EXAMPLE FOR ILLUSTRATION. 1. Reduce 288 of a £, to the fraction of a farthing. Ans. of a penny. Youwill see the manner in which I have placed this question, it is like the last case; only the parts between the denomination given, and that to which it is to be reduced, are reversed; the numerator of this being the denominator of that; and beginning here with the highest in 1920 stead of the lowest name. After placing it as in the margin, I reduced the compound fraction to a single one, by case 3; and to its lowest terms, by case 2. the result was when reduced to its lowest terms, for answer. This case, and case 6, prove each other. EXAMPLES. 2880 or, 2. Reduce of a shilling to the fraction of a penny. Ans. of a penny. Placed thus, 2 X 12 36 X 1 Remember to reduce it to its lowest terms. 3. Reduce 5 of a shilling to the fraction of a farthing. Ans, of a farthing. First the pence in a shilling, then the farthings in a penny. 4. Reduce 26 of a pound troy to the fraction of a penny. weight. Ans. of a pennywt. The ounces in a lb. the pennywts. in an ounce. Ans. of a min The hours in a day, the minutes in an hour. 784 6 Ans. of a Ib. The pounds in a cwt. or the qrs, in a C. and the lbs. in a qr. 7. Reduce 3528 of a hogshead of wine to the fraction of a pint. Ans of a pint, The l. in a hhd. the qts. in a gal. the pts. in à qt. CASE VIII. To find the proper quantity or value of a fraction in money, weights, measures, &c. RULE. Multiply the numerator of the fraction by the known parts in the next inferior or lower denomination, and divide the product by the denominator; if there be a remainder reduce it to the next lower denomination, and divide by the denominator as before; and thus proceed to the least denomination, or as far as necessary; the quotients will be the answer. EXAMPLE FOR ILLUSTRATION. 1. Reduce of a pound sterling, to its proper quantity. Ans. 4s. 5d. 1qr. 3. 2 20 9)40(4s. 36 4 12 According to rule, I multiplied by the next inferior or lower denomination to that given; viz. the shillings in a pound, and divided by the denominator; I had 4 remainder, which I multiplied by the next lower de9)48(5d. nomination, viz. the pence in a shilling; and divided again by the same divisor; I multiplied the next remainder by the farthings in a penny, and divided again; the last remainder was 3, or 3; which is when reduced to its lowest terms; so that 3 of a pound is, 4s. 5d. 1gr. 3. 45 3 4 9)12(1qr 2. What is the value of 14 of a pound sterling? 350 Ans. 8s. Od. 2qrs. 36038 What is the next lower denomination to pounds? answer shillings; the next, pence; and lastly, farthings; the denominator is the divisor. 3. What is the value of 3 of a shilling? First the pence in a shilling, &c. 4. Find the the value of Ans. 4 d. of a dollar, N.Y. Ans. 87cts. 5m. 5. Find the value of of 1£. 14s. 6d. Ans. 1£. 10s. 8d, Performed by Compound Multiplication and Division, multiplying by the 8, and dividing by the 9. 6. Reduce First 7. of a ton to its proper quantity. Ans, 11C, 1qr, 2016. by the C. in a ton and divide, &c. 1, and pennywts, in an oz. 8. Reduce of a lb. avoirdupois to its proper quantity. The oz. in a pound, &c. 9. What is the value of of a mile? Ans. 9oz. 2dr. 2. Ans. 502yds. 2ft. 6in. 2 b. c. 4. in. in a ft. b. c. in an in. The yds. in a mile ft. in a yd. of 22A. 1R. 10P? Ans, 13A. 1R. 22P. Multiply by the num. and divide by the denom. see ex. 5. 