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print 500 copies of a book containing 336 pages, allowing 2 quires of waste paper in each ream?

Ans. 24 reams 5 quires 12 sheets. 9. A farmer wishes to divide 108 acres into 8 equal fields: how much will there be in each field?

Ans. A. R.

10. Out of a pipe of wine, a merchant draws 12 bottles, each containing 1 pint 3 gills: he then fills six 5 gallon demijohns; then he draws off 3 dozen bottles, each containing 1 quart 2 gills: how much remained in the cask? Ans. 82gal. 1pt.

11. A man lends his neighbor £135 6s 8d and takes in part payment 4 cows at £5 8s apiece, also a horse worth £50: how much remained due? Ans. £ S. d. 12. A farmer has 6T. 8cwt. 2qr. 147b. of hay to be removed in 6 equal loads: how much must be carried at each load? Ans. 1T. 1cwt. 1qr. 21lb.

13. A person at his death left landed estate to the amount of £2000, and personal property to the amount of £2803 17s 4d. He directed that his widow should receive one eighth of the whole, and that the residue should be equally divided among his four children. What was the widow's and each child's portion?

Ans. Widow's portion

£600 9s 8d. Each child's portion £1050 16s 11d.

OF VULGAR FRACTIONS.

(Before proceeding farther let the pupil study carefully from $42 to Denominate Numbers.)

SECTION I.

1. If a unit be divided into two equal parts, what is each part called? How do you express one of the parts?

2. If a unit be divided into three equal parts, what is each part called? How do you express one of the parts? How do you express two of them? How do you express three of them?

3. If a unit be divided into four equal parts, how do you express one of the parts? Two of the parts? Three of the parts? Four of the parts?

4. How many halves are there in one thing? How many fourths or quarters are there? How much greater is a half than a quarter?

5. If a unit be divided into five equal parts, what is each part called? How do you express three of the parts? Four of them? Five of them?

6. If a unit be divided into six equal parts, what is each part called? How do you express one-sixth? How do you express two of the parts? Three of them? How do you express six of them?

7. How many thirds are there in a unit? How many sixths are there? How much greater then is one-third

than one-sixth?

8. If a unit be divided into seven equal parts, what is each part called? How do you express one part? Two parts? Four parts? Six parts? Seven parts?

9. If a unit be divided into eight equal parts, what is each part called? How do you express four of the parts? Five of them? Six of them? Seven of them? Eight of them?

10. How many fourths or quarters are there in a unit? How many eighths are there? How much greater, then, is a quarter than an eighth? How many eighths are equal to two quarters? How many to three quarters ?

11. If a unit be divided into nine equal parts, what is each part called? How do you express one part? Two parts? Four parts? Six parts? Nine parts?

12. If a unit be divided into ten equal parts, how do you express one of the parts? How do you express two of them? Ten of them?

13. How many fifths are there in one unit? How many tenths are there? How much greater is a fifth than a tenth? How many tenths are equal to two-fifths? How many tenths are equal to four-fifths? To five-fifths?

14. If a unit be divided into eleven equal parts, what is each part called? How do you express one of the

parts? Two of them? Four of them? Six of them? Seven of them? Eleven of them?

15. If a unit be divided into twelve equal parts, what is each part called? How do you express it? How do you express five of the parts? Six of them? Twelve of them?

16. How many sixths are there in one unit? How many twelfths are there? How much greater is a sixth than a twelfth? How many twelfths are equal to twosixths? How many to three-sixths? To four-sixths? To five-sixths? To six-sixths?

17. What is the half of one-half? What is the half of one-third? What is the half of one-fourth? What is the half of one-fifth? What is the half of one-sixth?

18. What is the sum of one-half and one-half? What is the sum of one-third and one-third? What is the sum of one-third and two-thirds?

19. What is the sum of one-fourth and two-fourths? Of one-fourth and three-fourths? Of two-fourths and two-fourths?

20. What is the sum of one-fifth and two-fifths? What is the sum of one-fifth and three-fifths? Of two-fifths and three-fifths?

