EXAMPLES. 1. Reduce & of a penny to the fraction of a pound. And 니아여 of of the answer. the proof 2. Reduce of a farthing to the fraction of a pound. Ans. 수니이 3. Reduce f. to the fraction of a penny. 4. Reduce of a dwt. to the fraction of a pound Troy. I Ans. 내아이 5. Reduce of a pound avoirdupois to the fraction of a cwt. 6 Ans. 784 6. Reduce 에어비 of a hhd. of wine to the fraction of a Ans. pint. 84 3 Ans. 8. *Reduce 7s. 3d. to the fraction of a pound. Ans. ४० 9. Express 6fur. 16pls. in the fraction of a mile. Ans. ADDITION OF VULGAR FRACTIONS, Reduce compound fractions to single ones; mixed numbers to improper fractions; fractions of different inte 1 gers The rule might have been distributed into two or three different cases, but the directions here given may very easily be applied to any question, that can be proposed in those cases, and will be more easily understood by an example or two, than by a multiplicity of words. * Thus 7s. 3d. = 87d. and 11.=240d.. the answer. † Fractions, before they are reduced to a common denominator, are entirely dissimilar, and therefore cannot be incorporated with one another; but when they are reduced to a common denominator, and made parts of the same thing, their sum or differ ence, gers to those of the same ; and all of them to a common denominator; then the sum of the numerators, written over the common denominator, will be the sum of the fractions required. EXAMPLES. : 5. Add . s. and of a penny together. 1 Ans. 13 109 Ans., or 3s. Id. 19. 6. What is the sum of 4 of 151. 31. of 옻 of of a pound and of of a shilling? 7. Add of a yard, of a foot and Ans. 71. 17s. 5윽d. of a mile to660yds. 2ft. gin. of an hour toAns. 2d. 14th. SUBTRACTION ence, may then be as properly expressed, by the sum or difference of the numerators, as the sum or difference of any two quantities whatever, by the sum or difference of their individuals; whence the reason of the rules, both for addition and subtraction, is manifest. K SUBTRACTION of VULGAR FRACTIONS. RULE. Prepare the fractions as in addition, and the difference of the numerators, written above the common denominator, will give the difference of the fractions required. Reduce compound fractions to single ones, and mixed numbers to improper fractions; then the product of the numerators is the numerator; and the product of the denominators, the denominator of the product required. EXAMPLES. * Multiplication by a fraction implies the taking some part of parts of the multiplicand, and, therefore, may be truly expressed by a compound fraction. Thus multiplied by is the same as of; and as the directions of the rule agree with the method already given to reduce these fractions to single ones, it is shewn to be right. EXAMPLES. I 1. Required the continued product of 2, off and 2. 5. Multiply of by of 3. 25 =the answer. Ans. I 9 Ans. 6. Multiply 4, of and 18号, continually together. Ans. 9시이 40 DIVISION of VULGAR FRACTIONS. RULE.* Prepare the fractions as in multiplication; then invert the divisor, and proceed exactly as in multiplication. * The reason of the rule may be shewn thus: Suppose it were required to divide by Now +2 is manifestly of, or 3 4X2 ; but of 2,.. of 2, or must be contained 5 times as often in as 2 is; that is 3×5 4X2 =the answer; which is ac cording to the rule; and will be so in all cases. NOTE. A fraction is multiplied by an integer, by dividing the denominator by it, or multiplying the numerator. And divided by an integer, by dividing the numerator, or multiplying the de nominator. A DECIMAL is a fraction, whose denominator is an unit, or 1, with as many cyphers annexed as the numerator has places; and is commonly expressed by writing the numerator only, with a point before it called the separatrix. Thus, 0.5 is equal to or A finite decimal is that, which ends at a certain number of places. But an infinite decimal is that, which is understood to be indefinitely continued. .. A repeating decimal has one figure, or several figures, continually repeated, as far as it is found. As '33, &c. which is a single repetend. And 20.2424, &c. or 20.246246, &c. which are compound repétends. Repeating decimals are also called circulates, or circulating decimals. A point is set over a single |