50. PROOF. Add the subtrahend and the remainder together, and the sum should be the minuend.

NOTE. This proof rests upon the self-evident truth, that the whole of a thing is equal to the sum of all its parts; thus, the minuend is separated into the two parts, subtrahend and remainder; hence the sum of those parts must be the minuend.

(45.)

(5) (9) (12) Minuend, 6 0 2 Subtrahend, 4 3 8

Remainder, 1 6 4

Here we cannot take 8 from 2, nor can we take from the tens' place, as there is 0 there; but we can take one of the 6 hundreds and separate the one hundred into 9 tens and 10 units; then, putting the 9 tens in the place of tens

and adding the 10 units to the 2 units, we can subtract 8 from 12, 3 from 9, and 4 from 5.

52. From 704 take 586.

53. From 876.4 take 32.89.

54. From 72068 take 36819. 55. Subtract 3247 from 8604.

56. Subtract 610.847 from 9476.728.

57. Subtract 2376948 from 9000000. 58. Take 78.604 from 754.29.

59. Take 2879046 from 9287406. 60. How many are 4236 less 1684 ?

61. How many are 98647 less 52046 ?

62. 74.98-43.68=?

63. 8274-4293=?

64. The difference between two numbers is 536, and the greater number is 768; what is the less?

65. What number added to 8763 will give 9764?

66. What number taken from 7284 leaves 4378?

67. From 875.8 take 87.886.

68. From 8948.71 take 2981.7814.

69. From $257.57 take $175.89.
70. From $7788.40 take $5999.99.
71. From 8654.78 take 334.986.
72. From 4168.946 take 683.78.

73. From 8469.762 take 2754.892.

74. From 4021.876 take 2174.941.

75. From one thousand eight hundred seventy-six, and decimal three hundred sixty-four thousands, take eight hundred sixteen, and decimal three hundred three thousandths.

76. From ten take six thousandths.

77. A man owned eighty-seven hundredths of a railroad and sold forty-eight hundredths of it; what part of the road did he still own?

78. If a man owes $87.55 and pays $ 69.78, how much does he still owe?

79. If a man sells his farm for $ 2763, and pays $1975.55 for a house and garden in the village, how much of this money has he left?

80. Of 1368 prisoners in the State Prison at Auburn, N. Y., 919 are under 30 years of age; how many are over 30 years of age?

81. Above the junction of the Missouri and Mississippi Rivers, the Missouri drains 518000 square miles and the Mississippi 169000 square miles. How many more square miles, above their junction, does the Missouri drain than the Mississippi?

82. From five million eight thousand four, and four thousandths, take three hundred fifteen thousand eight hundred six, and seven hundredths.

83. How many years from the discovery of America, 1492, to the birth of Washington, 1732?

84. If a merchant commences business with $3575.44 and retires with $10847.13, how much does he make?

85. The number of inhabitants in Massachusetts in 1870 was 1457351, and in Vermont 330551; how many more in Massachusetts than in Vermont?

86. If a man sells a factory which cost him $9784.85 for $13378.25, what does he gain?

87. In 1870 the population of the United States was 38555983, and in 1840 it was 17063353; what was the increase in 30 years?

88. A borrowed of B $ 876.55, and paid $598.78; how much remained due?

89. Subtract 4987.54 from 18745.6. 90. Subtract $253.97 from $ 431.23.

91. Take 217.657 from 413.2.

92. Take $874.23 from $1000.

93. How many are 8764-7985 ?

94. How many are 234.56-87.678 ?

95. The distance of the sun from the earth is about 92000000 miles, and of the moon 240000; how much farther from the earth is the sun than the moon?

96. The area of Texas is 274356 square miles, and of the six New England States 68348 square miles. Find by subtraction how many sections as large as New England can be cut out of Texas.

oners.

Miscellaneous Examples.

97. In the Auburn (N. Y.) State Prison there are 1368 prisOf these 51 have had an academical education, 16 a collegiate, 12 a high-school, 646 a common-school, 270 can only read and write, 187 can read only, and the rest have had no education. How many have had no education?

98. From their junction to their sources the Missouri River has a length of 3047 miles and the Mississippi 1330 miles, and from their junction to the Gulf of Mexico it is 1656 miles. How much longer is the Missouri from its source to the Gulf than the Mississippi?

99. Bought a barrel of flour for $9.50, four meters of cloth for $2.75, 8 kilos of sugar for $2.15, a gallon of syrup for $0.96, and 2 dozen of eggs for $0.48, and gave in payment a ten and two five dollar bills. How much change ought I to

receive back?

100. The area of Maine is 35000 square miles; New Hampshire, 9280; Vermont, 10212; Massachusetts, 7800; Rhode Island, 1306; Connecticut, 4750. How much greater is Maine than the other five States together?

101. If I am 783 kilometers from home Monday morning, and travel towards home 137 kilometers Monday, 143 Tuesday, 153 Wednesday, 148 Thursday, how many kilometers from home shall I be Thursday night?

in

102. If I have on deposit in one savings-bank $984.43, another $ 876.84, and in another $ 698.17, how much more must I borrow to enable me to build a house worth $4375?

103. If 87654 is the sum of three numbers of which two are 17896 and 25683, what is the other number?

104. Mr. Roe has cash to the amount of $ 276.87, but owes Mr. Doe $37.44, Mr. Lowe $137.15, and Mr. Poe $87.18. After paying these debts, how much will Mr. Roe have left?

105. Four men, A, B, C, and D, commencing business together, furnished money as follows: A, $2475; B, $ 3475; C, $2850; and D, $ 4500. At the end of a year they closed business, having lost $3225; how much money had they to divide between them?

106. During the year ending June 30, 1877, the value of the issue of ordinary postage stamps by the post-office department was $1815686; of newspaper stamps, $ 1000605; of stamped envelopes and wrappers, $4616932; and of postal cards, $1700000; while the total value of the issue of the following year was $27468867. Find the excess of the value of the issue of the year ending June 30, 1878, over that of the year ending June 30, 1877.

43. Only what kind of numbers can be subtracted? 44. What is Subtraction? 45. What is the Minuend? Subtrahend? Remainder? 46. What is the sign for Subtraction? Its meaning? 48. How is Ex. 22 performed? How Ex. 34? How Ex. 35? 49. Give the rule for Subtraction. 50. How is Subtraction proved? Proof rests upon what? Explain the solution of Ex. 45.