to their least common denomAns. 1 4 18 T 12 10 4. Reduce and to their least common denomnator. Ans. 112 114 9 16 16 CASE VII. To reduce the fraction of one denomination to the fraction 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 denomi nation you would reduce it to; lastly, reduce this com pound 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 y' of a pound. 5 × 1 × 1 6 x 12 x 20 5 12 2. Reduce of a pound to the fraction of a penny: Compared thus, Tʊ of 20 of 12 d. Then 5 X 20 440 1 12 1 3. Reduce of a farthing to the fraction of a shilling Ans. 'S. 4. Reduce of a shilling to the fraction of a pound. 933 Ans. T 5. Reduce of a pwt. to the fraction of a pound troy, Ans. 1800 6. Reduce of a pound avoirdupois to the fraction of Ans. cwt. a cwt. of of 6 7. What part of a pound avoirdupois is of a cwt Compounded thus, 8. What part of an hour is of a week. Ans. Ans. 168=1 9. Reduce of a pint to the fraction of a hhd. Ans. 10. Reduce of a pound to the fraction of a guinea. Compounded thus, of 20 ofs. Ans. 11. Express 5 furlongs in the fraction of a mile. Thus, 5 of }=}} Ans. 12. Reduce of an English crown, fraction of a guinea at 28s. Ans. CASE VIII. at 6s. 8d. to the of a guinea. To find the value of the 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 mferior denomination, and divide by the denominator as oefore, 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 75 and 76; but for the scholar's exercise, I shall give a few more examples in each. EXAMPLES. 1. What is the value of of a pound? 2. Find the value of of a cwt. Ans. 8s. 94d. Ans. Sqrs. 3lb. 1oz. 124dr. 3. Find the value of 7 of 3s. 6d Ans. 3s. Ù3d. 4. How much is of a pound avoirdupois ? Ans. 7oz. 10dr. 5. How much is of a hhd. of wine? Ans. 45 gals. 6. What is the value of 45 of a dollar? Ans. 5s. 7 d. 7. What is the value of of a guinea? Ans. 18s. 8. Required the value of 107 of a pound apothecaries, 9. How much is 4 of 51. 9s. ? 017 Ans. 2oz. Sgrs. Ans. £4 13s. 54d. Ans. 15gals. 3qts 10. How much is of of 4 of a hhd. 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 75.] EXAMPLES FOR EXERCISE. 1. Reduce 12 lb. 3 oz. to the fraction of a cwt. Ans. 195 2. Reduce 13 cwt. 3 qrs. 20 lb. to the fraction of a ton. Ans. 38 Aus. 3. Reduce 16s. to the fraction of a guinea. 4. Reduce 1 hhd. 49 gals. of wine to the fraction of a tun. Ans. . 5. What part of 4 cwt. 1 qr. 24 lb. is 3 cwt. 3 qrs. 17 lb. 8 oz. Ans. 7 ADDITION OF VULGAR FRACTIONS. RULE. REDUCE compound fractions to single ones; mixed numbers to improper fractions; and ail 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 54 and of together. Then 5 and of 7-14 14 reduced to their least common denominator by Case VI. Rule II. will become ΣΕ Then 132+18-+14-16-622 or 6 Answer. 2. Add S. Add 2 and together. and together. 4. Add 124 34 and 43 together. 5. Add of 95 and 7 of 144 together. NOTE 1.-In adding mixed numbers that are not compounded 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 74 and 15. I find the sum of and to be Then 1+5+7+15=2811 Ans. 7. Add and 17 together. 3. Add 25, 81 and of of 1 Ans. 17 5 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 of a pound. SUBTRACTION OF VULGAR FRACTIONS. RULE.* PREPARE the fractions as in Addition, and the dif ference of the numerators written above the common denominator, will give the difference of the fraction required. 12 9. From of a pound, take off. Then from 31 208 1373 O remains. of a shilling. take 15. 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 33 shilling. Ans. 5s. 6d. 24qrs. 11. From of an oz. take of a pwt. Ans. 11pwt. 3gr. 12. From of a cwt. take of a lb. Ans. 1qr. 27lb. 6oz. 10 dr. 13. From 33 weeks, take of a day, and of of of Ans. Sw. 4da. 12ho. 19min. 174sec an hour. *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 denomina tor, and placing the remainder over the denominator, then taking one from the whole number. |