LESSON II.

One Third.

IF I divide an apple in three equal parts, what is one of these parts called? Ans. One-third.

2. What are two parts called? Three parts? How many thirds in one apple?

3. What is one-third? Ans. One-third is one of the three equal parts into which anything is divided.

4. What is one-third of 6? Ans. One-third of 6 is 2, since 6 divided by 3 is 2.

5. What is 1 third of 9? Of 12? Of 18? Of 15?

6. What is 1 third of 24? Of 30? Of 27? Of 33?

7. Reuben had 18 apples, and gave 1 third of them away; how many did he give away?

SOLUTION.—If Reuben had 18 apples, and gave 1 third of them away, he gave away 1 third of 18 apples, or 6 apples.

8. Ada had 21 plums, and gave 1 third of them to Eddie; how many plums did she give to Eddie?

9. Peter bought 24 marbles, and lost of them in play; how many did he lose?

10. What are two-thirds of 6?

SOLUTION.-One-third of 6 is 2, and two-thirds of 6 are 2 times 2, which are 4. Therefore, 2 thirds of 6 are 4.

11. What are 2 thirds of 9? Of 12? Of 15? Of 18? 12. What are 2 thirds of 24? Of 21?

13. Anna had 9 oranges, and gave

them; how many did she give to Effie?

Of 30? Of 36?

Effie 2 thirds of

14. Laura had 30 peaches, and sold Lizzie 2 thirds of them; how many did Lizzie receive?

WRITTEN EXERCISES.

1. The fractions one-third, two-thirds, etc., are written

thus:

One-third,

}

Two-thirds,

Three-thirds,
}

Four-thirds.

2. What is of 45? † of 54? † of 69? † of 75? 8. Find of 60; of 96; of 216; } of 234.

4. A man had 150 dollars and spent of it; how much did he spend? How much remained?

5. A farmer had 405 sheep, and sold 2 thirds of them; how many did he sell? How many remained?

6. If 5 horses cost 860 dollars, how many dollars will one horse cost?

LESSON III.

One Fourth.

IF I divide an apple into four equal parts, what is one of these parts called?

2. What are 2 parts called? 3 parts? 4 parts?

3. How many fourths of an apple in one apple?

4. One-fourth is one of the four equal parts into which anything may be divided.

5. Since 8 divided by 4 is 2, what is 1 fourth of 8? 6. What is 1 fourth of 8?

SOLUTION.-One-fourth of 8 is 2, since 8 divided by 4 is 2. 7. What is 1 fourth of 12? Of 20? Of 28? Of 36?

8. What is 1 fourth of 16? Of 24? Of 32? Of 44?

9. What will 1 fourth of a barrel of flour cost if one barrel costs 8 dollars?

SOLUTION.-If one barrel of flour costs 8 dollars, 1 fourth of a barrel will cost 1 fourth of 8 dollars, which is 2 dollars.

10. Jacob having 12 pens, sold 1 fourth of them to Johnson; how many did he sell?

11. If Rachel gave her sister 1 fourth of 20 pears, bow many pears did her sister receive?

12. Marion lost 1 fourth of 40 quinces; how many quinces did she lose?

13. What are 2 fourths of 12?

SOLUTION.-One-fourth of 12 is 3, and 2 fourths of 12 are 2 times 3, which are 6.

14. What are 2 fourths of 8? Of 24? Of 20? Of 32?

15. What are 3 fourths of 12? Of 20? Of 16? Of 36?

16. What are 5 fourths of 8? Of 24? Of 28? Of 40? 17. Sarah gave her brother 2 fourths of 12 oranges; how many did he receive?

18. Mason's age is 2 fourths of 16 years; required the age of Mason.

19. A boy has 24 cents, and his brother has 3 fourths as many; how many have both?

WRITTEN EXERCISES.

1. The fractions one-fourth, two-fourths, etc., are written as follows:

2. What is of 84? Of 96? Of 104? Of 136?
3. What are 4 of 48? Of 84? Of 132? Of 236?
4. What are of 72? Of 100? Of 204? Of 368?

