1 is of 6, and is of, or of 6. Therefore is of 6.

is of, and or 1 is 3 times, or of ; and is 1⁄2 times, or of 3. Therefore § is 1§ of §.

85. To find a number when a fractional part is given.

1. 12 is of what number?

If of the required number is 12, 6 sixths, or the number, is 6 times 12, or 72.

From this solution we derive the following

RULE.

Divide the first number by the second.

86.-1. If 9 oranges cost 22 cents, what will 13 oranges

cost?

PROCESS.

9 cost 22 cents,

1 cost 2 cents,

13 cost 13 x 2 = 32 cents.

If 9 oranges cost 22 cents, 1 orange will cost of 22 cents, or 2 cents; and 13 oranges will cost 13 times 2 cents, or 32 cents.

2. If 7 bushels of apples cost $43, what will 11 bushels cost?

3. If 11 yards of calico cost 483 cents, what will 33 yards

cost?

4. What will 15 hats cost, if 12 hats cost $40%?

5. If 16 cows cost $320, what will 24 cows cost at the same rate?

6. What will 9 barrels of flour cost, if 18 barrels cost $1134?

7. What will 100 pigs cost, if 42 pigs cost $1361⁄2?

8. If of a barrel of oil cost $3.20, what will a barrel cost?

9. If 7 of a ton of coal cost $7.70, what will a ton cost?

10. If of the cost of a horse is $120, what will 12 horses cost at the same rate?

11. What will 21 acres of arable land cost, if 4 acres cost $360?

12. M bought 32 cords of wood at the rate of 63 cords for $44; what did it cost?

13. What will 80 bushels of potatoes cost at the rate of 12 bushels for $10?

14. What will a farm of 120 acres cost at the rate of 8 acres for $515?

15. If 10 yards of muslin cost $1.20, what will of a yard 2383 cost?

16. If 8 barrels of apples cost $48, what will of a barrel cost?

17. If 12 pounds of beef cost 62 cents, what will 60 pounds cost?

18. What must I pay for 423 tons of coal, if 121 tons cost $37?

19. What will 100 bushels of wheat cost at the rate of 5 bushels for $6?

20. If of an acre of land cost $80, what will of an acre cost?

21. If 63 pounds of sugar cost 40 cents, what will 83. pounds cost?

22. A sold of his land, and had 415 acres remaining; how many acres had he at first?

23. B withdrew of his money from bank, and still had $4160 on deposit; what was his original deposit?

24. C sold of his cattle, and had 161 remaining; how many had he at first?

MISCELLANEOUS EXAMPLES.

1. Reduce 24374 to a mixed number.

315

2. Reduce 421 to an improper fraction. 3. Reduce to its lowest terms.

952

5

4. Arrange in order of magnitude 7, §, 11. 5. Multiply by 17.

17. Reduce 35 to a fraction having 101 for a denominator.

19. Reduce 6254 to an improper fraction.

20. Reduce to 1098ths.

21. What is the value of 47

(165 - 148)?

22. Multiply of 4,8 of 6,

by 17.

23. of is 1 of what number?

24. Divide 144 by 17.

25. Divide 126 by 13.

32.

26. Reduce 402 to an improper fraction.

27. 15 is of 5 of what number?

28. Reduce, 8, 11, 13, and to a common denominator.

32. Divide 72 by 3 of 2 of 1.

33. Reduce 574o to a mixed number.

34. Add 3, 3, 3, and §.

35. Subtract of 18 from 100.

36. Multiply 193 by 672.

37. Divide 12 by 311.

38. Add 37%, 43, 57, and 35.

39. Reduce 8165, to an improper fraction.

40. Find the value of (163 +144) × 7.

41. Add,,, 1%, and 11.

42. Subtract 8615 from 1006.

43. Multiply 10205 by 1278.

44. Divide 40211 by 271.

45. Reduce 15 to 786ths.

46. of 43 is of what number?

47. What is g of of 4?