34. Multiply 4.14 by 0.6; by 0.3; by 0.9. 35. Multiply 89.73 by 1.5; by 2.5; by 1.3. 36. Multiply 27.06 by 2.3; by 3.2; by 4.6. 37. Multiply 245.14 by 0.7; by 0.9; by 3.1. 38. Multiply 187.415 by 3.2; by 2.3; by 7.2. 39. Multiply 0.0048 by 0.12; by 1.2; by 12.2. 40. Multiply 0.0374 by 0.05; by 0.55; by 5.5. 41. Multiply 818.76 by 8.5; by 0.85; by 0.085. 42. Multiply 76.54 by 5.15; by 51.5; by 0.515. 43. Multiply 123.484 by 10.5; by 11.5; by 20.5. 44. Multiply 0.0045 by 450; by 4.5; by 540. 45. Multiply 75.4 by 1.35; by 53.1; by 3.51. 46. Multiply 88.05 by 0.024; by 2.4; by 420. 47. Multiply 37.57 by 0.0094; by 9.4; by 4.9. 48. Multiply three, and thirty-five hundredths by fourteen thousandths.

49. Multiply five hundred forty-seven, and eightyfive thousandths by fifty-six, and two tenths.

Divide as in whole numbers, and point off as many figures for decimals in the quotient as the number of decimal places in the dividend exceeds the number in the divisor.

NOTE 1. If there are not as many decimal places in the dividend as in the divisor, make as many by annexing ciphers.

NOTE 2. If the number of figures in the quotient is less than the excess of decimal places in the dividend over those of the divisor, supply the deficiency by prefixing ciphers to the quotient.

NOTE 3. The pointing off is in reality the dividing of the denomi nator of the dividend by the denominator of the divisor, or it shows what that quotient is.

NOTE 4. The rule for pointing in the quotient is also evident from the rule in multiplication if we notice that the dividend is a product whose factors are the divisor and quotient.

53. Divide 17.15 by 0.5; by 0.7; by 0.035. 54. Divide 184.014 by 0.018; by 0.09; by 0.6. 55. Divide 75 by 0.05; by 1.5; by 0.15; by 0.5. 56. Divide 0.344 by 0.08; by 0.8; by 0.004. 57. Divide 21.15 by 0.015; by 4.5; by 0.09. 58. Divide 18.076 by 24; by 2.4; by 0.008. 59. Divide 0.001 by 100; by 1000; by 10. 60. Divide 100 by 0.001; by 0.01; by 0.1. 61. Divide 216.14 by 20; by 7.5; by 60. 62. Divide 8178.212 by 0.6; by 0.04; by 24. 63. Divide 76.148 by 8.7; by 7.8; by 4.7. 64. Divide 0.429 by 30; by 0.35; by 70. 65. Divide 7.15 by 250; by 125; by 2.5. 66. Divide 0.876 by 1.6; by 9.6; by 1.7. 67. Divide 4.563 by 0.027; by 0.18; by 84. 68. Divide 70.18 by 24.2; by 85; by 1.21. 69. Divide 185.25 by 0.075; by 7.5; by 18.1. 70. Divide 0.074 by 370; by 73; by 4.4. 71. Divide 370 by 0.074; by 4.7; by 850. 72. Divide 268.4 by 0.44; by 4.4; by 88.

73. Divide fourteen thousand five hundred six, and eight tenths by eight hundred forty.

74. Divide seven hundred eight, and three hundred twelve thousandths by two, and sixty-four hundredths.

75. Divide ninety-five, and sixteen thousandths by one hundred sixty.

76. Divide twenty-three thousand three hundred seven, and three hundredths by one, and five tenths.

105. To reduce any fraction to a decimal.

77. Reduce to a decimal.

4) 3.00
0.75, Ans.

The value of a fraction is the quotient obtained by dividing the numerator by the denominator (Art. 72, a). =3÷4; but as 4 is not contained in 3,

we reduce the 3 to tenths; 330 tenths; 30 tenths divided by 4 gives 7 tenths, and 2 tenths remainder; 2 tenths 20 hundredths; 20 hundredths divided by 4 gives 5 hundredths; therefore, 0.75, Ans.

=

Hence,

Rule.

Annex one or more ciphers to the numerator and divide the result by the denominator, continuing the operation until there is no remainder, or as far as desirable. Point off as in division of decimals.

78. Reduce to a decimal.

79. Reduce to a decimal.

80. Reduce to a decimal. 81. Reduce 15 to a decimal. 82. Reduce 12 to a decimal.

5

1

83. Reduce, 3, 1, 3, 1, 1. §, 4, 4, to decimals.

106. A decimal is a fraction, and, if its denominator is written, it will appear as such.

84. Reduce 0.25 to its lowest terms.

100

0.25 = 25 = , Ans. 85. Reduce 0.85 to its lowest terms. 86. Reduce 0.375 to its lowest terms. 87. Reduce 0.125 to its lowest terms.

88. Reduce 0.425 to its lowest terms.

89. Reduce 2.5, 3.35, 2.75, 3.25, 2.0125, to their lowest terms.

90. Reduce to a decimal.

91. Reduce 0.875 to its lowest terms.

92. Multiply 80.017 by 0.7; by 0.007; by 1.7. 93. Multiply 175.06 by 5.14; by 0.18; by 0.04. 94. Divide 757.061 by 2.4; by 3.15; by 15.2. 95. Divide 315.47 by 0.44; by 2.8; by 1.7. 96. Multiply 173.14 by 4.13; by 0.12; by 0.004. 97. Multiply 421.08 by 210; by 0.021; by 0.7. 98. Multiply 176.15 by 0.08; by 80; by 1.8. 99. Divide 718.4 by 0.02; by 20; by 1.5. 100. Divide 670.08 by 4.4; by 0.16; by 0.08. 101. Divide 108.06 by 3.2; by 22; by 0.11. 102. Multiply eighty-five, and seven hundredths by two hundred twenty.

103. Multiply three hundred, and fourteen hundredths by eight, and seven tenths.

104. Multiply two hundred, and two hundredths by thirty, and three tenths.

105. Multiply six thousand, and four thousandths by three hundred.

106. Divide thirteen hundred one, and fifteen thousandths by seven hundred fifty.

107. Divide forty-five hundred by fifteen thousandths.

108. Divide seven hundred fifteen thousandths by eighty-five.

109. Divide four hundred, and twenty-five hundredths by forty-five.

110. Divide one thousand by one thousandth.

111. Divide eight hundred, and six thousandths by two tenths.

112. Divide sixteen hundred five by fifteen hundredths.

113. Divide thirty-five thousand three hundred ten, and five hundredths by twenty-five thousandths.