tors of the given fractions, and it will be the common denominator required. 2. Divide the common denominator by the denominator of each fraction, and multipy the quotient by the numerator, and the product will be the numerator of the fraction required. EXAMPLES. 1. Reduce,, and to fractions, having the least common denominator. 6 the least common denominator. 62x1-3 the first numerator; 63x2=4 the second numerator; 6-6x5=5 the third numerator. 5 Whence the required fractions are,, 2. Reduce and to fractions, having the least common denominator. Ans. 1,3 22 3. Reduce, 1, 2, and to the least common denominaAns. 11. 6 8 10 tor. 9 4. Reduce, 4 ,,, and to the least common denomina 5. Reduce,,&, 7, 14, and 12 to equivalent fractions, having the least common denominator. Ans. 1, 2, 4, 1, 3, 2. 36 40 42 33 34 CASE VII. To find the value of a fraction in the known parts of the in teger. RULE.* Multiply the numerator by the parts in the next inferior the denominators, and consequently will divide by any of them; it is therefore manifest that proper parts may be taken for all the numerators as required. ** The numerator of a fraction may be considered as a re 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. 1. What is the value of of a shilling? 5 12 7)60(8d. 2 q. Ans. 56 4 16 14 2 2. What is the value of of a pound sterling? 3. What is the value of of a pound Troy? ៖ Ans. 7s. 6d. Ans. 7oz. 4dwt. Ans. 9oz. 24dr. 4. What is the value of of a pound avoirdupois? What is the value of of a cwt.? Ans. 3qrs. 3lb. 1oz. 124dr. 6. What is the value of of a mile ? Ans. 1fur. 16pls. 2yds. 1ft. 943in. 7. What is the value of of an ell English? Ans. 2qrs. 3 nls. 8. What is the value of of a tun of wine? Ans. 3hhd. 31gal. 2qts. 9. What is the value of of a day? Ans. 12h. 55' 233". mainder, and the denominator as a divisor; therefore this rule has its reason in the nature of compound division. CASE VIII. To reduce a fraction of one denomination to that of another, retaining the same value. RULE.* Make a compound fraction of it, and reduce it to a single one. EXAMPLES. 1. Reduce & of a penny to the fraction of a pound. 5 240 1 of 1 of 1 the answer. And of 20 of 12-28-d. the proof. 2. Reduce of a farthing to the fraction of a pound. Ans. T '1 40 3. Reduce. to the fraction of a penny. 4. Reduce of a dwt. to the fraction of a pound Troy. 45 Ans. 36 5. Reduce of a pound avoirdupois to the fraction of a cwt. 6. Reduce 1 3 Ans. 392. of a hhd. of wine to the fraction of a pint. 7. Reduce of a month to the fraction of a day. 8. Reduce 7s. 3d. to the fraction of a pound. 9. Express 6fur. 16pls. to the fraction of mile. ADDITION OF VULGAR FRACTIONS. BB RULE. Reduce compound fractions to single ones; mixed numbers to improper fractions; fractions of different integers The reason of this practice is explained in the rule for reducing compound fractions to single ones. 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. 87 † Thus 7s. 3d. = 87d. and 11.240d..828 the answer. Fractions, before they are reduced to a common denominaVOL. I. I 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. 1. Add 3,7, of, and 7 together. First 3, of 3=76, 7=1• Then the fractions are, 7, 7, and 1; .. 5. Add 1. s. and of a penny together. 3139 Ans. 13 199 Ans. 13, or 3s. 1d. 11. 6. What is the sum of 4 of 151. 331. of 4 of 3 of a pound, and of of a shilling? 3283 er. er. Ans 71. 17s. 54d. 7. Add of a yard, of a foot, and of a mile togeth Ans. 660yds. 2ft. 9in. 8. Add of a week, of a day, and of an hour togeth- 13 Ans. 2d. 14th. tor, 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 difference 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. 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. 1. Required the continued product of 21, 1, of, and 2. 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 shown to be right. |