21. What is the sum of one-sixth and four-sixths? What is their difference? What is the sum of three-sixths and two-sixths? What is their difference?

22. What is the sum of one-seventh and four-sevenths? What is their difference? What is the sum of five-sevenths and two-sevenths? What is their difference?

23. What is the difference between five-eighths and three-eighths? What is their sum? What is the difference between six-eighths and one-eighth? What their sum?

24. What is the difference between seven-ninths and two-ninths? What is their sum? What is the difference between four-ninths and three-ninths? What is their sum?

25. What is the difference between one-tenth and sixtenths? What is their sum? What is the difference between six-tenths and four-tenths? What is their sum?

26. What is the difference between one-eleventh and four-elevenths? What is their sum? What is the difference between three-elevenths and eight-elevenths? What is their sum?

27. What is the sum of three-twelfths and six-twelfths? What is their difference? What is the sum of five-twelfths and seven-twelfths? What is their difference? What is the sum of eight-twelfths and four-twelfths? What is their difference?

28. How many halves are there in one? How many thirds? Fourths? Sevenths? Elevenths? Twelfths? 29. How many halves are there in two? How many thirds? Fourths? Fifths? Sixths? Sevenths? Twelfths? 30. How many thirds are there in three? How many fourths? Fifths? Sixths? Tenths? Twelfths?

31. How many fourths are there in four? How many fifths? How many sixths? How many sevenths? Eighths? Ninths? Twelfths?

32. How many sixths are there in five? sevenths? How many eighths? How many Twelfths?

33. How many sixths in nine? ten? How many elevenths in six? In eight?

How many

How many elevenths?

How many twelfths in seven, how many

In

y?

34. How many twelfths in two? In four, how many? In five? How many ninths in five? In eight? In ten? In eleven? In twelve?

35. How many whole units in two halves? In four halves? In five halves? In seven halves?

halves?

In nine

36. How many whole units are there in three-thirds? In six-thirds? In nine-thirds? In five-thirds? In eightthirds? In eleven thirds?

37. How many whole units are there in four-fourths? In six-fourths? In eight-fourths? In eleven-fourths? In sixteen? In twenty-nine? In thirty-six fourths?

38. How many whole units are there in five-fifths? In eight-fifths? In nine-fifths? In twelve-fifths? In twenty fifths? In twenty-six fifths? In twenty-eight fifths? 39. How many whole units are there in six-sixths? In

twelve-sixths?

In fifteen-sixths? In eighteen-sixths? In twenty-five sixths? In twenty-six sixths? In thirtyseven sixths?

40. How many whole units are there in seven-sevenths? In fourteen-sevenths? In nineteen-sevenths? In twentynine sevenths? In thirty-five sevenths? In forty-two sevenths?

41. How many whole units are there in eight-eighths? In twenty-four eighths? In sixteen eighths? In thirty eighths? In thirty-four eighths? In forty eighths?

42. How many whole units are there in nine-ninths? In eighteen ninths? In twenty-four ninths? In thirtyfive-ninths? In forty-five ninths ?

43. How many whole units are there in ten-tenths? In twenty tenths? In thirty tenths? In forty-five tenths?

In sixty tenths?

44. How many whole units are there in eleven-elevenths? In twenty-two elevenths? In thirty-three elevenths? In forty-four elevenths? In sixty elevenths? In sixty-seven elevenths?

45. How many whole units are there in twelve-twelfths? In twenty-four twelfths? In twenty-six twelfths? In forty-eight twelfths? In fifty twelfths? In sixty twelfths?

46. What is the sum of one-half and one-fourth? What is the sum of one-half and three-fourths? Of threefourths and six fourths?

47. What is the sum of one-third and one-sixth? (How many sixths is one-third equal to?) What is the sum of two-thirds and five-sixths? Of one-third and five sixths?

SECTION II.

§ 77. There are five kinds of Vulgar Fractions, Proper, Improper, Simple, Compound, and Mixed.

A PROPER FRACTION is one in which the numerator is less than the denominator. The value of every proper fraction is less than 1. (See § 44.)

The following are proper fractions:

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