can be made from 48 yards of silk? How many containing 16 yards each?

6. How many cords of wood, at $7 a cord, can be bought for $84? How many cords, at $8 a cord?

7. If there are 12 months in a year, how many years are there in 96 months? In 75 months?

8. If there are 30 days in a month, how many months are there in 90 days? In 60 days?

9. If there are 16 ounces in a pound, how many pounds are there in 80 ounces? How many if there are 12 ounces in a pound?

10. How many pounds of raisins, at 11 cents a pound, can you buy for 55 cents? How many at 10 cents a pound? At 15 cents?

11. Six men bought a houselot for $96; their shares being equal, what did each man pay?

12. Hired a horse and carriage for 77 cents, and rode 7 miles; what was the price per mile?

13. A man hired a horse and carriage for a ride, agreeing to pay 12 cents a mile; he paid 87 cents; how far did he ride?

14. Bought 15 cords of wood for $75; what was the price per cord?

15. Mr. Holt can do a piece of work in 78 hours; how many days will it take him to do it, if he works 12 hours each day? How many if he works 10 hours each day?

16. One man can do a piece of work in 90 hours; in how many hours can 6 men do it? 10 men? 12 men ?

17. One man can do a piece of work in 90 hours in how many hours can 6 men do half as much work? In how many hours can 10 men do twice as much work?

18. A dairy woman wishes to put 75 pounds of butter into 5 boxes; how many pounds shall she put into each box?

19. Eight cheeses weigh 100 pounds; what is their average weight?

20. If an orange is worth 6 apples, how many oranges are 66 apples worth??

21. If there are 20 shillings in 1 pound, how many pounds are there in 80 shillings? In 85 shillings?

22. How many miles in 96 furlongs, if there are 8 furlongs in 1 mile? How many miles in 82 furlongs? In 78 furlongs?

23. At 12 cents a pound, how many pounds of beef can be bought for 144 cents? For 93 cents?

24. How many wheelbarrows, at 7 dollars apiece, can be bought for 84 dollars? For 63 dollars? 25. A boy sold 6 doves for 75 cents; how many cents did he receive for 1 dove? For 3 doves? For 4 doves?

26. A boy sold chickens at 25 cents apiece, and received 1 dollar, or 100 cents, for them; how many chickens did he sell?`

27. If wine is worth 20 cents a pint, how many pints may be bought for 1 dollar How many quarts? 28. If brandy is worth 20 cents a gill, how many gills may be bought for 1 dollar? How many pints? 29. What is the price of a shawl, if 9 shawls cost $108?

30. A boy divided 80 chestnuts equally among 5 of his companions; how many did he give to each?

31. If 8 bushels of apples make 1 barrel of cider, how many barrels will 92 bushels make? 74 bushels? 78 bushels?

32. At $10 a barrel, how many barrels of flour can be bought for $85? For $92 ?

33. Eight times 10 are how many times 8?

34. Eight times 11 are how many times 12?

35. A man divided $84 equally among his 3 sons and 4 daughters; how many dollars did he give to each?

36. A boy having 7 melons, gave away 2 of them, and sold the rest for $1; what did he receive for each of those he sold?

37. A man having 75 dollars, bought 7 sheep, and had $5 left; what did he pay for each sheep?

38. A boy bought 5 hens at 20 cents each, and paid for them with apples at 10 cents a dozen; how many dozen did it take?

39. A man had 75 sheep, and bought 5 more; he then divided them equally in 8 pens; how many sheep did he put in each pen?

40. A boy had 50 peaches, and found 22 more; he then divided all of them equally among himself and 11 of his companions; how many did he give to each ?

REMARKS. 1. A single thing of any kind is called a unit or one. A unit is represented by the figure 1. 2. When any thing is divided into two or more equal parts, each of these parts is called a fraction of the thing which is divided.

3. A fraction, as well as a whole number, may be expressed by figures. Each fraction is usually expressed by means of two numbers, one written above the other, with a line between them; thus,

3

4. The number below the line shows into how many parts a unit is divided. It is called the DENOMINATOR, because it denominates or gives name to the parts; thus, if an apple, or any thing, is divided into three equal parts, each part is one third of the apple or thing; if into eight, each part is one eighth.

5. The number above the line is called the NuMERATOR, because it numerates or numbers the parts taken; thus the fraction, indicates that a unit has been divided into three equal parts, and that two of the parts are used.

6. The numerator and the denominator are the TERMS of the fraction.

7. A PROPER FRACTION is one whose numerator is less than its denominator; as 1, 2, 3. The value of a proper fraction is less than one.

8. An IMPROPER FRACTION is one whose numerator equals or exceeds its denominator; as, 4, 8, 1. The value of an improper fraction is one or more than one; for this reason it is called an improper frac tion.

9. A MIXED NUMBER is a whole number and a fraction united; as 2, read two and one half; 5, read five and two thirds.

LESSON II.

1. IN 3 apples how many halves of an apple? Solution. There are 2 halves in 1 apple; therefore there are 3 times 2 halves, which are 6 halves, in 3 apples.

2. What fraction represents 6 halves? Ans. §. 3. A man divided 5 barrels of flour among his workmen, giving them of a barrel apiece; to how many men did he give the flour?

4. How many halves are there in 5 whole ones? 5. A man having 3 barrels and 1 half of a barrel of apples, wishes to give them to some poor people;

to how many can he give them, if he gives them of a barrel apiece?

6. How many halves are there in 3 and 1 half?

Solution. In 3 whole ones there are 3 times 2 halves, which are 6 halves; to this add the 1 half, and we have 7 halves or ; therefore, in 3 and 1 half there are 7 halves.

7. A man paid 1 half of a dollar apiece to several workmen; it took 4 dollars and 1 half of a dollar to pay them; how many men did he pay ?

8. How many halves are there in 4 and 1 half; that is, in 4?

9. How many halves are there in 1? In 2? In 3? In 4? In 5?

in

10. How do you know how many halves there are any number?

Ans. There are twice as many halves as there are whole ones, because it takes two halves to make one whole one.

11. In 6 melons how many half melons?

12. In $8 how many half dollars?

13. Change 9 to halves.

14. Change 6 and 1 half to halves.

15. Change 7 to halves.

16. Change 12 to halves.

17. If you cut 2 melons each into 3 equal pieces, how many pieces will you have? What part of a melon will each piece be?

18. If you cut 3 apples each into 3 equal pieces, how many pieces will they make? What part of an apple will each piece be?

19. If you cut 4 pies each into 3 equal pieces, how many pieces will they make?

20. How many thirds are there in 1? In 2? In 3? In 4? In 5? In 9?

21. How do you know how many thirds there are in any number?