6. Reduce 1r. 2sq. rd. 20sq. yd. 1sq. ft. 72sq. in. to the fraction of an acre. Ans.. 7. Reduce 4oz. 6dwt. 93gr. to the fraction of a pound. Ans. NOTE 2. In Example 7, by Rule 1, reduce 4oz. 6dwt. 9}gr. to fifths of a grain for a numerator, and 1lb. to fifths of a grain for a denominator. How shall it be done by Rule 2? Which mode is preferable? Why? 8. Reduce 1pk. 3qt. 1pt. to the fraction of a bushel. 9. Reduce 6s. 20° 20′ 30′′ to the fraction of a circumference. 10. Reduce 1m. 2fur. 11rd. 2yd. 1ft. 24b. c. to the fraction of a league. 11. Reduce 1qr. 2na. in. to the fraction of a yard. year. 12. Reduce 3wk. 6d. 9h. 27m. to the fraction of a Julian 13. Reduce 1qt. 1pt. 14gi. to the fraction of a gallon. 14. Reduce 4 cord feet, 12 cubic feet, and 1382 cubic inches to the fraction of a cord. Ans. 3. 15 Reduce 3oz. 4dr. 1sc. 10gr. to the fraction of a pound. 16. Reduce 4fur. 5ch. 2rd. 20li. to the fraction of a mile. 17. Reduce 11cwt. 11lb. 1oz. 123dr. to the fraction of a ton. 18. Reduce 3 bushels, 1 peck, 4 quarts, and 1 pint to the fraction of a bushel. Ans. 24. 17 NOTE 3. Sometimes, as in Ex. 18, the number called the part is greater than the unit with which it is compared; sometimes it is equal to the unit. PROBLEM 14. 152. If numbers of the same kind are added together, their sum will be of the same kind as the numbers added; thus, 3 books+4 books = 7 books; 3 hats 4 hats 7 hats; and for a like reason, 3+; 3+13=13, etc., etc. (a) Numbers of different kinds cannot be united by addition; thus, 3 hats + 4 books are neither 7 hats nor 7 books; so + are neither nor ; but numbers that are unlike may sometimes be made alike by reduction, and then added; thus, 3+3=33+28 (Art. 147)=13. (b) Again, 2bush. +3pk. are neither 5bush. nor 5pk.; but 2bush. Spk., and then 8pk. + 3pk. = 11pk.; so bush. + pk. are neither bush. nor pk.; but bush.pk. (Art. 148), and then pk.pk.pk. Hence, To add fractions: RULE. Reduce the fractions, if necessary, first to the same denomination, then to a common denominator; after which write the sum of the new numerators over the common denominator. 10. Add together §8, §4, 48, and Z. 11. Add together £5, 175, f/‰, 135, and. 12. Add together 7, %, §, and ‡. 13. Add together 24, 18, 18, and 13. 14. Add together 3, 12, and 1. } + A+ A = 18+38+48 (Art. 147, Rule 2) = 15. Add together 3 and §. 3+8=18+38 (Art. 147, Rule 1) = 13=133, Ans. 16. Add together ft, 3, and 4. 17. Add together 31⁄2, 1, and §. A+ A+ =1+1+1=1=14, Ans. 152. Rule for adding fractions? Can unlike numbers be added? Of what kind is the sum of two or more numbers? 23. Add s. to 3d. fs.+3d.2d.+3d.=73d.+18d.=ffd.=57d., Ans or, fs.+3d.=3s. +18s.=3&s.+s.= $s., 2d Ans. 1st Ans. 24. Add gal. to jqt. 25. Add together bush. pk. and qt. 26. Add together ton cwt. and qr. Ans. qt. or gal. (c) To add two fractions that have a common numer ator: Multiply the sum of the denominators by either numerator, and place the product over the product of the denominators. and §? =17, Ans. and ? 28. What is the sum of 29. What is the sum of (d) To add mixed numbers: Add the sum of the fractions to the sum of the integers. 30. What is the sum of 3 and 43? #+8=38+18=43=177; 3+4=7; Ans. 211 31. What is the sum of 54, 35, and 123? 8 36. What is the sum of 38, 63, and of ? 37. What is the sum of 3, 4, 85, and 25? 38. How many are 83+33 +83+14? 152. Mode of adding two fractions that have like numerators? adding mixed numbers? Mode of PROBLEM 15. 153. To subtract a less fraction from a greater: RULE. Prepare the fractions as in addition, and then write the difference of the numerators over the common denominator. 12. From & take 3. 123 (a) ‡ — 3=13—18, Ans. (See Art. 152, a). Ans. 1. 13. From 4 take fr 14. From 1 15. From Ans. take . 19. From take 36 20. From take. 21. From of take of #. X-X=8—4=}}-1}=}}, 22. From of take of fr Ans. . 153. Rule for subtracting one fraction from another? How are the fractions prepared in addition? 61 善 29. From take 30. From s. take d. (See Art. 152, b). (b) s.-fd.2d.d.§gd.d.§3d.=1}}d., Ans. or, s.d.fs.fs. = s. 30s. 53s., 2d Ans. 31. From qt. take pt. = = Ans. qt. or 14pt. Ans. 18a. or 6733rd. NOTE. The answer to these examples may be in any denomination of the table. 34. From of a week take of an hour. (c) To subtract when the fractions have a common numerator: Multiply the difference of the denominators by either numerator, and write the product over the product of the denominators. (d) To take a mixed number from a whole or mixed number. 38. From 6 take 23. 62341, Ans. (See Art. 152, d). 153. Mode of subtracting when the fractions have a common numerator? |