11. Reduce of a yd. to its proper quantity. The feet in a yd. &c. Ans. 1ft. 2in. 1 b. c. } Ans. 2W. 2D. Ans. 112 feet. The gal. in a hhd. 16. Reduce of a month, to its proper quantity? The weeks in a mo. the days in a week. 17. Reduce of a cord of wood to its proper quantity? The feet in a cord. 18. Suppose I own of a lot of boards, consisting of 3680 feet, what is my part? 19. What is the value of 5 of 1706D. 85cts. CASE IX. Ans. 2070 feet. Ans. 948D. 25cts. To reduce money, weights, or measures to fractions. RULE. Reduce the given quantity to the lowest name, or denomination mentioned, for a numerator; reduce the integral part to the same name for a denominator; said fraction reduced to its lowest terms will be the answer required. EXAMPLE FOR ILLUSTRATION. 1. Reduce 4s. 5d. 1qr. to the fraction of a pound. Ans. of a £. EXAMPLES. 2. Reduce 8s. Od. 2qrs. 39 to the fraction of a pound sterling? Ans. 1 of a £. Examine the example for illustration. 3. Reduce 41d to the fraction of a shilling? Ans. of a shil. Reduce the 44d. into halfpence; reduce the integral part, or shilling, to the same name, then reduce the fraction to its lowest terms. 4. Reduce 87cts. 5m. to the fraction of a dollar, N.Y. Ans. of a doll. Reduce the given sum into mills; reduce the cts. in a doll. into mills; reduce the fraction to its lowest term. the other to the same name for a numerator, &c. 6. What part of a ton is 11C. 1qr. 20lbs? Reduce the given sum to lbs. reduce the C. in a ton to the same name, proceed. 5. What part of 1£. 14s. 6d. is 1£. 10s. 8d.? The first to pence, the lowest name mentioned for a denominator; Ans. & Ans. 4. Ans.. What part of a pound troy is 4oz. 10pwt.? to the lowest name mentioned then - the oz. in a pound e same name, and go on as before. at part of a pound avoirdupois is 9oz. 2dr. ?? Ans. of a lb. the oz. to dr. and the drams, to sevenths, adding in the 2 then reduce the oz. in a pound to the same name, &c. 9. What part of a mile is 502yds. 2ft. 6in. 2b. c. 4? Ans. of a mile. The yds. &c. into barleycorns, and then into sevenths; then the yds. in a mile to the same name, and go on. Ans.. 10. What part of 22A. 1R. 10P. is 13A. 1R. 22P.? Reduce both to perches; place the perches in the first for the denominator; then reduce the fraction to its lowest term. 11. Reduce 1ft. 2in. 1b.c. }, to the fraction of a yd, Ans. of a yd. The given sum to barleycorns; then multiply by 5, and add in the 1 to reduce the b.c. to fifths, reduce the ft. in a yd. to the same name, &c. 12. What part of an acre is 1R. 24P.? Ans. of a acre. 13. What part of a yd. is 3qr. 1na. §? of a yd. Sevenths are the lowest; reduce the qrs. to na. then multiply by 7, and add in the 5; reduce the qrs. in a yd. to the same name, &c. 14. Reduce 21hrs. 20min. to the fraction of a day. Ans. Ans. of a day. 15. Reduce 42 gallons of wine to the fraction of a hhd. Ans. of a hhd. The 42 gal. for the num. the gal. in a hhd. for the denom. and proceed. 16. What part of a month is 2w. 2d.? Ans.. Ans. of a cord. 17. What part of a cord is 112 feet? The given feet for num. the feet in a cord for a denom. &c. 18. If of a lot of boards consisting of 3680 feet, I own 2070 ft. what part of them are mine? Ans. 9 The 1st mentioned, the denominator; the last, the numerator. 19. What part of 1706D. 85cts. is 948D. 25cts.? The cents in the 1st. the denom. the cents in the last the num. &c. Ans. 5. ADDITION OF VULGAR FRACTIONS. Note 1. To add fractions together, having different denominators. RULE. Reduce the given fraction to a common denominator by case 1, Reduction; then, add all the numerators together, under which subscribe the common denominator; and, if it is an improper fraction, reduce it to its proper terms, by case 5, and you have the sum of all the fractions. Note 2. To add fractions that are mixed numbers. RULE. Reduce the fractions to a common denominator, and add them together, as before directed; then add or annex their sum to the whole numbers. |