IXI XIX2X3=6 least common denominator. 62X13 the first numerator; 6÷3 X 24 the second numerator; 6÷6×5=5 the third numerator. 4 5 Whence the required fractions are 2, %, 2. Reduce and to fractions, having the least comAns. 36 36 mon denominator. 2 2 x 2 2 3. Reduce, 3, 4 and, to the least common denomi nator. 4. Reduce 2 inator. ,,and, to the least common denom 5. Reduce,,,, Ans. gogo ya and 14, to equivalent frac tions, having the least common denominator. 2 3 3 34 6 36 Ans. 48, 48, 48, 46, 48, 4+. CASE VII. To find the value of a fraction in the known parts of the integer. RULE,* Multiply the numerator by the parts in the next inferior denomination, and divide the product by the denominator; and if any thing remain, multiply it by the next inferior denomination, and divide by the denominator as before and so on as far as necessary; and the quotients placed after one another, in their order, will be the answer required. EXAMPLES. * The numerator of a fraction may be considered as a remain der, and the denominator as a divisor; therefore this rule has its reason in the nature of compound division. EXAMPLES. 1. What is the value of of a shilling? 5 12 7)60(8s. 2 d. Ans. 56 4 4 16 14 2 2. What is the value of of a pound sterling? 6. What is the value of of a mile ? Ans. 1fur. 16pls. 2yds. 1ft. 9-in. 7. What is the value of of an ell English ? Ans. 2qrs. 3nls, 8. What is the value of of a tun of wine? Ans. 3hhd. 31gal. 2qts. To reduce a fraction of one denomination to that of another, re taining the same value. RULE.* Make a compound fraction of it, and reduce it to a sin gle ones Cop EXAMPLES. *The reason of this practice is explained in the rule for reducing compound fractions to single ones. The EXAMPLES. 1. Reduce of a penny to the fraction of a pound. of of the answet. 1440 28 22 And of of d. the proof. 40 288 2. Reduce of a farthing to the fraction of a pound. 3. Reduce 4. Reduce Ans. 1440 I Ans. 40 3 to the fraction of a penny. of a dwt. to the fraction of a pound Troy. Ans. 5. Reduce of a pound avoirdupois to the fraction of a cwt. 6 Ans. 784° 6. Reduce of a hhd. of wine to the fraction of a Ans. pint. 7. Reduce of a month to the fraction of a day. 8. *Reduce 78. 3d. to the fraction of a pound. 9. Express 6fur. 16pls. in the fraction of a mile. ADDITION of VULGAR FRACTIONS. RULE.† Reduce compound fractions to single ones; mixed numbers to improper fractions; fractions of different inte 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. 3 *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. 7 Then the fractions are, and 7 ; 29X8X10X 1=2320 7X8X10X 1= 560 2 5. Add 1. s. and of a penny together. Ans.-13- 109 Ans. 13, or 3s. Id. 119. 6. What is the sum of 4 of 151. 341. of of of a pound and of of a shilling? 7. Add of a yard, of a foot and Ans. 71. 17s. 54d. of a mile to Ans. 660yds. 2ft. 9in. of an hour to gether. Ans. 2d. 14. 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 or 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. |
