Applications in the preceding Ruies.

60. 1. What will 5 yards of cloth cost, at 7 dollars a yard? ANALYSIS. Five yards of cloth will cost 5 times as much as 1 yard; since 1 yard of cloth costs 7 dollars, 5 yards will cost 5 times 7 dollars, which are 35 dollars: Therefore, 5 yards of cloth, at 7 dollars a yard, will cost 35 dollars: hence,

The cost of any number of things, is equal to the price of a single thing multiplied by the number.

We have seen that the product of two numbers will be the same (that is, will contain the same number of units), whichever be taken for the multiplicand (Art. 51). Hence, in practice, we may multiply the two factors together, taking either for the multiplier, and then assign the proper unit to the product. We generally take the least number for the multiplier.

2. There are ten bags of coffee, each containing 48 pounds: how much coffee is there in all the bags ?

3. There are 24 hours in a day, and 7 days in a week: how many hours in a week?

4. A merchant bought 49 hogsheads of molasses, each containing 63 gallons: how many gallons of molasses were there in the parcel ?

5. If a regiment of soldiers contains 1128 men, how many men are there in an army of 106 regiments?

6. A merchant buys a piece of cloth containing 97 yards, at 3 dollars a yard: what does the piece cost him?

7. Suppose a man were to travel 32 miles a day: how far would he travel in 365 days?

8. There are 20 pieces of cloth, each containing 37 yards, and 49 other pieces, each containing 75 yards: how many yards of cloth are there in all the pieces?

9. A farmer bought a farm containing 10 fields; three of he fields contained 9 acres each; three other of the fields, 2 acres each; and the remaining 4 fields, each 15 acres :

60. How do you find the cost of any number of things? How may it be done in practice?

the whole cost, at 18 dollars an acre?

10. In a certain city, there are 3751 houses. If each house, on an average, contains 5 persons, how many inhabitants are there in the city?

11. If 786 yards of cloth can be made in one day, how many yards can be made in 1252 days?

12. If 30009 cents are paid for one man's labor on a railroad for 1 year, how many cents would be paid to 814 men, each man receiving the same wages?

13. There are 320 rods in a mile: how many rods are there in the distance from St. Louis to New Orleans, which is 1092 miles ?

14. Suppose a book to contain 470 pages, 45 lines on each page, and 50 letters in each line: how many letters in the book?

15. Supposing a crew of 250 men to have provisions for 30 days, allowing each man 20 ounces a day: how many ounces have they?

16. There are 350 rows of trees in a large orchard, 125 trees in each row, and 3000 apples on each tree: how many apples in the orchard?

17. How many soldiers are there in a body of men that is 7 deep, if each line has 758 men?

18. If a railroad car goes 27 miles an hour, how far will it run in 3 days, running 20 hours each day? How far would it run, if its rate were 37 miles an hour?

19. If 1327 barrels of flour will feed the inhabitants of a city for 1 day, how many barrels will supply them for 2 years?

20. A regiment of men contains 10 companies, each company 8 platoons, and each platoon 34 men: how many men in the regiment ?

21. Two persons start from the same place, and travel in the same direction; one travels at the rate of 6 miles an hour, the other at the rate of 9 miles an hour: if they travel 8 hours a day, how far will they be apart at the end of 17 days? How far, if they travel in opposite directions?

22. The Erie railroad is about 425 miles long, and cost 65 thousand dollars a mile: if 9645635 dollars had been paid, how much would remain unpaid?

23. A drover bought 106 oxen, at 35 dollars a head; it cost him 6 dollars a head to get them to market, where he sold them at 47 dollars: did he make or lose, and how much?

24. The great Illinois Central railroad reaches from Chicago to the mouth of the Ohio river, 815 miles, and cost 23500 dollars a mile: what was its entire cost?

Bills of Parcels.

61. When a person sells goods, he generally gives with them a bill, showing the amount charged for them, and acknowledging the receipt of the money paid; such bills are called, Bills of Parcels.

