3. What is the value of of a yard? Ans. 3qr. Ona. 4. What is the value of of an acre? Ans. 1R. 28p. 155ft. 82 in. 5. What is the value of of a mile? Ans. 1fur. 31rd. 1ft. 10in. 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. XI. To reduce any mixed quantity of weights, meas ures, &c. to the fractions of the integer. 1. What part of a pound is 3s. 6d. ? OPERATION. 42d. 3s. 6d. = 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 a fraction. We then reduce the one pound to pence, and make them the denominator of a 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. 7 Ans. 4. What part of 2m. 3fur. 20rd. is 2fur. 30rd. ? 5. What part of 2A. 2R. 32p. is 3R. 24p. ? OPERATION. 3R. 24p. 144p. 2A. 2R. 32p.432p. - Ans. 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 denomina tor. RULE. Write the sum of the numerators over the common denominator. 1. Add 4, 4, 4, 4, and together. 2. Add OPERATION. 1+2+4+5+6—8—24 Ans. ,, Tr, fr, fr, and if together. 3. Add, r, fr, fr, and together. 5. Add 17, 19, 27, and 4 together. 6. Add 119, 14, and 78 together. 7. Add 17, 19, and 11 together. Ans. 319. Ans. 24. Ans. 22. 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 ? A OPERATION. 2) 6 8 12 2×3×2×2: = 24 common denominator. = 2. What is the sum of §, 12, and 18? 8 9. Add ,,, t, &, and together. 10. Add &,, 11, 14, 1, 12, and 1 11. Add of to of 7. together. Ans. 1. 12. Add of 7 to 12 of 2. Ans. 1. Ans. 1. Ans. 36 Ans. 8. Ans. 1017. Ans. 36. 17. Add 4 to 59. 18. Add 172 to 18,5. 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 numerators 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 19. Add to, to, to, to, to J. 20. Add to, to, 21. Add to, to, Section 22. SUBTRACTION OF VULGAR FRACTIONS. 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 compound fractions to simple fractions, and mixed fractions to improper fractions, then having found a common denominator divide this by each of the denominators of the fractions, and multiply their quotients by their respective numerators. The difference of these products, written over the common denominator, will give the answer required. |