SECTION 9.

1. If 48 dollars should be divided equally among 8 men, what part of the money,-and what number of dollars would 3 men receive?

Solution. 3 men would receive 3-eighths of the money. 1-eighth of 48 dollars is 6 dollars; 3-eighths is 3 times 6 dollars, or 18 dollars.

2. A tierce, holding 42 gallons of molasses, has been emptied into 6 kegs, of equal size. What part of the molasses, and what number of gallons in 5 kegs?

3. What part of 6 is 5? What is 5-sixths of 42 ? 4. If a piece of broad-cloth containing 30 yards will make ten suits of clothes, what part of the piece,-and what number of yards, will make 6 suits?

5. What part of 10 is 6? What is 6-tenths of 30? 6. 5 girls had 15 oranges, which they shared equally: 2 of the girls gave their shares to a sick woman. What part of 15 oranges did the woman receive ?-and what number of oranges did she receive?

7. What part of 5 is 2? What is 2-fifths of 15? 8. 7 men owned 56 sheep in company, and 3 of the men took out their shares. What part of the flock,-and what number of sheep did they take out?

9. What part of 7 is 3? What is 3-sevenths of 56 ? 10. If 4 men eat 28 biscuit in a day, what part of 28 biscuit, and what number of biscuit will 2 men eat?

11. What part of 4 is 2? What is 2-fourths of 28 ? 12. 3 brothers owned 60 acres of land together, and the 2 younger sold their shares to the oldest. What part of the land, and how many acres did they sell?

13. What part of 3 is 2? What is 2-thirds of 60 ?

SECTION 10.

1. If 3 men can fell 18 trees in a day, how can 4 men fell in the same time?

many trees

Solution. If 3 men can fell 18 trees in a day, 1 man can fell 1-third of 18 trees, or 6 trees; 4 men can fell 4 times 6 trees, or 24 trees.

2. What is 4 times 1-third of 18?

Solution. 1 third of 18 is 6: then 4 times 6 is 24.

3. If 5 men will cut 20 cords of wood in a day, how many cords will 3 men cut in the same time?

4. What is 3 times 1-fifth of 20 ?

5. If 4 barrels of flour cost 24 dollars, how much will 7 barrels cost, at the same price per barrel?

6. What is 7 times 1-fourth of 24 ?

7. If 2 boats will carry 16 passengers across the river, how many passengers will 5 boats carry?

8. What is 5 times 1-half of 16 ?

9. Suppose a cooper can make 27 barrels in 9 days;how many barrels can he make in 5 days?

10. What is 5 times 1-ninth of 27 ?

11. Suppose 6 kegs will hold 36 gallons of molasses;— what number of gallons will 4 kegs hold?

12. What is 4 times 1-sixth of 36?

13. If 8 soldiers eat 56 pounds of beef in a week, how many pounds will 9 soldiers eat in a week?

14. What is 9 times 1-eighth of 56 ?

15. If a workman can earn 49 dollars in 7 weeks, how many dollars can he earn in 6 weeks?

16. What is 6 times 1-seventh of 49?

17. If 10 casks of claret wine cost 80 dollars, what would be the price of 8 casks of the same wine?

SECTION 11.

1. Suppose there are 10 links in 2-thirds of a watch chain;-how many links are there in 1-third of the chain? How many links in the whole chain?

Solution. If there be 10 links in 2-thirds of the chain, there is 1-half of 10 links in 1-third of it: 1-half of 10 is 5.—If 5 links be 1-third of the chain, there are 3 times 5 links in the chain: 3 times 5 is 15.

2. 10 is 2-thirds of what number?

3. If 3-fourths of a pound of honey cost 15 cents, what will 1-fourth cost? What will a pound cost?

4. 15 is 3-fourths of what number?

Solution. Since 15 is 3-fourths of the required num. ber, 1-third of 15 must be 1-fourth of the number: 1-third of 15 is 5. If 5 be 1-fourth of the number, 4 times 5, or 20, is the whole number.

5. If 2-fifths of a bushel of oats cost 18 cents, what will 1-fifth cost? What will a bushel cost?

6. 18 is 2-fifths of what number?

7. If 4-sevenths of a kite line be 36 yards long, how long is 1-seventh? How long is the whole line? 8. 36 is 4-sevenths of what number?

9. If 3-sixths of a chest of tea cost 21 dollars, what will 1-sixth cost? What will a whole chest cost?

10. 21 is 3-sixths of what number?

11. If 5-eighths of a pipe of wine be worth 30 dollars, what is the value of the whole pipe?

Direction. First find what 1-eighth is worth.

12. 30 is 5-eighths of what number?

13. If a man can earn 40 cents by working 4-sevenths of a day, how much can he earn by working a whole day?

14. 40 is 4-sevenths of what number?

15. If 7-ninths of a hogshead of sugar be worth 49 dollars, what is the whole hogshead worth?

16. 49 is 7-ninths of what number?

