3. Reduce į i j and to their least common denominator. Ans. 3 4 4. Reduce } and io to their least common denominator. Ans. * 18 19 CASE VII. To Reduce the fraction of one denomination to the frac. tion of another, retaining the same value. RULE. nation you 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 denomi 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 zo of a pound. 5 X 1 X ] 5 Ans. 1440 Compared thus iti of of yd. 1488= 1 3. Reduce į of a farthing to the fraction of a shilling. Ans. 3 4. Reduce of a shilling to the fraction of a pound. Ans. Th='. 5. Reduce of a pwt. to the fraction of a pound troy. Ans. j'a=ste 6. Reduce of a pound avoirdupois to the fraction of a cwt. Ans. Tho cwt. 7. What part of a pound avoirdupois is ide of a cwt. Compounded thus the off of == Ans. 8. What part of an hour is aža of a week. Ans. 11 0. Reduce of a pint to the fraction of a bhd. Ans. siz 10. Reduce of a pound to the fraction of a guinea. Compounded thus, f of of s= Ans. 11. Express 5. furlongs in the fraction of a mile. Thus 5=of1Ans. 12. Reduce of an English crown, at 6s. Ed. to the fracțion of a guinea at 28s. Ans. of a guinea. 2 1 CASE VIII. To find the value of a fraction in the kno:vn 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 un 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 schoJar's exercise, I shall give a few more examples in ench, EXAMPLES. 1. What is the value of aid of a pound? Ans. Ss. 9 d. 2. Find the value of 1 of a cwt. Ans. 3 qrs. 3 lb. 1 oz.12, dr 3. Find the value of 1 of 3s. Od. Ans. 3s. 03d. 4. How much is not of a pound avoirdupois ? Ans. 7 oz. 10 di 5. How much is of a bhd, of wine? Ans. 1.5 gals. 6. What is the value of of a dollar? Ans. 5s. 7!4. 7. What is the value of ,'of a guinea ? Ans. 188 8. Required the value of 117 of a pound apothecaries. Ans. 2 oz. 3 grs. 9. How much is of 51. 9s. ? Ans. £4 13s. 5;d. 10. How much is į of ; of of a lshd. of wine ? Ans. 15 gals. 3ats. CASE IX. To reduce any given quantity to the fraction of any greater denomination of the same kind. EXAMPLES FOR EXERCISE. 1772 1. Reduce 12 lb. 3 oz. to the fraction of a cwt. Ans. 2. Reduce 13 cwt. 3 qrs. 20 lb, to the fraction of a ton. Ans. 37 3. Reduce 16s. 10 the fraction of a guinea. Ans. 4. Reduce 1 hlid. 49.gals, of wine to the fraction of a Ans. $ 5. What part of 4 cwt. I qr. 24 lb. is 3 cwt. 3 qrs. 17 lb. Ans. 8 oz.? tun. ADDITION OF VULGAR FRACTIONS. RULE. Reduce compound fractions to single ones; mixed numbers to improper fractions; 9:d all of thein to their least common denominator, (by Case VI. Rule II.) then the sum of the numerators, writien over the common denominator will be the sum of the fractions required. EXAMPLES. 1. Add 5.1 and of; together.. 5,= and of 1=1 Then ♡ , , 11 reduced in their least common denominator by Case V!. Rule 1!. will become ܕ 13 2. Add 3, ., and together. ANSWERS. 13 3. Add į, i, and together. 17 4. Add 12; 3 and 4 together. 2011 5. Add 1 of 95 and 1 of 14) together. 4417 Note 1.-In adding mixed numbers that are not corso pounded with other fractions, you may first find the sum of the fractions, to which add the whole liuinbers of the given inixed numbers. 33 € 6. Find the sum of 57,74 and 15. Then 1 ó 15+7+15=281; Ans. 7. Add ; and 17! together. ANSWERS. 1745 8. Add 25, 81 and į of z of io 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 fivd the value of each fraction by Case VIITin Reduction, and then add them in their proper terms. 9. Add # of a shilling to of a pound. Ist inethod 2d method. of brio£. 3£=7s. 6d. Oq.. Thenio+=£. 4s=0 6 33 Whole value by Case VIII. is 8s. Od. 3 qrs. Ans. Ans. 8 By Case VIII. Reduction. 10. Add lb. Troy, to ã of a pwt. Ans. 7 oz. 4 prot. 13) grs. 11. Add 4 of a ton, to so of a cwt. Ans. 12 cwt. I gr. 8 lb. 12, 4. oz. 12. Add of a mile to o of a furlong. Ans. 6 fur. 29 po. 13. Add of a yard, i of a foot, aud of a mile toyetlier. Ans. 1510 yds. 2 ft. 9 in. 14. Add of a week, į of a day, of ivi hour, aud & of a minute together. Ans. 2 da. 2 ho. 30 min. 45 sec. SUBTRACTION OF VULGAR FRACTIONS. RULE.* Prepare the fraction us in Addition, and the difference ot'the numerators written above the common denominator, will give the difference of the fraction required. EXAMPLES. 31 203 1315 10 171 1. From takes of Therefore 9—7=ia= the Ans. 2. From já take 4 Answers. 11 3. From take 15 4. From 14 take 13 5. What is the difference of in and 17 ? Ta 6. What differs is from } ? 7. From 14 take of 19 17 8. From 37 take 15 O remains. 9. From is of a pound, take of a shilling. of zo=£. Then from 11.. take ;£. Ans. 1£. Note.-In fractions of money, weight, &c. you may, is you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their proper terms. 10. From 1£, take 37 shillings. Ans. 5s. 6d. 23 qrs. 11. From of an oz. take of a pwt. Ans. Il pwt. 3 gr. 12. From of a cwt. take i of a lb. Ans. 1 qr. 27 lb. 6 oz. 10,, dr. 13. From 3j weeks, take ţ 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 ihe 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 diiference add the upper numerator, carrying one to the unit's place of the lower whole number. Also, a fraction may be subiracted from a whole mimber by tüking the numerator of the fraction from its denonyinator, and placing the remainder over the denominator, then taking one from the whole number, |