4. Reduce of a scruple to the fraction of a pound. 5. Reduce weight. 6. Reduce 7. Reduce 8. Reduce 9. Reduce 10. Reduce 11. Reduce ure. of an ounce to the fraction of a hundred of a pound to the fraction of a ton. of an inch to the fraction of an ell English. of a barleycorn to the fraction of a league. of a quart to the fraction of a tun, wine meas 12. Reduce of a pint to the fraction of a bushel. 13. Reduce of a minute to the fraction of a year (3651 days). CASE X. To reduce fractions of a higher denomination to a lower. 1. What part of a penny is OPERATION. 640 X 20 = 240 = = 35. 332 X 12 of a pound? We explain this question in As the following manner. shillings are twentieths of a pound, there will be 20 times ʊ of a pound, as there are of a pound is equal to 20 = And as pence are twelfths of a shilling, there will be twelve times as many parts of a penny in of a shilling, as there are parts of a shilling; therefore, of a shilling is equal to of 42 == # of a penny, of a shilling. o of The operation of this question may be facilitated in the following manner. OPERATION. 640 X 22 X 42 = 348 = 8d. Ans. RULE. Let the given numerator be multiplied by all the denominations between it and the one to which it is to be reduced; then place the product over the given denominator and reduce the fraction to its lowest terms. bo of a pound to the fraction of a farthing. 2. Reduce 3. Reduce 4. Reduce fraction of a scruple. 5. Reduce 6. Reduce 89 of a cwt. to the fraction of an ounce. 7. Reduce of an ell English to the fraction of an inch. 8. Reduce TT0's of a mile to the fraction of an inch. 9. Reduce corn. ʊ of a league to the fraction of a barley 10. Reduce 25090560 of an acre to the fraction of an inch. of a tun of wine measure to the fraction 11. Reduce T of a quart. 12. Reduce of a bushel to the fraction of a pint. 13. Reduce 42068ʊ of a year to the fraction of a minute. CASE XI. To find the value of a fraction in numbers of a lower denomination. 1. What is the value of of a £.? = By Case IX. £. = 3 × 20 = fis. 1qr. s. = 5,5s.; and ffd. 5d.; and d. X 4 = ffqr. = X: Ans. 5s. 5d. 1qr. = = 5s.; and if ls. is 12d., This question may be analyzed thus: - If 1£. is 20s., of a £. is of 20s. of a shilling is of 12d. = 5,5d.; and if 1d. is 4qr., of a penny is of 4qr.=1qr., Answer, as before. Or, it may be performed in the following manner. RULE. Multiply the numerator by the next lower denomination of the integer, and divide the product by the denominator; if any thing remain, multiply it by the next less denomination, and divide as before, and so continue as far as may be required; and the several quotients will be the answer. 4. What is the value of √ of a cwt.? Ans. 3 d. of a guinea, at 28 shillings? Ans. 21s. 9d. 14qr. Ans. 2qr. 15lb. 4oz. 5dr. 5. What is the value of of a lb. avoirdupois? 6. What is the value of § of a lb. troy? 7. What is the value of 8. What is the value of 10. What is the value of 1 Ans. 7oz. 13dr. Ans. 10oz. 13dwt. 8gr. of a b. apothecaries' weight. Ans. 33 53 19 12gr. 15. What is the value of of a hhd. of wine? Ans. 6gal. 2qt. 1pt. 0gi. 16. What is the value of of a hhd. of beer? 17. What is the value of Ans. 42gal. of a year (365 days)? Ans. 174d. 16h. 26m. 55 sec. 18. What is the value of 731 of a dollar ? Ans. $7.742. CASE XII. To reduce any mixed quantity of weights, measures, &c., to the fraction of the integer. 1. What part of a shilling is 1d.? is 2d.? is 3d.? is 4d. ? 2. What part of a pound is 2s. ? 3s.? 4s.? 5s.? 6s.? 9s.? 3. What part of a furlong is 3rd.? 4rd.? 5rd.? 8rd.? 9rd.? 4. What part of a hogshead is 5gal.? 8gal.? 10gal.? 5. What part of a foot is 2 inches? 3in.? 4in. ? 5in.? 8in. ? RULE. qr. Ans. In this question, the shillings, pence, farthings, &c. are reduced to elevenths of farthings for the numerator of a fraction. A pound is also reduced to the same denomiThe nation, for a denominator. fraction is then reduced to its lowest terms. Reduce the given number to the lowest denomination it contains for a numerator; and then reduce the integer to the same denomination, for the denominator of the fraction required. 7. Reduce 34d. to the fraction of a shilling. Ans. 8. Reduce 21s. 9d. 14qr. to the fraction of a guinea. Ans. 7. 9. Reduce 2qr. 15lb. 4oz. 5 dr. to the fraction of a cwt. Ans. T 10. What part of a pound are 7oz. 17dr. ? 12. What part of a pound apothecaries' weight 19 12 gr.? Ans. 8. are 33 53 Ans.. Ans. 73 13. What part of a yard are 2qr. Ona. 1-in. ? Ans. §. 15. What part of a mile are 6fur. 30rd. 12ft. 8in. 013br.? Ans.. 16. Reduce 35rd. 9ft. 2in. to the fraction of a furlong. Ans. . 17. What part of an acre are 2R. 6rd. 4yd. 5ft. 127in.? Ans. 18. What part of a square rod are 144ft. 19 19. What part of a cord are 9ft. 1462in. ? 20. What part of a hogshead of wine are 0,4 gi.? 21. What part of a hhd. of beer are 42gal.? 22. What part of a year (3654 da.) are 174d. sec. ? 6gal. 2qt. 1pt. Ans. g. Ans. 7. 16h. 26m. 52 Ans.. SECTION XVII. ADDITION OF VULGAR FRACTIONS. CASE I. To add fractions that have a common denominator. and ? and ? and ? and? and and? 12, 1, and 1. What part of an apple is ? 4. What part of an orange is and ? and ? § and ? 5. Add 2, 12, 1, and together. OPERATION. 3+5+7+11=25=3=2 Ans. In this question, we add the numerators, and divide their sum by the denominator. RULE. Write the sum of the numerators over the common denominator, and reduce the fraction if necessary. 19 29, 29 6. Add r,, fr, 14, 14, and 1 together. 7. Add 23, 23, 11, 13, and 13 together. 8. Add, 7, 7, 14, and 7 together. 9. Add , T, 4, and 11 together. 10. Add $19,491, 867, and together. 11 子, 11. Add 1, 71, 981, and 781 together. 12. Add 1671, 8747, and 7126 together. 13. Add 3361, 3333, and 3990 together. 631 6311 6319 3370 14. Add 999 888 1000, 1000, 631 To add fractions that have not a common denominator. 1. What is the sum of 7, 12, 14, and 18 ? First Method. OPERATION. 4)8 12 16 20 4×2×3×2×5=240 common denominator. 2)2 3 4 5 |