78. Divide four hundred eighteen thousand six hundred fortyeight, by twenty-four. Ans. Quo. 17443, Rem. 16. 79. Divide two hundred one thousand five hundred ninetyfive acres of land, into twenty-three equal parts.

80. A railroad that cost $ 4076500 was divided into 8153 equal shares; what was the cost of each share?

81. A farmer raised 2047 hektoliters of wheat on 89 hektars of land; how many hektoliters did he raise on a hektar?

82. In how many days will a ship sail 3456 miles, if it sails 144 miles a day?

83. A farmer raised 4118 hektoliters of corn, his crop averaging 58 hektoliters a hektar; how many hektars did he plant?

84. A drover paid $ 7663 for 79 oxen; how many dollars did he pay for each ox?

85. The product of two numbers is 10707, and one of the numbers is 129; what is the other number?

86. The earth, in its revolution round the sun, moves about 1641600 miles in one day; how far does it move in one second, there being 86400 seconds in a day?

87. Divide $6024 equally among 24 men.

78. As removing a figure one place to the right divides it by ten, two places divides it by a hundred, etc., to divide by 10, 100, 1000, or 1 with any number of ciphers annexed,

Rule.

Move the decimal point as many places to the left as there are ciphers in the divisor.

NOTE 1. In order to move the decimal point the required number of places to the left, it may be necessary to prefix ciphers. (See Ex. 94.)

NOTE 2. The figures at the right of the decimal point can be left standing as decimals, or written separately as the remainder.

88. Divide 756 by 10.

Ans. 75.6, or 75 and 6 Rem.

89. Divide 276403 by 10.

90. Divide 94763 by 100.

91. Divide 98765423 by 100000. Ans. 987 and 65423 Rem.

92. Divide 7830652143 by 100000000.

93. Divide 56.3 by 10.

94. Divide 4.6 by 100.

95. Divide 964.8 by 100.

Ans. 0.046.

As 85000 85 × 1000, we first divide by 1000, obtaining (Art. 79) 817.468; then we divide 817.468 by 85.

595

23

If the exact remainder is sought the work is as follows:

two remainders together, we have 52468 as the full remainder.

NOTE. If the work is carried into decimals, and there is still a remainder, we can at any point we choose cease dividing and write + at the right of the quotient, as in the first operation above.

104. If I pay $1170 for 180 tons of coal, what do I pay a

ton?

105. If $7856.50 are divided equally among 50 men, how much will each have?

106. The highest volcano in the world, Sahama, is 23014 feet high, and there are 5280 feet in a mile, how many miles high is this volcano?

Miscellaneous Examples.

107. A steamer sometimes crosses the Atlantic, 2880 miles, in 8 days of 24 hours each; what is the rate an hour?

108. If a ship sails 10 miles an hour, how many days will it take it to cross the Atlantic?

109. How many hektoliters of corn, at $ 2.75 a hektoliter, must be given for 6 barrels of flour at $8.50 a barrel ?

110. If the yearly expenses of a boy at school are $5.50 a week for 40 weeks' board, $50 for tuition, $15 for books, $50 for clothes, $8 for travelling expenses, and $16.50 for other purposes, what will be the expenses of 5 boys for 5 years?

111. If 24 men can build a certain wall in 81 days, how many days will it take 216 men to build the same wall?

112. If it costs a man $5 an acre to secure a title to 640 acres of government land, how much will he make if he sells the whole for $5000? How much on each acre?

113. The product of four factors is 86500, and three of these factors are 25, 4, and 173; what is the fourth?

114. The first of three numbers is 13, the second is 8 times the first, and the third is 10 times the product of the other two divided by 4. What is the difference between the first and third?

115. Sold two cows at $30 apiece, 3 tons of hay at $20 a ton, 50 bushels of corn for $50, and 10 cords of wood at $7 a cord, and received in payment $ 200 in money, a plough worth $15, 50 pounds of sugar worth $5, and the balance in broadcloth at $4 a meter; how many meters did I receive?

116. If I receive $60 and spend $ 40 a month, in how many years of 12 months each shall I save $2160 ?

117. Bought 87 acres of land at $50 an acre, and paid $ 3150 in cash, and the balance in labor at $240 a year; how many years of labor did it take ?

118. Bought 42 meters of cloth at 15 cents a meter, and paid for it in corn at 30 cents a dekaliter; how many dekaliters did it take?

119. If I take 13729 from the sum of 8762 and 14967, divide the remainder by 50, and multiply the quotient by 19, what is the product?

120. How many days will it take a person to walk from Boston to New York and back, if he walks 9 hours a day and 3 miles an hour, and the distance from New York to Boston is 216 miles?

121. A man earns $1065 a year, and each of his two sons $517, and each of the three spends $ 255 a year. If at the end of 7 years they make an equal division of their savings, what will each receive?

122. If a man sells 19 bushels of potatoes at $0.55 a bushel, 23 bushels of oats at $0.63 a bushel, and with the proceeds buys 8 meters of broadcloth, how much does he pay a meter for the broadcloth?

123. If a farmer exchanges 51 acres of woodland worth $125 an acre for cleared land worth $85 an acre, how many acres will he get?

GENERAL PRINCIPLES OF DIVISION.

79. The value of a quotient depends upon the relative values of the divisor and dividend, and not upon their absolute values, as will be seen by the following propositions.

(a.) If the divisor remains unchanged, multiplying the dividend by any number is, in effect, multiplying the quotient by the same number; thus,

that is, multiplying the dividend by 4 multiplies the quotient by 4.

(b.) Dividing the dividend by any number is dividing the quotient by the same number; thus,

that is, dividing the dividend by 3 divides the quotient by 3. (c) Multiplying the divisor divides the quotient; thus,

30215
3

3065=153;

that is, multiplying the divisor by 3 divides the quotient by 3.

(d.) Dividing the divisor multiplies the quotient; thus,

that is, dividing the divisor by 5 multiplies the quotient

by 5.