17. If a rail-road car run 24 miles in 8-tenths of an hour, what distance will it run in an hour?

18. 24 is 8-tenths of what number?

19. Henry is 10 years old; and his age is equal to 5-sixths of Andrew's age. How old is Andrew?

Suggestion. You may perceive that 1-fifth of Henry's age must be equal to 1-sixth of Andrew's age.

20. 10 is 5-sixths of what number?

21. If 21 workmen will perform 3-fifths of a certain piece of work in a week, what number of workmen would it take to perform the whole work in a week? 22. 21 is 3-fifths of what number?

23. A coach-man purchased a horse, and after paying 5-eighths of the price, he still owed 30 dollars. What was the price of the horse?

Solution. If he paid 5-eighths of the price, the 30 dollars, which he still owed, was 3-eighths of the price. 30 dollars being 3-eighths of the price, 1-third of 30 dol lars, or 10 dollars, is 1-eighth. 10 dollars being 1-eighth of the price, 8 times 10 dollars is the price.

24. 30 is 3-eighths of what number?

25. If 2-fifths be taken from the whole of any thing, how many fifths are there left?

26. While George was fishing, a pickerel broke off 2-fifths of his line; he then had 12 feet of the line left. How long was his line at first?

27. Suppose a laborer can earn 60 cents a day, by working 5-sixths of the time;-how much could he earn by working constantly?

28. After 3-sevenths of a cask of wine had leaked out, the owner drew off the remainder, and found there were 48 gallons. How many gallons had he lost?

29. A farmer improved 3-ninths of his farm in tillage, appropriated 4-ninths to pasturage, and had 18 acres of wood-land. How many acres had he in all?

30. 2-eighths of Edward's books are bound in leather, 3-eighths of them in marble paper, and 15 of them in blue paper. How many has he of each description?

SECTION 12.

Note to Teachers. This section embraces all the operations taught in the preceding sections of this chapter. Prefixed to each example, is the number of the section in which the operation involved in the example taught. If the pupil fail in any part of this section, he should be put back to the section whose number is prefixed to the example in which he fails.

REVIEW.

1. (§1.) James found 4-eighths of a dollar, and earned 5-eighths. How much money had he then?

2. (§2.) If we divide any thing into 6 equal parts, and take away 4 parts, how much of the thing is left? 3. (§3.) If you have 7-ninths of 1 dollar, what part of a dollar must you get to make up 1 dollar?

4. (§4.) If a man can walk 1 mile in 1-fourth of an hour, how many miles can he walk in 1 hour?

5. (§4.) What part of 6 is 5? What part of 7 is 3? What part of 10 is 4? What part of 18 is 7?

6. (§ 5.) If 1-fourth of an acre of land will produce 9 bushels of corn, how much will 1 acre produce?

7. (§5.) If 1-eighth of a barrel of beef be allowed to 3 soldiers for a week's provision, what number of soldiers will 1 barrel supply for a week?

8. (§ 6.) Suppose a yard of gold wire to be worth 28 dollars; what is 1-fourth of a yard worth?

9. ($7.) If 50 day's work is to be done by 5 men, how many day's work must each man perform?

10. (§8.) If one pound of Hyson tea be worth 96 cents, what is 7-eighths of a pound worth?

11. (§9.) A company of 14 men gave 84 dollars for a boat. What part of 84 dollars did 5 men pay?

12. (§ 9.) If 8 dollars will buy 72 pounds of brown sugar, how many pounds will 6 dollars buy?

13. (§ 10.) Suppose 18 yards of cloth will make 6 coats; how many yards are required for 10 coats?

14. (§ 11.) If 5-ninths of a yard of cotton cambric be worth 50 cents, what is the value of one yard?

15. (§ 11.) Suppose a man by working constantly can dig 40 bushels of potatoes in a day, how many bushels will he dig, if he be idle 2-fifths of the day?

FRACTIONS AND RELATIONS.

SECTION 13.

Note to Teachers. The remainders, that will arise in the several examples of division in this section, must be expressed in the language of fractions. See answers under examples 4th. and 8th. If the learner should not readily understand the process of converting the remainders into fractions, he may be referred to section 4th. in this chapter, and, after reviewing the examples therein, may return immediately to this section.

1. How much cloth, at 2 dollars a yard, can I buy for 1 dollar? How much for 3 dollars?

2. What part of 2 is 1? How many times 2 in 3? 3. How many yards of ribbon, at 2 cents a yard, can you buy for 7 cents?—I mean, how many whole yards, and what part of another yard can you buy?

4. How many times 2 in 7?—I mean,-how many twos are there, and what part of 1 more two, in 7 ?

Solution. 2 is contained in 7, 3 times, and 1 over: the 1 over is 1-half of another time 2. Ans. 3 and 1-half. 5. How many times 2 in 9? in 12? in 13?

6. How much wine, at 3 dollars a gallon, can I buy for 1 dollar? How much for 4 dollars?

7. What part of 3 is 1?

How many times 3 in 4?