5. A farmer raised 240 bushels of grapes, and sold & of them; how many bushels did he sell?

6. There are 480 grains in one ounce Troy; how many grains in of an ounce Troy?

7. If 6 acres of land are worth 540 dollars, what is one acre worth?

LESSON IV.

One Fifth.

IF we divide an orange into five equal parts, what is one of these parts called?

2. What are 2 parts called? 3 parts? 4 parts? 5 parts? 3. How many fifths of an orange in one orange?

4. One-fifth is one of the five equal parts into which anything may be divided.

5. What is one-fifth of 10? Ans. One-fifth of 10 is 2, since 10 divided by 5 is 2.

6. What is 1 fifth of 15? Of 25? Of 35? Of 40?

7. What are 2 fifths of 5? Of 30? Of 10? Of 45?

8. What are 3 fifths of 15? Of 20? Of 55? Of 45? 9. What are 4 fifths of 20? Of 30? Of 40? Of 60? 10. Mary has 15 oranges, and Rachel has 1 fifth as many; how many has Rachel?

11. Fanny's age is 30 years, and her sister is 3 fifths as old; how old is her sister?

12. A dog killed 3 fifths of a flock of turkeys, consisting of 25; how many were killed?

13. A cow cost 30 dollars, and a coat cost 4 fifths as much; required the cost of the coat.

14. A watch cost 10 dollars more than 4 fifths of 40 dollars; required its cost.

15. Joseph bought 2 fourths of 40 pears, and sold 10 of them; how many remained?

16. Mary has 1 third of 30 roses, and Sarah has 1 half of 20 roses; how many have they both?

WRITTEN EXERCISES.

1. The fractions one-fifth, two-fifths, etc., are written

2. Required the value of the following:

of 75; of 135; of 145;

of 560; of 745; % of 750,

Five-Fifths.

of 230; of 540; 4 of 95;

of 965.

3. There are 1760 yards in a mile; how many yards in of a mile? In of a mile?

4. If 8 cows cost a farmer 320 dollars, how much did he pay for each cow?

LESSON V.

One Sixth and One Seventh.

IF you divide an orange into 6 equal parts, what is 1 part called? 2 parts? 3 parts? etc.

2. How many sixths in one? What is one-sixth of anything?

8. What is 1 sixth of 18? Of 12? Of 24? Of 30?

Of 48?

Of 60? Of 72?

6. What are 5 sixths of 42? 7. Janson had 30 plums, and gave 2 sixths of them away; how many did he give away?

8. Arthur bought 24 pens, and sold 3 sixths of them; how many did he sell?

9. Peter walked 18 miles and rode 5 sixths as far; how far did he ride?

10. If you divide an orange into 7 equal parts, what is 1 of these parts called? 2 parts? 3 parts? etc.

11. How many sevenths in one? What is one-seventh of anything?

Of 70?

Of 49? Of 63?

Of 35?

Of 56? Of 70?

Of 63?

Of 49? Of 84?

12. What is 1 seventh of 14? Of 21? Of 35? Of 42? 13. What are 2 sevenths of 7? Of 28? Of 42? Of 77? 14. What are 3 sevenths of 21? 15. What are 4 sevenths of 28? 16. What are 5 sevenths of 42? 17. A watch was bought for 21 dollars, and sold for 6 sevenths of its cost; for how much was it sold?

18. Jane had 35 roses, and Sarah had 4 sevenths as many as Jane; how many roses had Sarah?

19. Robert walked 14 miles in one day, and 6 sevenths as far the next day; how far did he walk both days?

WRITTEN EXERCISES.

1. One-sixth is written; 2 sixths, 4; 3 sixths, §; 1 seventh, 4; 2 sevenths, 4, etc.

2. Required the value of the following:

of 84; of 108; of 216; of 570; # of 720; § of 840; of 98; of 203; 4 of 287; of 679; of 896; of 952. 3. A farmer raised 5034 bushels of oats and sold § of the crop; how many bushels did he sell?

4. If a locomotive runs 875 miles in a week, how far did it run in of a week?