LESSON CXXIII.

1. When the numerator and denominator of a fraction are equal, the value of the fraction is equal to 1; as =1; 4=1; f=1, etc.

2. When the numerator is greater than the denominator, the value is greater than 1; as 4=13; =2, etc.

3. A whole number and a fraction written together are called a Mixed Number; as 5, read 5 and 3 fourths. 4. Read the following mixed numbers:

3; 9; 7; 10; 87; 12; 14; 51. 5. How many fifths are 43?

SOLUTION,-Since in 1 there are 5 fifths, in 4 there are 4 times 5 fifths, or 20 fifths, and 3 fifths added make 23 fifths. Hence 4ğ are 23.

6. How many fourths are 91? 7. How many thirds are 12?

are 7? Fourths are 104?

Are 7? Are 82 ?
Fifths are 64? Sixths

8. Change 4 to eighths; 94 to sevenths; 8 to tenths; 53 to ninths; 4 to twelfths.

9. How many ones are 12?

SOLUTION.-Since 4 fourths equal 1, 12 fourths are as many 1's as 4 fourths are contained times in 12 fourths, or 3 times. Hence are 3 ones or 3. Or 42=12÷4=3.

10. Find the value of 15; of 18; of 21; of 28; of 36. 11. Change to a whole or a mixed number 30; 21; 36; 42; 8; 45; 37; 99.

57

12. What is the value of 44? 50? 78? go? f7 ? zo? 13. Find the value of ; ff; 84; 1 §; 100.

66

LESSON CXXIV.

1. How many are 2 fifths and 3 fifths?

Ans. 5 fifths, or §=1.

2. Can you add 3 apples and 5 figs? Why not? 3. Can you add 3 fourths and 5 sixths? Why not? 4. Only fractions having the same denominator can be added.

5. How many are 3+?

Ans. 10=13.

6. What is the sum of and ? of and? Of and ? Off and †?

7. Add

and 1% and 1

and 3. and §.

8. How many are 7 ninths less 2 ninths?

Ans. 5 ninths, or §.

9. Can you take 6 books from 9 slates? Why not? 10. Can you subtract 6 sevenths from 9 twelfths? Why not?

11. Only fractions having the same denominator can be subtracted.

12. How many are 3-?-?

13. Subtract from §. from

14. How many are +++§.

-? H
from 1.

14

?

Ans. 18=24.

Ans. 13-15.

15. How many 1's are +1+3+8+4?.

16. From ++ take 3.

18. John spent of his money and lost of it. What 용

part of his money had he left?

19. James paid of a dollar for a book, and of a dol

lar for a slate. How much did he pay for both? How much more for the book than for the slate?

LESSON CXXV.

1. If a cake is cut into 12 equal pieces, what part of the whole cake is each piece?

2. How many twelfths make a whole thing?

3. How do we find 1 twelfth of any number?

Ans. One-twelfth.

4. If a cake is divided into 3 equal parts, each part is called 1 third.

5. If each third of the cake is divided into 4 equal parts, into how many parts is the whole cake divided?

6. How many twelfths in 1 third? In 2 thirds? 3 thirds? 7. If a cake is cut into 4 equal parts, each part is called 1 fourth.

8. If each fourth of the cake is di

vided into 3 equal parts, into how many parts is the whole cake divided?

9. How many twelfths in 1 fourth? In 2 fourths? In 3 fourths? In 4 fourths?

10. If Edie has

have both? 1+1

of a cake and Asa of it, what part

= ?

SOLUTION. Since is equal to †, and is equal to, they have the sum of and 12, or 12.

11. How much more has Edie than Asa?

-1=?

12. How many twelfths in? In? In? In? In ? 13. Which is greater or ? or? for?

14. If Mary has, and Jennie of a melon, what part of the whole melon have both?

LESSON CXXVI.

1. Draw lines upon the slate or board of equal length, and divide them into 12 equal parts.

2. By a heavier mark these lines may be divided into halves, thirds, fourths, and sixths, respectively.

3. Hence, it is plain that halves, thirds, fourths, sixths, and twelfths, may be added or subtracted when changed to parts of equal size or magnitude.

When fractions have different denominators, they must be changed to fractions of like value, having the same denominators, before they can be added or subtracted.

LESSON CXXVII.

1. 4 is of what number?

SOLUTION.-Since 4 is 1 half of a number, 2 halves or the num.

ber are 2 times 4, or 8. Hence 4 is of 2 times 4, or 8.

8. If of a ton of coal cost 2 dollars, what will 1 ton cost? 9. George gave a beggar 6 cents, which was of all the money he had; how much money had he?

10. If of a pound of coffee cost 8 cents, what will of a pound cost?

SOLUTION. Since 1 fourth of a pound costs 8 cents, 3 fourths of a pound will cost 3 times 8 cents, or 24 cents.

11. If of a bushel of pears cost 9 cents, what will of a bushel cost?

12. In of a dollar are 10 cents; how many cents in of a dollar?

· 13. If a man walk 6 miles in of a day, how many miles can he walk in 1 day?

14. A pencil cost 8 cents, which was the cost of a book; what was the cost of the book?

15. If of a melon cost 7 cents, what will § of it cost? 鲁

16. If of a barrel of flour is worth 2 dollars, what is § of a barrel worth? What is a whole barrel worth?