Hence the following 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 this denominator, and reduce the fraction to its lowest terms. 2. What part of a grain is go of a pound Troy? 8640 X 12 X 20 X 24=3788 = Ans. 3. Reduce ʊ of a furlong to the fraction of a foot. T320 X 40 X 16t=668 = Ans. 4. What part of a square foot is 50gʊ of an acre? 58080 × 1 × 40 × 2724 = 18888 = & Ans. 5. What part of a peck is 6. What part of a pound is X. To find the value of of the integer. of a bushel? dʊ of a cwt. ? Ans.. Ans. a fraction in the known parts 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 of a pound? Ans. 5s. 10d. 7. What is the value of 8. What is the value of of a hogshead of wine? of a year? Ans, 232da. 10h. 21m. 49 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. ? OPERATION. 3s. 6d. 42d. 20s. = To perform this question, we reduce the 3s. 6d. to pence, 240d. Ans. it being the lowest denomination in the question, and we We then re make them the numerator of the fraction. duce 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 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. 12lb. ? OPERATION. 4cwt. 3qr. 12lb. = 544lb. 20cwt. =2240lb. Ans. 4. What part of 2m. 3fur. 20rd. is 2fur. 30rd. ? 5. What part of 2A. 2R. 32p. is 3R. 24p. ? 6. What part of a hogshead of wine is 18gal. 2qt. ? Ans. 7. What part of 30 days are 8 days 17h. 20m. ? Ans. 17. 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. . 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 denominator. 1. Add 4, 4, 4, 4, and together. OPERATION. 1+2+4+5+6=4=24 Ans. 2. Add,,, fr, fr, and if together. Ans. 311. 3. Add,,,, and together. Ans. 2. 4. Add,,, and together. 5. Add 17, 19, 27, and 44 together. 6. Add 11, 1, and 7. Add 1978, H, and II. To add fractions that have not a common denominator. Ans. 2. Ans. 214. together. together. Ans. 1+14. Ans. 11991. 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 §,, and? OPERATION. 2) 6 8 12 2×3×2×224 common denominator 3)3 4 2)1 4 6 2 1 2 1 6, 4×5=20 8 3X3 9 12 2X7=14 43 2. What is the sum of §, 1, and 18? 3. What is the sum of,, and? 4. What is the sum of, and 34 ? 5. What is the sum of 2, §,, and1⁄2? 6. Add 4, 2, 4, and together. ΣΤ 9. Addį, ž, §, t, &, f, and together. 9 24 =1 Ans. Ans. 217. Ans. 152. Ans. 1977. Ans. 138. 10. Add §, fo, 11, 11, 13, 18, and 1 together. Ans. 13. Ans. 2388. Ans. 5. 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 numerators are a unit, their sum may be found by writing the sum of the |