Let the pupil examine the second method of reducing fractions to a common denominator in Case VIII., Sec. XVI. 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. NOTE.If the quantity be a mixed number, the better way is to add their fractional parts separately, as in the following example. 14. What is the sum of 112, 157, 12, and 17% ? 15. What is the sum of 114, 195, and 23§? 16. What is the sum of 184, 277, and 491? 17. What is the sum of 21, 183, and 26§ ? = 69 24-27 Ans. 54299. 18. What is the sum of 173, 142, and 13? Ans. 45126· 19. What is the sum of 163, 87, 93, 31, and 17? Ans. 40. 20. What is the sum of 37111, 6141%, and 81% ? Ans. 106837. 23. Add & of 154, and § of 1074 together. Ans. 93. to 3391 Ans. 6. 42 105 To add any two fractions, whose numerators are a unit. RULE. ·Place the sum of the denominators over their product. 1. Add to. EXAMPLE. 4-5=9 Answer. 2. Add to, to, to, to, to, to, too. 3. Add to, to, to, to, to, to, to 4. Add to, to, to, to, to, to . 5. Add to, o to, o to, to to, ro to , To to 4. to, to, to, to, to, to, to . to,to,to,to,to,to,to. 6. Add 7. Add to . 8. Add to, to,to,to,to,to, 9. Add to,to,to,to,to,to 4, to . NOTE. The truth of this rule is evident from the fact, that this process reduces the fractions to a common denominator, and then adds the numerators. If the numerators of the given fractions be alike, and more than a unit, multiply the sum of the denominators by one of the numerators for a new numerator, then multiply the denominators together for a new denominator. 10. Add to %. 11. Add to, 12. Add tor, 13. Add to §, 14. Add to fr, 15. Add to 16. Add to, 17. Add to, 18. Add 1 19. Add NOTE. to, to, to, to , to, to . to, &to, & to, to, to r 6 to fr, to f, fr to fa, f to fr, fr to 1. 8 to 19. 8 T, To to 14, 10 to 16, 10 to 17, fo to 19. to, to, to 2, 3 to 7, to 14. to f, to f,&to, &to, & to 1. to 19, 11 to 19, 11 to 19, 19 to 19, 19 to 19. to 11, 11 to 11, 12 to 11, 12 to 1, 12 to 14. The preceding rule may be found very useful, because all similar questions may be readily performed mentally. XI., Sec. XVI. The fractions and of a £. by Case and are added by Case II. of Addition of Fractions. The following questions are performed in the same manner. The above question may be performed by first adding the fractions of the pounds together, and then finding their value by Case XI.; thus: OPERATION. 73£.+££. = tff£. = 1£. 7s. 1d. 2qr. Ans. 2. Add together § of a £., ‡ of a £., and 3 of a shilling. The above question may be solved by first reducing of a shilling to the fraction of a pound by Case IX., Sec. XVI. and then adding it to the other numbers, and finding their value by Case XI., Sec. XVI. Thus: of a shilling=2×20=180=5£. #£. +7 £.+3% £. = Z}}} £. = 0£. 17s. 10d. 1,31qr. Ans. NOTE.- The pupil should solve the following questions by both pro yard. of a furlong, and of a 22 Ans. 5fur. 16rd. Oft. 3in. 142gbar. How 6. A. has three house-lots; the first contains of an acre, the second of an acre, and the third of an acre. many acres do they all contain ? Ans. 2A. IR. 9p. 142ft. 87 in. 7. A man travelled 183 miles the first day, 2311 miles the second day, and 19 miles the third day. How far did he travel in the three days? Ans. 61m. 2fur. 3rd. 13ft. 4 in. of a gallon of wine to of a hhd. 8. Add Ans. 6gal. Oqt. 1pt. 14gi. Ans. 2d. 9h. 18m. 9. Add of a week to of a day. 10. Add of a square foot to a foot square. 11. Add 6 inches to 11rd. 16ft. 5in. Ans. 1 foot. