SECTION VII.

FRACTIONS.

LESSON I.

1. If I divide any number or thing, as an apple or a pear, into two equal parts, what is cach of those parts called?

2. What is then meant by one half?

3. How many halves make a whole one?

Ans. Two.

4. If I cut a sheet of paper into halves and give you 1 half, what part of the sheet shall I have left? If I give you 2 halves, how much would be left?

Note. The meaning of the terms one half, one third, one fourth, &c., should be illustrated to the pupil by actually cutting some familiar object, as an apple or a pear, into halves, thirds, fourths, &c. In this way, he will easily comprehend the meaning of the terms used in fractions, and will be able to perform operations in them with as much facility as in whole numbers.

5. If any number or thing is divided into three equal parts, what is each of the parts called?

Ans. One third.

6. What then is meant by one third? What is meant by two thirds?

7. If I cut an apple into thirds and give away 1 third, what part will be left? If I give away 2 thirds, what part will be left?

8. How many thirds make a whole one?

9. If a number or thing is divided into four equal parts, what is each of the parts called?

Ans. One fourth, or one quarter.

10. What is meant by 2 fourths? By 3 fourths?

11. If you divide a stick of candy in fourths, and give 3 fourths of it to your companions, what part of it would you have left?

12. If you give away 1 fourth, what part would be left?

13. Two fourths and one fourth make how many fourths? Three fourths and one fourth, make how many fourths?

14. How many fourths make a whole one?

LESSON II.

1. What is meant by 1 fifth?

Ans. When any thing is divided into five equal parts, one of these parts is called 1 fifth.

2. What is meant by 2 fifths? By 3 fifths? By 4 fifths?

3. If you cut a pie into fifths, and take fifths, how many fifths will remain ?

away 2

4. 3 fifths and 2 fifths make how many fifths? 5. How many fifths make a whole one?

6. What is meant by 1 sixth? By 2 sixths? By 5 sixths? By 3 sixths?

7. James Irad 2 sixths of a dollar, and his father gave him 3 sixths more: what part of a dollar had he then?

8. How many sixths make a whole one?

9. What is meant by 1 seventh? By 2 sevenths? By 3 sevenths? By 5 sevenths?

10. What part of a dollar will 2 sevenths and 4 sevenths make?

11. A man hoed 3 sevenths of an acre of corn in one day, and 2 sevenths of an acre the next day. what part of an acre did he hoe in boʼn days?

12. How many sevenths make a whole one? 13. What is meant by 1 eighth? By 2 eighths? By 3 eighths? By 5 eighths? By 7 eighths?. 14. How many eighths make a whole one?

15. What is meant by 1 ninth ? By 2 ninths? By 8 ninths?

16. How many ninths make a whole one?

17. What is meant by 3 tenths? By 5 tenths? By 7 tenths?

18. What is meant by 1 fifteenth? By 2 fifteenths? By 3 fifteenths? By 7 fifteenths? By 10 fifteenths? 19. What is meant by 1 twentieth? By 2 twentieths? By 8 twentieths? By 12 twentieths?

20. How many thirtieths make a whole one? How many forty-fifths make a whole one? How many sixty-fourths make a whole one? How many hun

dredths make a whole one?

LESSON III.

1. If one half of a pear costs 1 cent, how much will two halves or a whole pear cost?

Suggestion.-2 halves or a whole pear will cost twice as much as 1 half. Now if 1 half costs 1 cent, 2 halves or a whole one will cost 2 times 1 cent, and 2 times 1 cent are 2 cents. Ans. 2 cents.

2. If 1 half an orange costs 2 cents, how much will a whole orange cost?

3. If 1 half a yard of ribbon costs 3 cents, what will a whole yard cost?

4. If 1 third of a pie costs 2 cents, how much will 2 thirds of a pie cost? How much will 3 thirds or

a whole pie cost?

5. If i fourth of a pour.d of sugar costs 2 cen.s,

how much will 2 fourths cost? 3 fourths? A whole pound?

6. A man sold 1 fifth of a cord of wood for 3 shillings: how much would 3 fifths come to at the same rate? A whole cord?

7. If 1 sixth of a barrel of flour costs 1 dollar, how much will 4 sixths of a barrel cost? 6 sixths?

8. If 1 seventh of a ton of hay is worth 2 dollars, what is 3 sevenths worth? 4 sevenths? 6 sevenths? 7 sevenths?

7

9. If 1 eighth of a yard of cloth costs 1 dollar, how much will 5 eighths cost? 3 eighths? eighths? 8 eighths?

10. If 1 ninth of an acre of land is worth 3 dollars, how much is 4 ninths worth? 5 ninths? 7 ninths? 8 ninths?

11. One tenth of a hogshead of molasses is worth 3 dollars: how much is 5 tenths of a hogshead worth? 7 tenths? 9 tenths? How much is a hogshead worth?

LESSON IV.

1. If a yard of tape is worth 2 cents, how much is I half a yard worth?

Solution.-Since a whole yard is worth 2 cents, 1 half of a yard is worth 1 half as much: and 1 half of 2 cents is 1 cent. Ans. 1 cent.

2. What is 1 half of 4 cents? Ans. 2 cents.

Why?

Ans If 4 cents are divided into two equal par.s, one of the parts is 2 cents.

3. If an orange costs 4 cents, how much will half an orange cost?

4. What is 1 half of 6 cents? What is 1 half of 8 cents? Of 10 cents? Of 12 cents? Of 16 cents? Of 20 cents?

5. If a lemon costs 6 cents, how much will 1 third of a lemon cost? What is 1 third of 6 cents?

6. What is 1 third of 9 cents? What is 1 third of 12 cents? Of 18 cents? Of 15 cents? Of 24 cents? Of 30 cents?

Observation.-From the preceding examples, the learner will perceive that a half of a number is equal to as many units as 2 is contained times in that number; a third of a number is equal to as many units as 3 is contained times in that number; a fourth of a number is equal to as many units as 4 is contained times in that number, &c.

7. How do you find a half of a number? Ans. Divide the number by 2.

8. How find a third of a number? How find a fourth of a number? A fifth? A sixth? A seventh ? An eighth? A ninth? A tenth?

9. What is 1 fourth of 12 dollars? Of 16 dollars? Of 20? Of 32? Of 24? Of 28? Of 36? Of 40? 10. If a ton of coal is worth 10 dollars, what is 1 fifth of a ton worth?

11. What is 1 fifth of 15 dollars? Of 20 dollars? Of 30 Of 25? Of 40? Of 50?

12. What is one seventh of 7 ?

Of 49? Of 70?

Of 14? Of 28 ?

13. What is one eighth of 16? Of 24? Of 40? Of 80? Of 72 ?

14. What is 1 ninth of 9? Of 27? Of 18? Of 36 ? Of 45? Of 72 ? Of 90?

15. What is one tenth of 10? Of 30? Of 20? Of 60? Of 50? Of 100?