quotient by the divisor, and to the product add the remainder; the sum should equal the div. idend.

17. How many pounds of sugar at 8 cents a pound can

be bought for 196 cents? for 248 cents?

18. How many tons of coal at $9 a ton can be bought for $828? for $593?

20. It is sometimes necessary to find one of the equal parts of a given number; this process is also called Division, and is performed in the same manner as that taught above; thus, to find one half of a number, we divide by 2; to find one third of a number, we divide by 3; to find one fourth, we divide by 4; to find one fifth, we divide by 5; to find pne tenth, we divide by 10, etc.

1. What is one half of 18? of 22? of 24?

Ill. Ex. VI.

Operation. 2) 64

32

What is one half of 64?

64 equals 6 tens and 4 units; one half of 6 tens is 3 tens, and one half of 4 units is 2 units; therefore, one half of 64 is 32.

2. What is one half of 34? of 82? of 106?
3. What is one third of 18? of 183? of 981?
4. What is one fourth of 64? of 144? of 232?
5. What is one fifth of 55? of 505? of 1,035?
6. What is one sixth of 72? of 96? of 6,738?
7. What is one seventh of 28?
8. What is one eighth of 88?
9. What is one ninth of 63? of 234? of 7,263?

of 91? of 7,546? of 864?

of 2,952?

10. If 3 coats cost $135, what will 1 coat cost?

11. If 5 shares of railroad stock cost $505, what will 1 slare cost?

12. If 6 cows cost $234, what will 1 cow cost?

13. How many eggs must I put into each of 5 baskets that I may put 480 eggs in all?

14. If a man earns $128 in 4 weeks, how much does he earn in 1 week?

15. There are 168 hours in one week; how many hours are there in one day?

16. If 1 man can do a piece of work in 186 hours, in how many hours can 6 men do it?

17. How many Sundays are there in 728 days?

18. If $117 is paid for 9 weeks' board, what must be paid for 1 week's board?

19. A man divided $15,000 equally among his children, 5 sous and i daughter; what was the share of each?

21. LONG DIVISION.

NOTE. In the preceding articles, division has been performed mostly in the mind, results only being expressed. When the divisor is a large number, it is generally more convenient to have the work expressed in full; the process is then called Long Division.

Ill. Ex. VII. Divide 5,682 by 13.

Hunds.

coTens.

Units.

Operation. 13) 5682 (437 5 2 hund.

48 tens.

39 tens.

In 56 (hundreds), there are 4 (hundred) 13's. We write a figure 4 for the first figure of the quotient; 4 (hundred) 13's equal 52 (hundred), which taken out of 56 (hundred), leaves 4 (hundred). Uniting the remainder with the next term of the dividend, we have 48 (tens), in 48 (tens), there are 3 (tens) of 13's; we write 3 for the second figure of the quotient; 3 (tens) of 13's equals 39 (tens), which taken out of 48 (tens), leaves 9 (tens). Uniting the remainder with the next term of the dividend, we have 92 units; in 92 units there are seven 13's, and 1 remains; therefore, etc.

92 units.

91 units.

1 rem.

Ill. Ex. VIII. Divide 4,327 by 14.
Operation.

14) 43 27 (309
42

127

126

1

Whenever the divisor is not contained in any partial dividend, put a zero in the expression for the quotient, bring down the next figure of the dividend, and divide.

1. Divide 3,680 by 13; by 14; by 15.
2. Divide 1,006 by 14; by 16; by 18.
3. Divide 3,060 by 21; by 32; by 153.
4. Divide 8,164 by 73; by 36; by 232.
5. Divide 180,000 by 54; by 82; by 176.
6. Divide 123, 456 by 98; by 76; by 543.

Ill. Ex. IX. Divide 485 by 100. 100) 485

Ans. 4.

85 rem.

Whenever the divisor is a unit of any order, as 10, 100, 1,000, etc., we can express the

quotient by cutting off as many of the right hand figures of the expression for dividend as the expression for divisor has zeros. The figures which are not cut off denote the quotient, and the figures cut off denote the remainder.

7. Divide 1,850 by 10; by 100; by 1,000. 8. Divide 45,867 by 10; by 100; by 1,000. 9. Divide 8,560 by 1,000; by 100; by 10.

Ill. Ex. X. Divide 748 by 30. 30) 748

Ans. 24 28 rem.

Whenever the expression of the divisor has zeros at the right, cut them off, also cut off as many figures at the right of the expression of the dividend, and then divide. If there be a remainder after this division, at the right of the expression of the remainder, express the undivided part of the dividend; the true remainder will be thus expressed.

10. Divide 543 by 80; 3,654 by 240.

11. Divide 37,806 by 2,500; 59,004 by 3,000.

12. If 27 acres of land cost $945, what will 1 acre cost? 13. A farmer had 576 eggs to pack in baskets which held 48 eggs each; how many baskets did it require?

14. From Albany to Boston is 200 miles; how many hours would it take a locomotive to go that distance, at the rate of 40 miles an hour?

15. How many pieces of cloth are there in 535 yards, if there are 43 yards in each piece?

16. A barrel of flour contains 196 pounds; how many barrels can be filled from 5,836 pounds?

17. If in one hogshead there are 63 gallons, how many hogsheads are there in 81,045 gallons?

18. If a man saves $3 in 1 week, how many weeks will it take him to save $1,575? How many years will it take?

MISCELLANEOUS EXAMPLES.

22. 1. A man left $366,000 to his wife and 3 children: his wife was to have 1 half, and his children were to share the remainder equally; what was the share of each?

2. A man whose salary was $1,300, found at the end of the year that his expenses had been as follows: for gro ceries, $216; for milk, $18; meat, $83; wood, $13; coal, $89; clothing, $290; hired help, $156; medical service, $55; house rent, $225; taxes, $27; repairs and incidental expenses, $95; charity, $19. How much did he save during the year?

3. The product of two numbers is 3,705, one of the numbers is 57; what is the other number?

4. If the dividend is 1,312, and the divisor is 82, what is the quotient?

5. If the quotient is 43, and the dividend 1,333, what is the divisor?

6. If the quotient is 800, and the divisor 176, what is the dividend?

7. If the quotient is 37, the divisor 56, and the remainder 16, what is the dividend?

8. A merchant bought 200 barrels of apples at $8 a barrel: he sold 50 barrels at $11 a barrel; what must he receive a barrel for the remainder, that he may gain $450 on the whole?

9. The length of the Atlantic coast belonging to the United States is 6,186 miles; of the Pacific coast, 2,281 miles; of the shore of the Gulf of Mexico, 3,467 miles; of the shore of the Northern Lakes, 3,600 miles. How many

days would it take to row this distance, at the rate of 25 miles a day?

10. How many days would it take a Laplander to travel in his sledge from the Arctic Ocean to the Black Sea, the distance being 1,700 miles, at the rate of 50 miles a day?

11. How many days would it take a vessel to go from Havana to New Orleans, the distance being 650 miles, at the rate of 200 miles a day?