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SECTION 24.

1. Suppose 3-fourths of a yard of flannel to cost 32 rents; what does 1-fourth of a yard cost? What would a yard cost?

Solution. If 3-fourths of a yard cost 32 cents, 1fourth of a yard costs 1-third of 32 cents. 1-third of 32 cents is 10 cents and 2-thirds of a cent...... 4-fourths, or a whole yard would cost 4 times 10 cents and 2-thirds. 4 times 10 cents are 40 cents; 4 times 2-thirds are Sthirds, equal to 2 and 2-thirds. Then, 40 cents plus 2 cents and 2-thirds are 42 cents and 2-thirds.

2. 32 is 3-fourths of what number? Solution. Since 32 is 3-fourths of the number, 1third of 32 is 1-fourth of it. 1-third of 32 is 10 and 2-thirds. 4 times 10 and 2-thirds are 42 and 2-thirds. 3. If 2-fifths of an acre of land will produce 9 bushels of rye; how many bushels will 1-fifth of an acre produce? How many bushels will an acre produce?

4. 9 is 2-fifths of what number?

Instruction.

Observe, that 1-half of 9 must be 1-fifth of the required number.

5. If a man drink 6 gallons of beer in 5-sixths of a month, how many gallons does he drink in 1-sixth of a month? How many gallons will he drink in a month? 6. 6 is 5-sixths of what number?

7. A inan, who spends 43 cents a day, finds his expenses to be 5-sevenths of his wages. What is 1-seventh of his wages? What is the whole of his wages? 8. 42 is 5-sevenths of what number?

9. If 5-eighths of a dollar will pay for 24 pounds of flour, how many pounds will 1-eighth of a dollar pay for? How many pounds will a dollar pay for? 10. 24 is 5-eighths of what number?

11. Suppose 6 gallons of wine to leak from a cask in 8-ninths of an hour; how much will leak out in 1-ninth of an hour? How many gallons in 1 hour?

12. 6 is 8-ninths of what number?

13. If 4-tenths of a yard of cloth be worth 33 cents, how much is 1 yard worth?

Direction. First find what 1-tenth of a yard is worth.

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14. If 3-eighths of a bale of cotton be worth 17 dollars, what is the whole bale worth?

15. A laborer spent 30 cents a day, and still saved 3-sevenths of his wages. How much was his wages?

16. Suppose that I have read 5-ninths of the pages in a certain book, and there are 35 pages more to be read; --how many pages are there in the book?

NOTATION OF FRACTIONS.

Learners will now attend to the meaning of the words, FRACTION, DENOMINATOR, and NUMERATOR.

A Fraction is any part of one. For example, one-half of an orange is a fraction of 1 orange; three-fourths of an orange is another fraction of 1 orange.

In this book, fractions have been expressed by a number joined with a word; thus, 4-ninths. Fractions are commonly expressed by two numbers, standing one above the other, with a line between them; thus,

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4 four- 3 three

fifths,

ninths.

one

hall,

17. What fraction is expressed, when there is a 4 with a 1 over it? 7 with 2 over it? 8 with 5 over it? 10

with 6 over it?

18. Which is the greater fraction; oror? / or /?

19. Which is the greater fraction; or? or ? for 1?

oror }?

or 2? or 2?

The Denominator of a fraction, is the number of equal parts into which a whole one is divided. For example, if a whole orange be divided into 4 equal parts, the denominator is 4; the parts being denominated fourths.

The Numerator of a fraction is the number which shows how many of the equal parts the fraction ex presses. For example, the fraction expresses 3 of the four equal parts; therefore 3 is the numerator.

20. What numerator, and what denominator, would express the fraction, four-fifths? two-eighths?

ninths

one-fifteenth? five-eighteenths?

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ared

ead

ds

When the numerator is equal to the denoininator, thus,, then the fraction is equal to 1; as 4-fourths of an orange, when joined together make 1 orange.

