FOXGLOVE

The Digitalis purpure a; a common Indigenous plant, the leaves of which, when carefully dried and powdered, or made into a tincture or infusion, are used in medicine. In small and repeated doses it lowers the pulse in an extraordinary manner, and produces debility and fainting: combined with other remedies, it forms an ingredient in some powerful diuretics. FKACTION, in Arithmetic, is an aliquot part of unity.' In order to form a precise idea of a fraction of any unit, we must consider the unit to be divided into a certain whole number of equal parts, of which parts we take one, two, three, .: the number of parts so taken is what constitutes the fraction. The expre ion of a fraction therefore nece arily involves two whole numbers; namely, one to denote the number of parts into which the unit is divided, and the other to expre how many of these parts are to be taken to form the fraction. The first of these numbers is called the denominator, and the second the numerator. Thus, seven eighths of a foot, five twelfths of a pound, are fractions. In the first we suppose the foot or unit to be divided into eight equal parts, of which seven are taken; so that eight is the denominator and seven the numerator. In the second the unit or pound is supposed to be divided into twelve oqual parts, of which five are taken; here twelve is the denominator and five the numerator. From these considerations it results that a fraction is a magnitude referred to a certain part of the principal unit, which part may itself be considered as a particular kind of unit. Thus the fraction seven eighths of a foot being the same as seven times the eighth part of a foot, this eighth part is a particular unit which the proposed fraction contains eight times. Hence two fractions are said to be of the same kind when their denominators are the same. For c-x.a.m^\e, five twelfths, six twelfths,- eleven twelfths, are fractions of the same kind; but two thirds and three fourths are fractions of different kinds, because their denominators are different. In order to expre fractions by the numerical digits, the numerator is placed over the denominator, with a line or bar between them. Thus the fraction three fourths is written \, five twelfths j|, . Reciprocally, |2, H, . designate the fractions thirteen filteenths, seventeen twentieths, . A fraction may also be regarded as the quotient that arises from the division of its numerator by its denominator. For example, the expre ion seven eighths, or seven times the eighth part of unity, is identical with the expre ion the eighth part of seven, or seven divided by eight. From the definition which we have given of the numerator and denominator of a fraction, the following consequences result: — 1. If, without altering the denominator of a fraction, we multiply or divide its numerator by any number, the new fraction will be so many times greater or le than the original fraction. 2. If, without altering the numerator, we multiply or divide the denominator of a fraction by any number, the new fraction will be so many times smaller in the former case, and so many times greater in the latter, than the original fraction..3. The value of a fraction is not altered by multiplying or dividing both numerator and denominator by the same number. It is on these three principles that the practical rules for the addition, subtraction, multiplication, and division of fractions are grounded. Addition and Subtraction of Fractions. — In order that two fractions may be added together, or the one subtracted from the other, it is nece ary that they be both of the same kind, or denomination; for it is only homogeneous things that admit of amalgamation. The fractions | and| cannot be added together in their present form, because they are of different denominations. But fractions can always be reduced to the same denomination, or to a common denominator, by means of the third principle above laid down; for numbers can always be chosen such that if we multiply the terms of each fraction by them severally, the resulting equivalent fractions will have the same denominator. Thus, multiplying the terms of the fraction ^ by 4, we get the equivalent fraction ^; and multiplying the terms of | by 3, we get the equivalent <^473 [s. 486]