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16. If 1-eighth of a bar of silver be worth 1 dollar, what is 3-eighths of the bar worth? What is 5-eighths of the bar worth? What is the whole bar worth?

17. What part of 8 is 1? is 2? is 3? is 5? is 7? 18. If 1-ninth of a pound of sugar cost 1 cent, what will 2-ninths of a pound cost? What will 8-ninths of a pound? What will 1 pound cost?

19. What part of 9 is 1? is 2? is 4? is 6? is 8? 20. If a man can build 1 rod of fence in 1-tenth of a day, how many rods can he build in 4-tenths of a day? in 6-tenths of a day? How many rods in 1 day?

21. What part of 10 is 1? is 2? is 3? is 4? is 6? SECTION 5.

1. A carpenter having sawed a board into halves, finds by measuring, that 1-half of the board is 2 feet long. How long was the whole board?

2. Suppose 2 is 1-half of some number,-what is the whole of the number?

3. If 1-half of a pound of rice be worth 3 cents, what is a whole pound worth?

4. 3 is 1-half of what number? 4 is 1-half of what number? 7 is 1-half of what number?

5. How many times 1-half of any number will make the whole number?

6. There is just room for 2 boys to sit upon 1-third of a certain board. What number of boys could sit upon the whole of that board?

7. Suppose 2 is 1-third of some number,—what is the whole of the number?

8. If 1-third of a box of raisins be worth 3 dollars, what is the whole box worth?

9. 3 is 1-third of what number? 4 is 1-third of what number? 6 is 1-third of what number?

10. How many times 1-third of any number will make the whole number?

11. If 1-fourth of a yard of broad-cloth cost 2 dollars, what will a yard cost?

12. 2 is Solution.

fourth of what number?

2 is 1-fourth of 4 times 2. 4 times 2 is 8.

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13. If a ship sail 3 miles in 1-fourth of an hour, how many miles will she sail in an hour? 14. 3 is 1-fourth of what number? what number?

4 is 1-fourth of 10 is 1-fourth of what number? 15. How many times 1-fourth of any number will make the whole number?

16. 3 men reaped 1-fifth of a field of wheat in a day. What number of men would have reaped the whole field? Solution. If 3 men reaped 1-fifth, 5 times 3 men would have reaped 5-fifths, or the whole.

17. If 1-fifth of a pound of loaf sugar be worth 4 cents, what is 1 pound worth?

18. 4 is 1-fifth of what number? 5 is 1-fifth of what number? 8 is 1-fifth of what number ?

19. How many times 1-fifth of any number will make the whole number?

20. 4 sheets of paper is 1-sixth of a quire. How many sheets are there in a quire?

21. 4 is 1-sixth of what number? 2 is 1-sixth of what number? 3 is 1-sixth of what number?

22. How many times 1-sixth of any number will make the whole number?

23. If 1-seventh of a ton of hay be worth 2 dollars, what is a whole ton worth?

24. 2 is 1-seventh of what number? 3 is 1-seventh of what number? 9 is 1-seventh of what number? 25. 5 is 1-eighth of what number? 3 is 1-ninth of what number? 6 is 1-tenth of what number?

SECTION 6.

1. If a yard of cloth be worth 2 dollars, what is 1-half of a yard worth? What is 1-half of 2?

Observation. Since you know that 1-half of 2 is 1, you will perceive, that 1-half of any other number must be as many times 1 as there are twos in the number.

2. What is 1-half of 4? of 12? of 18?

3. If a bar of silver weigh 3 pounds, what will 1-third of it weigh? What is 1-third of 3?

Observation. Here notice, that 1-third of any number is as many times 1, as there are threes in the number.

4. If a peck of oats cost 9 cents what will 1-third of a peck cost? What is 1-third of 9?

5. What is 1-third of 6? of 15? of 24 ?

6. If a man earn 4 shillings in 1 day, how much does he earn in 1-fourth of a day? What is 1-fourth of 4? Observation. Here notice that 1-fourth of any number is as many times 1, as there are fours in the number? 7. If a pound of raisins cost 20 cents, what will 1-fourth of a pound cost? What is 1-fourth of 20?

8. What is 1-fourth of 8? of 28?

of 64 ?

9. If a yard of cambric cost 5 dimes, what will 1-fifth of a yard cost? What is 1-fifth of 5?

10. If 35 drums of figs will pay for a hogshead of sugar, how many drums will pay for 1-fifth of a hogshead? 11. What is 1-fifth of 35? of 25? of 40?

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12. If a man earn 6 dollars in a week, how much does he earn in 1-sixth of a week? What is 1-sixth of 6 ? 13. Suppose writing paper costs 24 cents a quire;— what will be the price of 1-sixth of a quire?

Solution. If a quire cost 24 cents, 1-sixth of a quire will cost 1-sixth of 24 cents. 1-sixth of 24 is 4. of 36? of 48?