25. James Johnson

NEW YORK, Oct. 1, 1854.

Bought of W. Smith.

4 Chests of tea, of 45 pounds each, at 1 doll. a pound

3 Firkins of butter, at 17 dolls. per firkin

4 Boxes of raisins, at 3 dolls. per box

36 Bags of coffee, at 16 dolls. each

14 Hogsheads of molasses, at 28 dolls. each

Received the amount in full.

26. James Hughes

27 Bags of coffee, at 14 dollars per bag 18 Chests of tea, at 25 dolls. per chest 75 Barrels of shad, at 9 dolls. per barrel

87 Barrels of mackerel, at 8 dolls. per barrel 67 Cheeses, at 2 dolls. each

59 Hogsheads of molasses, at 29 dolls. per hogshead

Amount,

Received the amount in full, for W. JONES,

dollars.

per James Cross.

61. What are bills of parcels ?

DIVISION.

62. 1. When a number is divided into 2 equal parts, each part is called, one-half of the number.

What is one-half of 4 apples? What is one-half of 4? How many times is 2 contained in 4?

2. When a number is divided into 3 equal parts, each part is called, one-third of the number.

What is one-third of 9 apples? What is one-third of 9? How many times is 3 contained in 9?

3. When a number is divided into 4 equal parts, each part is called, one-fourth of the number.

What is one-fourth of 12 pears? What is one-fourth of 12? How many times is 4 contained in 12?

4. When a number is divided into 5 equal parts, each part

is called, one-fifth of the number.

What is one-fifth of ten marbles?

What is one-fifth of 10?

How many times is 5 contained in 10?

5. When a number is divided into 6 equal parts, each part is called, one-sixth of the number.

6. If 12 apples be equally divided among 4 boys, how many will each have?

ANALYSIS.-If 12 apples be divided equally among 4 boys, each boy will have one of the four equal parts of 12 apples: one of the 4 equal parts of 12 is 3: Therefore, each boy will have 3 apples.

7. If 24 peaches are divided equally among 6 boys, how many will each have? What is one of the six equal parts of 24 peaches? How many times is 6 contained in 24?

8. How many yards of cloth, at 3 dollars a yard, can you buy for 24 dollars?

62. What is one-half of a number? What is one-third of a number? What is one-fourth of a number? What is one-fifth of a number?

ANALYSIS. Since 1 yard costs 3 dollars, you can buy as many yards as 3 is contained times in 24: 3 is contained in 24, 8 times: Therefore, at 3 dollars a yard, you can buy 8 yards of cloth for 24 dollars.

9. A farmer pays 28 dollars for 7 sheep: how much is that apiece?

ANALYSIS. Since 7 sheep cost 28 dollars, one sheep will cos as many dollars as 7 is contained times in 28, which is 4 Therefore, each sheep will cost 4 dollars.

10. If 12 yards of muslin cost 96 cents, how much does 1 yard cost?

11. How many oranges could you buy for 72 cents, if they cost 6 cents apiece?

63. DIVISION is the operation of dividing a number into equal parts; or, of finding how many times one number is contained in another.

64. The DIVIDEND is the number to be divided.

65. The DIVISOR is the number by which we divide: it shows into how many equal parts the dividend is divided.

66. The QUOTIENT is the result of division. It is one of the equal parts of the dividend, and if the numbers have the same unit, shows how many times the dividend contains the divisor. 67. The REMAINDER is what is left after the operation. 68. EXACT DIVISION is when the remainder is 0.

69. There are three signs used to denote Division: expresses that 18 is to be divided by 4.

184,

18

4

4) 18,

expresses that 18 is to be divided by 4.

expresses that 18 is to be divided by 4.

63. What is Division ?-64. What is the dividend?-65. What is the divisor?-66. What is the quotient? What does the quotient show?-67. What is the remainder?-68. What is exact division? -69. How many signs are there of Division? Write them.