LESSON XXVIII.

1. If a melon costs 8 cents, what will 1 fourth of a melon cost?

2. At $5 a yard, what will 1 fifth of a yard cost?

3. At $6 a ton, what will 7 sixths of a ton cost?

4. At $12 a barrel, what will 1 barrel and 1 sixth of a barrel of flour cost?

5. When a man is working for $15 a week, how much does he earn in 2 weeks and 1 fifth of a week?

6. At 16 cents a pound, what cost 3 pounds and 3 fourths of a pound of sugar?

7. At $8 a cord, what cost 4 cords and 3 fourths of a cord of wood?

8. At 6 dimes a bushel, what cost 10 bushels and 2 thirds of a bushel of corn?

9. A teacher, being asked how many scholars he had, replied that the smallest number that ever had been present was 18, which was just 3 ninths of his whole number; how many had he?

10. Sold a horse for $150, which was 5 thirds of what he cost; what did he cost?

11. I have $4, which is 1 fifth of what I divided among 10 men; how much did each receive?

12. William has 63 cents in his pocket, which is 9 fifths of what he has in his money-box; how much has he in his money-box?

13. A boy, being asked how many chickens he had, answered that his largest brood contained 20, which was 4 fifths of the whole number, and the whole number was 5 times as many as he had in the smallest brood; how many had he, and how many were there in the smallest brood?

14. A farmer had 42 sheep, and sold 5 sevenths of them to 5 of his neighbors, each receiving an equal number; how many did each receive?

15. I had 24 cherries, but have divided 5 sixths of them among 10 children; how many does each receive?

16. A gentleman had 36 pears, and gave 1 sixth of them to Frank, and divided the remainder equally among his 5 brothers; how many did Frank receive more than each of his brothers?

17. At 10 cents a pound, what cost 20 pounds and 3 tenths of a pound of raisins?

18. At 18 cents a pound, what cost 8 pounds and 5 ninths of a pound of butter?

19. Henry gave $5 for a vest, which was just 1 half of 4 times as much as he gave for a hat; how much did he give for the hat?

20. What cost 5 barrels of flour, if 1 tenth of a barrel cost 9 dimes?

21. John has 20 cents, which is 4 fifths of 5 times as many as Joseph has; how many has Joseph ?

22. Emma is 12 years old, and 7 sixths of her age is just 7 eighths of her sister's age; what is her sister's age?

23. A pier of a certain bridge stands 10 feet in the water, which is 2 fifths of the height of the pier lacking 5 feet; what is the height of the pier?

24. Bought 4 pounds and 3 fourths of a pound of rice at 8 cents a pound, and paid for it with berries at 5 cents a quart; how many quarts did

it take?

25. Bought a watch for $40, and a chain for $5 more than 2 fifths the cost of the watch; what did both cost?

26. Sold a hogshead of molasses for $36, which was 9 eighths of what it cost; what did it cost?

27. A farmer has 6 cows, and 2 thirds the number of cows is equal to 1 fourth the number of his sheep; how many sheep has he?

28. Four boys wished their father to divide 50 cents equally among them. "No," said he; "but I will give you 4 fifths of it, and one half of the remaining fifth to the one that will tell how to divide it; " how much would the one who could tell receive?

29. If 6 pounds of sugar cost 96 cents, what cost 5 eighths of a pound?

30. A man, wishing to draw the water from a well containing 120 gallons, found that while he could draw out 12 gallons in a minute, 2 thirds as many gallons would run in during the same time; how long would it take him to exhaust the well?

31. Bought 9 yards of broadcloth for $36, which was 4 fifths of its real value; what was its real value per yard?

32. James, in reciting, had given in one day 8 imperfect answers, and 3 fourths of the imperfect answers were just 2 thirds of the number of perfect answers; how many perfect answers had he given?

33. In a small basket there are 12 pears, and 2 thirds of these are 2 sixths of the number in a large basket; if the whole be divided among 4 boys, how many will each receive?

34. A pole stands 3 fifths in the water, 1 half of the remainder in the mud, and 4 feet above the water; what is the length of the pole?

35. Frank had 2 bags filled with nuts, and his brother wished to buy 1 of them. "William," said Frank, “I have 9 quarts in the smaller bag, and 2 thirds of that number is just 1 half the number of quarts in the larger bag; and if you will

tell me the number of quarts in the larger bag, I will give them to you; how many were there in both bags?

36. George spent 6 elevenths of his money for a suit of clothes; he then paid $2 for a hat, which was just 1 fifth of all he had left; how many dollars had he at first?

37. A certain school is divided into three classes; in the first class there are 54 pupils, which is 9 tenths of the number in the second class, and the number in the second class is equal to 6 fifths of 2 times the number in the third class; how many are there in each of the classes?

LESSON XXIX.

Such expressions as one half, one third, two thirds, &c., are called fractions, and denote one or more equal parts of a unit. Fractions are expressed thus:

NOTE.The figure or figures above the short horizontal line are called the numerator of the fraction, and the figure or figures below the line are called the denominator. The denominator shows into how many equal parts a unit has been divided, and the numerator shows how many of these equal parts have been taken.

When the numerator is less than the denominator, the fraction is called a proper fraction; when the numerator is equal to or larger than the denominator, the fraction is called an improper fraction; when a fraction is joined with a whole number, the expression is called a mixed number.

1. What kind of a fraction is ? What is the 2 called? What does it show?'

2. Into how many equal parts is the unit divided, to give the fraction? How many of these equal parts are taken?

3. What kind of a fraction is ? Why?

4. In the fraction, what is the 2 called? What does it show?

5. In the fraction 7, what is the 9 called? Into how many equal parts does it show the thing to be divided?

6. What kind of a fraction is ? Why?

7. In the fraction, what does the 7 show? What does the 8 show?

8. What is the expression 5 called? Why? 9. Into how many equal parts is the unit divided to give the fraction? How many of the parts are taken?

10. How can you find g of any thing?

11.

How can you find of any thing?

12. In 12 how many fourths?

13. Reduce 15 to thirds. To fifths.

14. How can you reduce a whole number to a fraction having any given denominator?

15. How many times

in 5? In 16?

16. How many times in 7? 17. How many times in 9? 18. In 6 how many thirds?

In 10?

In 12?

19. Reduce 7 to an improper fraction. NOTE. That is, change 7 and 2 fifths to fifths.

20. Reduce 9g to an improper fraction. 21. Express 124 by an improper fraction. 22. Express 18 by an improper fraction. 23. How do you change a mixed number to an improper fraction?

24. How many times 1 in? In ?