66. From 9000 subtract 7685.

8 99 10

EXPLANATION.

Since 5 units cannot be subtracted from 9000 0 units, and since there are no tens nor hundreds, 1 thousand 7685 must be changed into hundreds, leaving 8 thousand; 1 of the hundreds must be changed into tens, leaving 9 hundreds and 1315 1 of the tens into units, leaving 9 tens. The expression 8 thousands, 9 hundreds, 9 tens, and 10 units is thus equivalent to the minuend, from which the units of the subtrahend can be readily subtracted.

Subtract and prove:

67. 50000 - 38517. 68. 60000 - 29365. 69. 55000 - 51093. 70. 39000 - 28739. 71. 80000 - 65004. 72. 30040 - 18391. 73. 70101 - 43217. 74. 99003 - 45009. 75. 834760-83290. 76. 410506 - 23837. 77. 175004 — 23516. 78. 393400-16042. 79. 913043 – 4009.

93. A borrowed of B $6450, and paid back $3740. How much does he still owe?

94. A merchant bought a quantity of goods for $15,125, and sold them for $17,015. What was the gain?

95. The sum of two numbers is 9416, and the greater is 6809. What is the less number?

96. The year 1891 was 399 years after the discovery of America by Columbus. In what year did that event take place?

97. B bought some goods which he sold for $11,325, and thereby gained $2150. How much did they cost him?

STAND. AR. - 4

98. I bought a horse for $325 and a cow for $150. I sold the horse for $410, and the cow for $216. How much did I gain by the sale?

99. A merchant deposited in a bank on Monday $584; on Tuesday, $759; and on Wednesday, $327. During this time he drew out $987. How much did his deposits exceed what he drew out?

100. A man bought 16,750 bricks, and then sold B and C each 4926. How many had he left?

101. In an army of 7569 men, 388 were killed, 432 were wounded, and 273 deserted. How many remained for duty?

102. A man bought a farm for $7850. He expended $2169 for improvements, paid $97 for taxes, and then sold it for $10,650. Did he gain or lose, and how much?

103. A man left $3450 to his son, $2765 to his daughter, and the remainder to his wife. How much did his wife receive if the fortune was $20,000?

104. If the distance of the moon from the earth is 240,000 miles, and that of the sun 95,000,000, how much farther is it to the sun than to the moon?

105. On Monday morning a bank had on hand $2862. During the day $1831 were deposited, and $2172 drawn out; on Tuesday, $3126 were deposited, and $1954 drawn out. How many dollars were on hand Wednesday morning?

106. B had $12,000; but after paying his debts and giving away $3105, he had remaining only $7000. What was the amount of his debts?

107. A had $ 425, B had $160 more than A, and C had as much as A and B together. How much had C ?

108. A merchant bought 500 yards of silk for $375, 3500 yards of muslin for $175, and 600 yards of linen for $235; he sold the whole for $1000. How much did he gain?

109. An estate of $12,350 was divided among a widow and two children. The widow's share was $6175, the son's, $2390 less than the widow's, and the rest fell to the daughter. What was the daughter's share?

What was

110. A drover bought 300 horses for $32,150, and 150 cows for $4265, and sold them all for $37,000. the gain?

111. Mr. E bought two farms. For one he paid $4560, and for the other $6000. He spent on each $537 for improvements, and paid taxes which amounted to $78. He sold both farms for $12,450. Did he gain or lose on the sale, and how much?

112. If a ship was bought for $43,650, and sold for $45,000, what was the gain?

113. A gentleman gave $13,465 for a house and some land. The house alone was worth $8978. What was the value of the land?

114. If two candidates for office received in the aggregate 93,565 votes, and the successful one had 47,659 votes, how many did the other have ?

115. A lumberman, having 632,000 feet of boards, sold 328,582 feet of them. How many feet remained unsold?

116. A man is worth $16,425, of which $3750 is invested in bank stock, $ 2746 in mortgages, and the rest in land. How much has he invested in land?

MULTIPLICATION.

57. 1. How many cents are there in 3 two-cent pieces ? 2. How many blocks are there in 3 piles containing 3 blocks each?

3. How many are two 4's? Two 3's?

Three 3's?

4. What have you been doing with the numbers given above?

5. When numbers are used without reference to any particular thing, what name is given to them? Abstract Numbers.

6. What name is given to numbers used in connection with some thing? Concrete Numbers.

7. How many trees are 3 times 3 trees? What is taken 3 times in this example?

8. How many ponies are 4 times 3 ponies? What is taken 4 times in this example?

9. How many cents are 3 times 4 cents? What is taken 3 times in this example?

10. In each example, is the number in the answer like the number taken or like the number which tells how many times the number is taken?

11. Is the number which tells how many times the other number is taken concrete or abstract?

12. How does 3 times 2 compare with 2 times 3? 4 times 2 with 2 times 4? 3 times 4 with 4 times 3?

58. The process of taking one number as many times as there are units in another is called Multiplication; or,

Multiplication is a short process of adding equal numbers.

59. The number taken or multiplied is called the Multiplicand.

60. The number showing how many times the multiplicand is taken is called the Multiplier.

61. The result obtained by multiplying is called the Product.

62. The multiplicand and multiplier are called the Factors of the Product.

63. The Sign of Multiplication is an oblique cross x. It is read multiplied by when the multiplicand precedes it and times when the multiplier precedes it.

Thus, 4 × 3 is read 4 multiplied by 3 when 4 is the multiplicand, but it is read 4 times 3 when 4 is the multiplier.

64. A number used without reference to any particular thing is called an Abstract Number.

Thus, 4, 7, 9, etc., are called abstract numbers.

65. A number used in connection with some thing is called a Concrete Number.

Thus, 4 books, 7 days, 9 dollars, are concrete numbers.

66. PRINCIPLES.-1. The multiplier must be regarded as an abstract number.

2. The multiplicand and product must be like numbers.

3. Either factor may be used as multiplier or multiplicand when both are abstract.

In practice, for convenience, the smaller number is generally used as the multiplier.