Hence the following RULE. Let the given numerator be multiplied by all the denom. inations between it and the one to which it is to be reduced ; then place the product over this denominator, and reduce the fraction to its lowest terms. 2. What part of a grain is goto of a pound Troy? TO X 4X4 X2=3748= Ans. 3. Reduce o of a furlong to the fraction of a foot. 1920 X 4 X yat=1998 = 1 Ans. 4. What part of a square foot is 58080 of an acre ? 58780 X 4 X 4 X 272 = 43568 = Ans. 5. What part of a peck is of a bushel ? Ans. Q. 6. What part of a pound is ado of a cwt. ? Ans. X. To find the value of a fraction in the known parts of the integer. RULE. Multiply the numerator by the next lower denomination of the integer, and divide the product by the denominator; if any thing remains, 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. 1. What is the value of 2 of a pound? Ans. 58., 10d. 2. What is the value of g af a cwt. ? Ans. 3qr. 3lb. loz. 12fdr. 0 9) 7 0 0 0 0 3 3 1 124 3. What is the value of of a yard? Ans. 3qr. Ofna. 9) 7 0 0 0 3 00 4. What is the value of # of an acre ? Ans. IR. 28p. 155ft. 824 in. 0 1 28 155 8 24 5. What is the value of g of a mile ? Ans, 1fur. 31rd. Ift. 10in. 6. What is the value of į of an ell English ? Ans. lqr. 1 Ina. 7. What is the value of of a hogshead of wine ? Ans. 18gal. Oqt. Opt. 8. What is the value of 1 of a year? Ans. 232da. 10h. 21m. 4914 sec. XI. To reduce any mixed quantity of weights, measures, &c. to the fractions of the integer. 1. What part of a pound is 3s. 6d. ? To perform this question, 3s. 6d. = 42d. we reduce the 3s. 6d. to pence, 20s. = 240d. it being the lowest denomina tion in the question, and we make them the numerator of the fraction. We then reduce the one pound to pence, and make them the denominator of the fraction. This fraction we reduce to its lowest terms, and we have the answer required.; wherefore the following OPERATION. RULE. Reduce the given number to the lowest denomination it contains for a numerator, and reduce the integers to the same denomination, for the denominator of the fraction required. 2. Reduce 4s. 8d. to the fraction of a pound. 3. What part of a ton is 4cwt. 3qr. 121b. ? OPERATION. 4cwt. 3qr. 121b. = 5441b. 20cwt. = 2240lb. = 17 Ans. 4. What part of 2m. 3fur. 20rd. is 2fur. 30rd. ? 5. What part of 2A. 2R. 32p. is 3R. 24p. ?. OPERATION. & Ans. 3R. 24p.= 144p. 2A. 2R. 32p. = 432p. 6. What part of a hogshead of wine is 18gal. 2qt. ? Ans. 1276 7. What part of 30 days are 8 days 17h. 20m. ? Ans. 37. 8. From a piece of cloth, containing 13yd. Oqr. 2na. there were taken 5yd. 2qr. 2na. What part of the whole piece was taken ? Ans. 4. Section 21. ADDITION OF VULGAR FRACTIONS. I. To add fractions, that have a common denominator. RULE. Write the sum of the numerators over the common de. nominator. 1. Add 7, 4, 4, , and & together. OPERATION. 1+2+4+5+6= 4= 2# Ans. 2. Add 1 , IT, it, it, and if together. Ans. 311. 3. Add to 14 , 1t, and I together. Ans. 214 4. Add 25, , 5, and it together. Ans. 275. 5. Add 17, 19, 37, and 41 together. Ans. 2. 6. Add 119, 117, and 7's, together. Ans. 1114 7. Add 7471, 1111, and 1741 together. Ans. 11441 II. To add fractions that have not a common denominator. RULE. Reduce mixed numbers to improper fractions, and compound fractions to simple fractions ; then reduce all the fractions to a common denominator ; and the sum of their numerators, written over the common denominator, will be the answer required. 1. What is the sum of b, g, and ? 1/2 OPERATION. 2) 6 8 12 2 X3 X 2 X 2= 24 common denominator 3)3 4 6 6 4 X 5=20 21 4 2 8 3 X3= 9 1 2 1 1 2 2 X 7=14 43 = 14 Ans. 2. What is the sum of 5, 11, and 18 ? Ans. 213. 3. What is the sum of , 15, and ? Ans. 1527 1260 4. What is the sum of li, and 37 ? Ans. 1977. 5. What is the sum of , /, $, and Ił ? Ans. 224 6. Add $, di, , and together. Ans. 1385 7. Add 2, $t, and ft together. Ans. 11315 8. Add 25, 48, 74, and soy together. Ans. 2368 9. Add 1, 5, 1, $, &, 4, and } together. Ans. 5730 10. Add f, io, If, it, 1}, it, and 14 together. Ans. 614436 11. Add f of i to & of }. Ans. 145. 12. Add of } to 13 of 4. Ans. 136. 13. Add } of to of You Ans. 2330 14. Add qof of to off of yo. Ans. 12 15. Add 1 of 3 of 13 to 4 of . Ans. 36 16. Add 3 to 411. Ans. 814 17. Add 44 to 56. Ans. 1015. 18. Add 174 to 1817 Ans. 364. Note 1. If the quantities are mixed numbers, the better way is to add the fractional parts separately, and then to add their sum to the amount of the whole numbers. NOTE 2. If there be but two fractions to add, and their numera. tors are a unit, their sum may be found by writing the sum of the |