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What part

2. Of 54 is 9 ?
3. Of 75 is 15 ?
4. Of 84 is 77 ?
5. Of 100 is 20 ?

6. Of 100 is 75 ?
7. Of 100 is 40?
8. Of 168 is 147 ?
9. Of 132 is 24?

10. What part of 6 is ?

1 is 4 of 6, and is of ļ, or s of 6. Therefore if is į of 6.

What part-
11. Of 8 is ?

15. Of 100 is 621?
12. Of 9 is?

16. Of 100 is 831? 13. Of 12 is ?

17. Of 125 is 12; ? 14. Of 100 is 163 ?

18. Of 80 is ? 19. What part of j is ? } is į of s, and for 1 is 3 times ), or of s; and is times , or if of k. Therefore & is it of s. What part20. Of is ?

24. Of 41 is 38 ? 21. Of 11 is 24?

25. Of 124 is 8? 22. Ofis ?

26. Of 373 is 2į? 23. Of is it?

27. Of 407 is 10}?

CASE II.

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.

2. 120 is { of what number? 3. 150 is of what number? 4. 62 is in of what number? 5. 124 is of what number? 6. 374 is ils of what number? 7. Ğ is zo of what number? 8. 60 is of what number? 9. 120 is of what number? 10. 17 is g of what number? 11. 101 is } of what number? 12. f is of what number? 13. 41 is of what number? 14. 183 is 3 of what number? 15. 663 is of what number? 16. 62: is of what number? 17. 871 is of what number?

ARITHMETICAL ANALYSIS.

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WRITTEN EXERCISES. 86.-1. If 9 oranges cost 222 cents, what will 13 oranges cost ? PROCESS.

If 9 oranges cost 221 cents, 1 orange 9 cost 227 cents,

will cost ģ of 22} cents, or 21 cents; 1 cost 21 cents,

and 13 oranges will cost 13 times 21 13 cost 13 x 24 = 322 cents. cents, or 321 cents.

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

3. If 11 yards of calico cost 48} cents, what will 33 yards cost?

4. What will 15 hats cost, if 12 hats cost $404 ?

5. If 16 cows cost $3203, what will 24 cows cost at the same rate?

6. What will 9 barrels of four cost, if 18 barrels cost $1137?

7. What will 100 pigs cost, if 42 pigs cost $1364 ?

8. If 4 of a barrel of oil cost $3.20, what will a barrel cost ?

9. If 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 41 acres cost $360?

12. M bought 32 cords of wood at the rate of 6; cords for $44; what did it cost?

13. What will 80 bushels of potatoes cost at the rate of 121 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 s of a yard. cost?

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

17. If 12 pounds of beef cost 622 cents, what will 60 pounds cost ?

18. What must I pay for 42 tons of coal, if 12j tons cost $37 ?

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

20. If of an acre of land cost $80, what will 15 of an acre cost?

21. If 63 pounds of sugar cost 405 cents, what will 81. pounds cost?

22. A sold 4 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 i of his cattle, and had 161 remaining; how many had he at first ?

MISCELLANEOUS EXAMPLES. 1. Reduce 24374 to a mixed number. 2. Reduce 42131 to an improper fraction. 3. Reduce it is to its lowest terms. 4. Arrange in order of magnitude ], ā, jt. 5. Multiply it by 17. 6. Divide 43 by 22. 7. Add i, ii, if, and 1 i. 8. Subtract 1824 from 34718. 9. Find the value of 33 X 43 X 4tí: 10. Reduces to its lowest terms.

24 X 33 X 65 11. Simplify

363. X 8 X 169

12. Find the value of (8} – 23) X 81.
13. Add 8 , 91, 105, and 11ų.
14. Divide 143 by 73.
15. Subtract 100911 from 200118.

3 + 5 16. Reduce to a simple fraction.

of s

17. Reduce 35 to a fraction having 101 for a denominator. 18. Reduce 13:} to its lowest terms. 19. Reduce 6254 to an improper fraction. 20. Reduce 11 to 1098ths. 21. What is the value of 47 = (165 – 14) ? 22. Multiply 343 of 4 of 61: by 12. 23. of g is 1% of what number? 24. Divide 144 by 17. 25. Divide 126 by 13%. 26. Reduce 40232 to an improper fraction. 27. 16 is şof is of what number? 28. Reduce ș, s, il, is, and it to a common denominator.

29. Simplify

41 + 39 – 21.

7j - 33 + 2

75 30. Add 59, 4, and 4.

63.

31. Multiply 14; by

84 32. Divide 72 by of al of 11. 33. Reduce 5740 to a mixed number. 34. Add 3, 4, 5, and . 35. Subtract of 18ą from 100. 36. Multiply 193 by 67 12. 37. Divide 12 by 311. 38. Add 376, 439, 573, and 35. 39. Reduce 816 11 to an improper fraction. 40. Find the value of (16} + 141) X 3. 41. Add , , 8, 16, and 11. 42. Subtract 861, from 10064T. 43. Multiply 10202 by 1275. 44. Divide 4021 by 279. 45. Reduce 1 to 786ths. 46. 4 of 4; is ã of what number? 47. What is 5 of of 4; ?

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50. Simplify

3} +6} – 70+ 5.1.

416 -23 + 63 - 13 51. Simplify

(31 X 2) + (6] x 48). (163 + 1]) – (83 + 1})

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