54. By what must 73 of 33 be multiplied that the product may equal 4g of 2g? 55. Simplify 63 – 4 of 153 + 231; factor the 3 of 73-53÷3145 25 answer into two fractions so that one factor shall be a perfect square. 56. Find the H.C.F. and the L.C.M. of 18 and 20. 57. Subtract 1011 from 23%, and 152% from 203. 58. Simplify (34 +24 + 43) ÷ (1 + 3) of (1 − 4). 59. Simplify 60. A man gives away of his money and afterwards of the remainder. What fraction of the whole had he then left? 61. Reduce to a common denominator, and arrange in order of magnitude the fractions, 2, 15, 20, 12, 18. 5 13 19 62. Multiply the difference between 31 of 14+71 1 and 24 of by the sum of and 21 1 54 71 2(64+193) 64. After spending of his money, a boy found that of the remainder was 23 dollars. What had he at first? 65. Reduce to their lowest terms 28907 154241 66. A gave of his marbles to B, to E, and then had 105 left. How receive? 217 1496 and 4039 15309 67. Find 23 of {215 - 4 of (31 of 24 - 53) of 13 -1}· 68. 64 feet of brass rods cost 12 cents a foot; what was the cost of the rods? Find the amount of the above bill; answer in dollars and cents, letting 100 cents equal one dollar. What would be the answer in dollars, and the decimal of a dollar? 70. Find the H.C.F. and L.C.M. of 1.485 and 12.6. 72. Add, without changing positions: 67.04, 12, 567, 947, 4.17, 243157, 14, 827. 73. A certain lake is .327 of a mile long; what is its length compared with the length of a second lake 2 miles long? (Answer must be reduced to a circulating decimal.) 74. Three tanks contain 924, 1500, and 2520 gallons of water respectively; what is the largest number of gallons that can run from each of the tanks per minute and allow all to be emptied in a whole number of minutes, the rate of flow from each tank being the same? How many minutes are required to empty each tank? CHAPTER V. DECIMAL MEASURES. 137. Anything which can be increased or diminished is called a Magnitude. Lengths, areas, weights, etc., are magnitudes. To measure a magnitude is to compare it with some known magnitude of the same kind, which is taken as a unit, and to say how many times the unit must be repeated in order to make up the magnitude in question. For example, to measure any given length of string, is to find how many times some known length, say a foot, must be repeated to make up the given length; and this number of times is called the measure of the length. A measured magnitude is called a Quantity. Thus, any quantity is expressed by a number and a unit of the same kind as itself. 138. Numbers are first used in connection with distinct objects, and are afterwards used in measuring continuous magnitudes of any kind. If the continuous magnitude cannot be measured by one unit, a series of units smaller and smaller in value may be used. For example, to measure a string, some definite length, say a yard, is fixed on as a unit. Suppose the given string contains 6 yards. We may use a second unit, say a foot, to measure the yard will be 11 feet, This foot may be yard. If there are 3 feet in one yard, the and the string will measure 6 yards 1 feet. expressed in a smaller unit still, say an inch; if there are 12 inches in a foot, the foot will be 6 inches, and the string will measure 6 yards 1 foot 6 inches. 139. Quantities expressed in terms of a single unit are called Simple Quantities, and quantities which are expressed in terms of more than one unit are called Compound Quantities. To measure every different kind of quantity, some standard unit is employed, and also other units which are obtained by subdivisions and repetitions of the standard unit. Units which require 10 of one to make one of the next higher are the simplest to use. Such units are called Decimal Units. In numeration of quantities, units of different kinds are called units of different denominations. TABLES OF DECIMAL UNITS. 140.* Table of United States Money. Money is a measure of values. 10 mills (m.) 1 cent (ct.). 10 cts. 10 d. 10 $ = The eagle is usually called ten dollars, and the dime is usually called ten cents; so that the only names generally used are dollars and cents. It is advisable to study numeration and notation of decimal measures at the same time. Thus, $25.35 is read, 25 dollars 35 cents,' and not, 2 eagles 5 dollars 3 dimes 5 cents'; also, $.20 is read, ‘20 cents.' The notation is as follows: The figure representing eagles is put in tens' place, 141. A sum of money represented in any denomination may be represented in higher denominations by moving the decimal point to the left, one place for each denomination. A reduction is made to lower denominations by moving the decimal point to the right; thus, 142. We have already shown how to perform the operations of addition, subtraction, multiplication, and division of decimals; and the application of these rules to sums of money will require no further explanation, except to state that in cases of addition and subtraction care must be used in writing units of the same denomination in the same vertical column. This is not a necessity -only a convenience. 143. The coins in use are as follows: Gold coins the dollar, the quarter-eagle, the half-eagle, the eagle, and the double-eagle. Silver coins: the dollar, the half-dollar, the quarterdollar, and the dime. Nickel coin: the five-cent piece. Bronze coin: the cent. The mill is used only in computation. |