CHAPTER VIII.

DIVISION OF FRACTIONS.

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SECTION I.

1. How many fourths of a yard in 4 yards? 2. How many in 4 and 1 fourth? 3. How many in 5 and 2 fourths?

4. How many thirds of an inch in 3 inches? 5. How many in 5 inches and 2 thirds? 6. How many twelfths of a foot in 3 feet? 7. How many in 4 feet and 3 twelfths? 8. How many tenths of a dollar in 1 dollar? in 1 dollar and 7 tenths?

9. How many sixths in 4 dollars and 5 sixths? 10. How many days in 1 week and 4 sevenths of a week?

11. How many shillings in 2 dollars and 4 sixths of a dollar?

12. How many farthings in 2 pennies and 2 fourths?

13. How many feet in 2 yards and 2 thirds? 14. How many quarts in 3 gallons and 3 fourths?

15. How many ounces in 2 pounds and 4 sixteenths?

16. How many ounces in 3 pounds and 8 sixteenths?

17. How many barley-corns in 3 inches and 2 thirds ?

18. How many eggs make 1 dozen and 1 half?

19. There are 24 sheets in a quire of paper; how many sheets in 1 quire and 1 half?

20. How many furlongs in 1 mile and 2 eighths?

21. How many furlongs in 1 mile and 1 half? 22. How many furlongs in 2 miles and 1 fourth? 23. How many yards in 2 rods?

24. How many yards in 3 rods?

25. How many 9-pences in 1 dollar and 1 half? 26. How many 9-pences in 1 dollar and 1 quarter?

27. How many 3-pences in 1 shilling and 1 half?

28. In 8 shillings and 1 sixth, how many pence?

29. In 4 dollars and 1 third, how many shillings?

30. In 5 yards and 1 half, how many quarters ? 31. In 2 ells English and 2 fifths, how many quarters ?

32. In 3 ells Flemish and 2 thirds, how many quarters ?

33. In 4 ells French and 1 half, how many quarters?

34. 2 inches and 1 fourth make 1 nail; how many fourths of an inch in 2 nails?

35. Solomon made 2 cherubim for the temple, each 10 cubits high; (a cubit is 1 foot and 1 half) how many feet high were the cherubim ?

36. The wings of the cherubim were each 5 cubits; how many feet?

37. The molten sea in the temple at Jerusalem was 10 cubits from one brim to the other; how many feet!

38. It was 5 cubits high; how many feet? 39. The waters of the deluge rose 15 cubits above the highest hills; how many feet?

40. 20 quires of paper make 1 ream; how many quires in 1 ream and 2 fifths?

SECTION II.

1. 1 half is how many fourths?
2. 1 third is how many sixths?

3. A spider has 6 eyes; what is 1 third of them? 1 sixth? How many sixths in 1 third?

4. Byron lived 36 years; what is 1 twelfth of his life? I sixth? How many twelfths make 1 sixth ?

5. The Revolutionary war continued 8 years; what is 1 half of it? 1 fourth? How many fourths make 1 half?

6. John Urquhart lived 18 years; what is 1 third of his life? 1 ninth? How many ninths make 1 third?

7. Xerxes the Great reigned 21 years; what is 1 third of his reign? 1 seventh? How many thirds make 1 seventh?

8. Cincinnati has a population of 24 thousand; what is 1 fourth? 1 eighth? How many eighths make 1 fourth?

9. Albany has a population of 24 thousand; what is fourth of it? 1 twelfth? how many twelfths make 1 fourth?

10. New Haven has a population of 10 thousand; what is 1 half of it? 1 tenth? How many tenths make 1 half?

11. A cat lives 15 years; what is 2 thirds of it?

12. George IV. reigned 10 years; what is 2 fifths of it? 3 fifths? How many fifths make 1 half?

13. Alfred the Great reigned 28 years; what is 1 seventh ? 3 sevenths? how many sevenths equal 1 half of his reign? (App. A.)

14. George III. reigned 60 years; what is 1 fifth of his reign? 2 fifths? 4 tenths?

15. Mont Blanc is 15 thousand feet high; what is 1 fifth of it? 2 thirds?

16. Dofrafield Mountains are 8 thousand feet high; what is 3 fourths of the height?

17. Cotopaxi is 18 thousand feet high; what is 4 ninths of the height?

18. Mount Olympus is 6 thousand feet high; what is 1 third of 1 half the height?

19. 1 third of I half is what part of the whole? 20. The Snow Mountains of Africa are 10 thousand feet high; what is 1 fifth of 1 half the height?

21. Lake Wenner is 80 miles long; what is 1 half of 1 tenth of it?

22. How much is 1 fourth of 1 half dollar? 23. What is 1 fourth of 1 fourth of a yard? 24. What is 1 half of 6 twelfths of a foot? 25. What is 1 third of 1 half yard?

26. What is 2 thirds of a half dollar? 27. Jupiter revolves about the sun in 12 years; what is 1 half of 1 third of the time?

28. Saturn revolves in 30 years; what is 1 half of 1 fifth of the time?

29. Herschel revolves in 84 years; what is 1 half of 1 seventh of the time?

30. A stone falls 16 feet in one second; what is 1 fourth of 1 fourth of it?

31. The Earth has a diameter of 8 thousand miles; what is 1 third of 3 fourths of it?

SECTION III.

Compound Fractions, and Simple Multiplication. 1. 2 thirds of 1 sixth of John Urquhart's age is 2 years; what is the whole age?

2. 1 half of 1 seventh of the duration of the Peloponnesian war is 2 years; how long did it continue?

3. 1 half of 1 fourth of the American Revolu tion is 1 year; how long did it continue?

4. I half of 1 sixth of the duration of the three Punic wars is 4 years; how long did the Punic wars continue?

5. 1 third of 1 half of the reign of Alexander the Great is 2 years; how long did he reign? 6. 1 half of 1 fourth of the life of Alexander the Great is 4 years; how long did he live?

7. 1 fourth of 1 sixth of the age of Moses is 5 years; how old was Moses when he died?

8. 1 half of 1 fifth of the age of Joshua is 11 years; at what age did he die? (App. B.)

9. 1 fourth of 1 fourth of the whole length of the Jordan is 10 miles; how long is the Jordan? 10. 1 third of 1 fifth of the width of the Jordan is 2 yards; how wide is the river?