3. Reduce and to their least common denomi nator. 12 Ans. 4. Reduce 25 and to their least common denominator. CASE VII. To Reduce the fraction of one denomination to the frac⚫ tion of another, retaining the same value. RULE. Reduce the given fraction to such a compound one, as will express the value of the given fraction, by comparing it with all the denominations between it and that denomination you would reduce it to; lastly, reduce this compound fraction to a single one, by Case V. EXAMPLES. 1. Reduce of a penny to the fraction of a pound. By comparing it, it becomes of of 5 × 1 × 1 6 × 12×20 of a pound. 5 Ans. 1440 2. Reduce of a pound to the fraction of a penny. Compared thus T Then 5 X 20 X 12 of 20 of d. of a farthing to the fraction of a shilling. Ans. 4. Reduce of a shilling to the fraction of a pound. Ans. 5. Reduce of a pwt. to the fraction of a pound troy. Ans. To 6. Reduce of a pound avoirdupois to the fraction of a cwt. Ans. T cut. 7. What part of a pound avoirdupois is of a cwt. Compounded thus of 4 of 13 Ans. 8. What part of an hour is of a week. Ans. 9. Reduce 3 of a pint to the fraction of a hhd. Ans. pia 10. Reduce of a pound to the fraction of a guinea. Compounded thus, of 20 of 4s.=4 Ans. 11. Express 5 furlongs in the fraction of a mile. Thus 5 of }=}} Ans. 12. Reduce of an English crown, at 6s. 8d. to the frac tion of a guinea at 28s. Ans. 2 of a guinea, CASE VIII. To find the value of a fraction in the known parts of the integer, as of coin, weight, measure, &c. RULE. Multiply the numerator by the parts in the next inferior denomination, and divide the product by the denominator; and if any thing remains, multiply it by the next inferior denomination, and divide by the denominator as before, and so on as far as necessary, and the quotient will be the answer, NOTE. This and the following Case are the same with Problems II. and III. pages 70 and 71; but for the scho lar's exercise, I shall give a few more examples in each, EXAMPLES. 1. What is the value of 21 of a pound? Ans. 8s. 91d, 2. Find the value of of a cwt. Ans. 3 qrs. 3 lb. 1 oz. 3. Find the value of 1 of 3s. 6d. .12 dr Ans. 3s. 0ąd. 8. Required the value of 13 of a pound apothecaries. 9. How much is 4 of 5l. 9s.? Ans. 2 oz. 3 grs. Ans. £4 13s. 54d. Ans. 15 gals. 3 qts. 10. How much is of 3 of of a lhd. of wine? CASE IX. To reduce any given quantity to the fraction of any greater. denomination of the same kind. [See the Rule in Problem III. page 71.] EXAMPLES FOR EXERCISE. 1. Reduce 12 lb. 3 oz. to the fraction of a cwt. Ans. 195 1792 2. Reduce 13 cwt. 3 qrs. 20 lb. to the fraction of a ton. Ans. Ans. t 3. Reduce 16s. to the fraction of a guinea. 4. Reduce 1 hhd. 49 gals, of wine to the fraction of a tun. 5. What part of 4 cwt. 1 qr. 24 lb. is 3 cwt. 3 8 oz.? Ans. ADDITION OF VULGAR FRACTIONS. RULE. Reduce compound fractions to single ones; mixed numbers to improper fractions; and all of them to their least common denominator, (by Case VI. Rule II.) then the sum of the numerators written over the common denominator will be the sum of the fractions required. EXAMPLES. 1. Add 5 and of together.. 5)=V and 3 of 7=14 Then, 3, 4 reduced to their least common denominator by Case VI. Rule H. will become Then 132+18+14=1=632 or 63 Ans, NOTE 1.—In adding mixed numbers that are not com pounded with other fractions, you may first find the sum of the fractions, to which add the whole numbers of the given mixed numbers. 6. Find the sum of 53, 71⁄2 and 15. 7. Add I find the sum of 3 and 4 to be 1=111 and 17 together. 8. Add 25, 8 and of of ANSWERS. 17% 33 NOTE 2.-To add fractions of money, weight, &c. reduce fractions of different integers to those of the same. Or, if you please, you may find the value of each fraction by Case VIII. in Reduction, and then add them in their proper terms. 9. Add 4 of a shilling to 3 of a pound. 1st method 2d method. Ans. 80-33 SUBTRACTION OF VULGAR FRACTIONS. RULE.* Prepare the fraction as in Addition, and the difference of the numerators written above the common denominator, will give the difference of the fraction required. 1. From take of EXAMPLES. of 7-7 Then 3 and 7ù le 2. From take 4 3. Fromake 13 4. From 14 take 13 Therefore 9-7=}=} the Ans. 5. What is the difference of and 17? 6. What differs from? 7. From 14 take of 19 8. From 3 take 9. From of a pound, take § of a shilling. 20 = of £. Then from £. take £. Ans. £. NOTE. In fractions of money, weight, &c. you may, if you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their proper terms. 10. From £, take 37 shillings. Ans. 5s. 6d. 23 qrs. 11. From of an oz. take of a pwt. Ans. 11 pwt. 3 gr. 12. From of a cwt. take of a lb. Ans. 1 gr. 27 lb. 6 oz. 10,81⁄2 dr. 13. From 3 weeks, take of a day, and of of of an hour. Ans, 3 w. 4 da. 12 ho. 19 min. 174 sec. * In subtracting mixed numbers, when the lower fraction is greater than the upper one, you may, without reducing them to improper fractions, subtract the numerator of the lower fraction from the common denominator, and to that difference add the upper numerator, carrying one to the unit's place of the lower whole number. Also, a fraction may be subtracted from a whole number by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number, |