When the numerator is greater than the denominato. thus,, then the fraction is equal to as many times 1 as the denominator is contained times in the numerator.

21. How many times 1, [how many whole ones], in? in? in? in 29? in 30? in ?

22. How many times 1, and what fraction over, in
in in? in 19? in 36
in 19? in 36? in $5?

23. Where have you observed the numerator of a fraction to stand; above, or below the denominator?

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1. James has

one

SECTION 25.

of a dollar, and Henry has of a

dollar:- which of them has the most money?
Compare the fraction

with other fractions.

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6. is equal to how many twelfths? how many six teenths? how many twentieths?

7. Edward broke a slate pencil into 3 equal pieces, and Albert broke one into 6 equal pieces. How many of Albert's pieces were equal to I of Edward's pieces? Compare the fraction

with other fractions.

8. is equal to how ma

ny sixths?

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10. is equal to how many twelfths? how many sighteenths? how many thirtieths 2

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Suggestion. of 1 is equal to of 12-twelfths 11. is equal to how many eighths? how many twelfths? how many sixteenths?

12. is equal to how many tenths? how many twen tieths? how many twenty-fifths?

13. is equal to how many twelfths? how many eighteenths? how many thirtieths?

14. is equal to how many fourteenths? how many twenty-eighths? how many thirty-fifths? 15. is equal to how many twentieths?

Solution. is equal to, is equal to 3 times 5twentieths, which is 15.

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16. is equal to how many twelfths?

17. A boy, who had 3 of an orange, cut each fifth into 2 parts, (making tenths); his brother gave him more. What fraction of an orange had he at last? 18. Into how many parts must you cut a sixth of an orange, to make the parts eighteenths?...... Why? 19. is equal to how many eighteenths?

20. Change to fourteenths, and then add to it. 21. is equal to how many twenty-fourths?

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22. Change to eighteenths, and then take from it. SECTION 26.

1. What is meant by a Fraction ?. -How is a fraction commonly expressed?.What is the Denominator of a fraction?.. -What is the Numerator?

2 If the denominator of a fraction be 9, and the numerator 7, how should these numbers be written?and what would the fraction be called in reading it?

3. Suppose two fractions have numerators alike, and denominators different-which is the greater fractionthat with the greater, or the smaller denominator?

4. Suppose two fractions have denominators alike, and numerators different-which is the greater fraction -that with the greater, or the smaller numerator?

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Observation. If an orange be cut into eighths, and then 4 of the eighths be joined together, these 4-eighths become 1-half of an orange. And thus the fraction,, when reduced to its lowest terms, is 1.

5. Reduce to its lowest terms-that is, find the Jowest numerator and denominator, that will express a quantity equal to 2.

6. Reduce to its lowest terms.

7. Reduce to its lowest terms.
8. Reduce to its lowest terms.
9. Reduce to its lowest terms.

Reduce .

Reduce.

Reduce.

Observation. A fraction is reduced, by dividing the numerator and denominator by any number, which will divide them both without a remainder. For example, we reduce thus; 2 in 6, 3 times, 3 is a new numerator: 2 in 10, 5 times, 5 is a new denominator.

10. Reduce each of the following fractions to its lowest terms. 16. 15. 12. 12. 12. 12. 19.

4

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11. Stephen's knife cost of a dollar, and John's cost of a dollar. Whose knife cost the most?

12. Reduce the fractions, and 10 to their lowest terms, and then add them together.

36

and 13.
and 25.

4

20

13. Reduce, and then add together, 16
14. Reduce, and then add together, 2

SECTION 27.

1. of a water melon was divided equally among 3 boys. What part of the whole melon did 1 boy receive?

2. ofis equal to

what

part of 1?

Solution. If be divided into 3 equal parts, it will take 12 such parts to make a whole one.

ofis times is 12]

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3. What part of a whole one is of ?

Therefore,

Illustration. If of an orange were cut into 5 equal parts, it would take 6 times 5 such parts to make

whole orange.

Operation. times is yo

3

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