Miscellaneous Questions, involving the Principles of the preceding Rules, Page 12 19 26 Proper, Improper, &c. 102 To change an Improper Fraction to a Whole or Mixed Number, 103 a Mixed Number to an Improper Fraction, 104 To reduce a Fraction to its lowest Terms, 105 Greatest common Divisor, how found, 106 To divide a Fraction by a Whole Number; two ways, To multiply a Fraction by a Whole Number; two ways, General Rule for the Multiplication of Fractions, To divide a Whole Number by a Fraction, one Fraction by another,. 107 110 112 113 114 115 117 General Rule for the Division of Fractions, 118 Addition and Subtraction of Fractions, 119 Common Denominator, how found, 120 121 Rule for the Addition and Subtraction of Fractions, 124 Reduction of Fractions, 124 DECIMAL. Their Notation, 132 Addition and Subtraction of Decimal Fractions, 135 Multiplication of Decimal Fractions, 137 Division of Decimal Fractions, 139 To reduce Vulgar to Decimal Fractions, 142 Reduction of Decimal Fractions, 145 To reduce Shillings, &c., to the Decimal of a Pound, by Inspection, 146 the three first Decimals of a Pound to Shillings, &c., by Inspection, 157 a suc de vil in self able, by the SUS THAT Curious questions. servers s aut, vhich to the author has pesem yr ae Index Fractions have un vien ner mportance demands. The Practico are exuintet. but its detail of cases ce the mopcon and general use of federal purtun, s retained, and the soluDe urbanes of zooportion, by analysis, is ~ctaretteri uni Sermetrical Progression, me vegret ir M. Isa Forse, a mem erase snowiere of the subject, and e sarei impurant nut in other parts of Fractions arise from Division, 42 Miscellaneous Questions, involving the Principles of the preceding Rules, 52 COMPOUND NUMBERS. Different Denominations, 56 Federal Money, to find the Value of Articles sold by the 100, or 1000, 57 6.4 68 69 Reduction of Currencies, To reduce English, &c. Currencies to Federal Money, Time, Rate per cent., and Amount given, to find the Principal, Time, Rate per cent., and Interest given, to find the Principal, Principal, Interest, and Time given, to find the Rate per cent., Principal, Rate per cent., and Interest given, to find the Time, To find the Interest on Notes, Bonds, &c., when partial Payments have Same Questions, solved by Analysis, ¶ 65, ex. Having the Diameter of a Circle, to find the Circumference; or, having the 212 215 220 225 237 NUMERATION. ¶ 1. A SINGLE or individual thing is called a unit, unity, or one; one and one more are called two; two and one more are called three; three and one more are called four; four and one more are called five; five and one more are called six; six and one more are called seven; seven and one more are called eight; eight and one more are called nine; nine and one more are called ten, &c. These terms, which are expressions for quantities, are called numbers. There are two methods of expressing numbers shorter than writing them out in words; one called the Roman method by letters,* and the other the Arabic method by figures. The latter is that in general use. In the Arabic method, the nine first numbers have each an appropriate character to represent them. Thus, * In the Roman method by letters, I represents one; V, five; X, ten; L, fifty; C, one hundred; D, five hundred; and M, one thousand. As often as any letter is repeated, so many times its value is repeated, unless it be a letter representing a less number placed before one representing a greater; then the less number is taken from the greater; thus, IV represents four, IX, nine, &c., as will be seen in the following * I is used instead of to represent five hundred, and for every additional nexed at the right hand, the number is increased ten times. an † CIO is used to represent one thousand, and for every C and put at each end, the number is increased ten times. A line over any number increases its value one thousand times. |