Express as common fractions in smallest terms:

13. 10%; 12 %; 25 %.

16. 663 %; 75%; 80%.

14. 33%; 37%; 50%.

17.

125 %; 150%; 200 %.

15. 163 %; 62%; 833 %. 18. 40%; 60%; 14 %.

Change the following fractions to hundredths:

19. ;;; }; Į; t ; Į; J.

20. ; ; ; ; 20; 25; 30.

21.3; 7; 7; 8; &; &; 4.

22. ; ; ; Po; Pe; 20; 30; 80

The Base and the Rate given, to find the Percentage.

ORAL EXERCISES.

25. What is 5% of $4?

Solution. As 5% is 150, 5% of $4 is 15, or 1, of $4, which is $0.20.

26. What is 4 % of $40? 6% of $44? 3% of $400 ? 27. What is 8 % of 200? Of 500? Of 700? Of 600 ? 28. What is 10 % of 90 yards? 12% of 72 miles ? of a cubic yard?

29. What is 20 %

5% of an acre? 30. What is 163 % of a day? Of a foot?

Of a gross?

31. What is 3% of a ton? 75% of it? of it?

32. How many square inches in 663 % of a square foot? 33. What is the difference between of a mile and % of a mile?

Or,

240. The Amount is the base plus the percentage.

241. The Difference is the base less the percentage.

WRITTEN EXERCISES.

34. What is 37% of $8.24?

$8.24 0.37 $3.09

1.0 3

=

$8.74 x = $3.09

Solution. As 37% is 0.371⁄2, or 8, 371% of $8.24 is 0.37 times $8.24, or of $8.24, which is $3.09.

35. A's money is $2575. If by trading he should increase it by 40%, how much would he then have?

36. A's income is $1890. If he should spend 83% of it, how much would he have left?

242. Rule for finding the Percentage.

Multiply the base by the rate per cent.

Let b represent the base, r the rate per cent, p the percentage, a the amount, and d the difference, we have the

45. Johnson bought a house for $4850, and paid down.

15%.

How much did he then owe for it?

46. A merchant sold goods which cost him $9675.75, at a profit of 16%. How much did he get for the goods?

How

47. Bought a bill of goods amounting to $186.80, and for cash payment obtained a deduction from it of 5%. much was the deduction?

48. How many persons are engaged in agriculture, when they constitute 24% of a population of 61450?

49. How much bank currency could be bought for $4500, in coin, in 1864, when gold was at 285%?

50. A man having $8550 bequeathed 33% to his wife and the remainder to his children. How much did he give his

children?

51. A bought goods to the value of $345.75, and sold them to B at 15% advance on his outlay, and B sold them to C at 15% less than his outlay. How much did C give for them?

Base and Percentage given, to find the Rate per cent

ORAL EXERCISES.

52. What per cent of 12 is 3?

Solution. -3 is of 12; and, or 0.25, or 25%.

53. What per cent of $35 is $7? Is $14? Is $28? 54. What per cent of 24 is 6? Is 12?

What per cent

Is 18?

55. Of 42 miles is 21 miles ?

58. Of $6 is $4.50?

56. Of 75 tons is 45 tons?

59.

Of $64 is $ 40?

57. Of 48 pounds is 30 pounds? 60. Of $ 96 is $36?

61. If 4 quarts of grain are given for grinding a bushel, what per cent is the cost of grinding?

62. John earns each week $7.50. He spends for board $2.50, and as much more for other things. What per cent of his earnings are his spendings?

64. What per cent of 600 bushels is 57 bushels?

121% of 128.

243. Rule for finding the Rate per cent.

Divide the percentage by the base, extending the division to

73. Of a farm containing 1640 acres there are 246 acres in meadow. What per cent is in meadow?

74. If the income on $1346 is $168.25, what is the rate?

Rate and Percentage given, to find the Base.

ORAL EXERCISES.

75. $25 is 5% of my money.

.

How much have I ?

Solution. As $25 is 5% of my money, 1 % of my money is of $25, or $5; 100 % of my money must be 100 times $ 5, or $500. Or, As $25 is 5%, or of my money, 28 of my money must be 20 times $25, or $500.

76. $6 is 20% of what number? 40 rods is 12% of what number?

77. 1 pound 4 ounces is 25% of how many pounds?

78. A number increased by 25 % of itself is 60. What is the number?

Solution. As a number increased by 25 % of itself must be 125 %, or of itself, 60 must be of the number, and 4, or the number, must be 48.

79. Sold a watch for $55, which was 10% above its cost. What was its cost?

80. 42 is 33% less than what number? 33% more than what number?

Or, as $3550 is 25 %, or of the number, the number must be four times $3550, or $14200.

82. $16.22 is 5 % of what number?

83. Having sold 40% of my sheep, I have 177 left. What number had I at first?

244. Rule for finding the Base.

Divide the percentage by the rate per cent.

FORMULAS. b = p÷r. b = a ÷ (1+r). b = d÷ (1 − r).

90. I burned 1750 lb. of coal, or 25% of my supply, in a

single week. How much had I?

concert were 40% of the What were the expenses?

91. The expenses of a charity receipts. The poor received $ 250. 92. An agent's salary having been decreased 33% is now $1600. What was it at first?

93. A man owes $ 6750, which is 75% as much as he is worth. How much is he worth?

94. The voters of a certain city number 16386, which is 20% more than the number 3 years ago. What was the

number then?