7. What is the value of of a hogshead of wine? Ans. 18gal. Oqt. Opt. 8. What is the value of 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. 20s. = 42d. =240d. To perform this question, we reduce the 3s. 6d. to pence, Ans. it being the lowest denomination 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 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.. 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. 4. Add 4, 4, 4, 4, and together. OPERATION. 1+2+4+5+6=48=24 Ans. 2. Add, 1, 1, 1, 1, and if together. 6. Add 119, 114, and together. 7. Add 1978, 1, and TT together. Ans. 319. Ans. 2. Ans. 25. Ans. 219. Ans. 111. Ans. 11991. 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, %, and 12? OPERATION. 2)6 8 12 2×3×2×2=24 common denominator 2. What is the sum of §, 11, and 18 ? 24 = 12 Ans. Ans. 217. Ans. 1 527 Ans. 1977. Ans. 2. Ans. 138. Ans. 13. Ans. 2468. Ans. 57. 10. Add &,, 11, 12, 13, 18, and 1 together. 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 denominators over their product; thus, if it were required to find the sum of and, we should add the 3 and 7 together for a numerator, and multiply them together for a denominator, and the fraction would be I. To subtract fractions, that have a common denominator. RULE. Subtract the less numerator from the greater, and under the remainder write the common denominator, and reduce the fraction if necessary. II. To subtract fractions whose denominators are unlike. RULE. Reduce the fractions to a common denominator, as in Addition of fractions; then write the difference of the nu merators over the common denominator. 9. From 18 take 12. OPERATION. Ans. 4)16 12 4 X 4 × 3 = 48 common denominator. 4 3 16 3 x 13 39 11 10. From 97 take 511. OPERATION. 97 = 72, 511 = H· 48 Ans. Ans. 323 4)8 12 4 × 2 × 3 = 24 common denominator. 1 × 77 = 232, & × 415 = 230=23 6 × 8 × 1 = 48 common denominator. 8 1 |