14. What is 1-sixth of 12?

15. What number of days is 1-seventh of a week? 16. If you eat 21 meals in a week, how many do you eat in 1-seventh of a week, or 1 day?

17. What is 1-seventh of 14? of 21 of 56 ?

18. If a melon weigh 8 pounds, what is the weight of 1-eighth of it? What is 1-eighth of 8?

19. If a yard of silver wire cost 32 cents, what will 1-eighth of a yard cost?

20. What is 1-eighth of 16? of 32? of 64?

21. If a drum of figs weigh 9 pounds, what is the weight of 1-ninth of a drum? What is 1-ninth of 9 ? 22. Suppose a watch-chain consists of 18 links;-how many links are there in 1-ninth of the chain?

23. What is 1-ninth of 18 ? of 36 ? of 72 ?

24. What number of cents is 1-tenth of a dime?

25. If a chest of Souchong tea be worth 30 dollars, what is 1-tenth of a chest worth?

26. What is 1-tenth of 30? of 50? of 100?

SECTION 7.

Note to Teachers. In solving the following questions, the learner should first state what proportional part of the number to be divided will be the answer, and thence proceed to find the answer in the denomination of the dividend.See solution under example 2d.

1. If any number of oranges should be divided equally between 2 boys, what part of the number would 1 boy receive? What part would 1 boy receive, if the oranges were divided among 3 boys? 4 boys? 5 boys? 6 boys? 7 boys? 8 boys? 9 boys? 10 boys?

2. 5 sailors received 40 dollars, which they divided equally among them. What did 1 sailor receive? Solution. If 5 sailors received 40 dollars, 1 sailor must have received 1-fifth of 40 dollars. 1-fifth of 40

dollars is 8 dollars?

3. 2 fishermen caught 24 fishes, which they shared equally. How many was each man's share?

4. If a traveller spend 28 dollars in travelling a week, how much does he spend a day?

5. A farmer can keep 9 cows on 36 acres of land:how many acres would it take to keep 1 cow?

6. 3 men have a bill of 30 dollars to pay:-how much must each man pay?

7. If a stage run 42 miles in 6 hours, what distance does it run in 1 hour?

8. Suppose 8 dozen of biscuit to be worth 72 cents;what is the value of 1 dozen ?

9. A tailor made 10 cloaks of 40 yards of cloth. How many yards did he put into each cloak?

SECTION 8.

Note to Teachers. Require the learner, as in the last section, to commence every solution by stating what proportional part of the given number is to be taken for the answer.

1. If a man can travel 35 miles in a day, what distance can he travel in 1-seventh of a day? What distance in 4-sevenths of a day?

Solution. If he can travel 35 miles in a day, he can travel 1-seventh of 35 miles in 1-seventh of a day; 1-seventh of 35 miles is 5 miles.- He can travel 4 times 5 miles in 4-sevenths of a day; 4 times 5 miles are 20 miles.

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2. There are 24 sheets of paper in a quire. How many sheets are there in 1-eighth of a quire? How many sheets in 3-eighths of a quire?

3. What is 1-eighth of 24? 3-eighths of 24?

Solution.

1-eighth of 24 is 3; 3-eighths is 3 times 3. 4. If a pound of coffee be worth 15 cents, what is 1-third of a pound worth? 2-thirds of a pound?

5. What is 1-third of 15? 2-thirds of 15?

6. If a bushel of barley cost 50 cents, what does 1-fifth of a bushel cost? 4-fifths of a bushel?

7. What is 1-fifth of 50? 4-fifths of 50?

8. If a yard of ribbon cost 28 cents, what will 1-fourth of a yard cost? 3-fourths of a yard?

9. What is 1-fourth of 28? 3-fourths of 28? 10. If an acre of land will produce 30 bushels of how much will 2-sixths of an acre produce?

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Direction. First get what 1-sixth of an acre will yield. 11. What is 5-sixths of 30?

Direction. First get 1-sixth of 30; thence 5-sixths. 12. If a stage run 81 miles in a day, what number of miles will it run in 7-ninths of a day?

13. What is 7-ninths of 81?

14. There are 100 cents in a dollar. What number of cents are there in 8-tenths of a dollar?

15. What is 8-tenths of 100?

16. Albert's kite line was 32 yards long, and he cut off 2-eighths of it for a fish line. What was the length of the fish line?

17. Suppose a boy having 42 quills, should give away 3-sevenths of them;-how many would he give away?and how many would he have left?

18. A man having 40 dollars, paid away 3-eighths of his money for a ton of hay. What was the price of the hay? and how many dollars had he left?

19. A boy, who had 45 cents, paid away 3-fifths of his money for a quire of paper. What was the price of the paper?—and how many cents had he left?

20. If 75 men can build a mile of fence in a day, what number of men must be employed, to build 2-thirds of a mile in the same time?

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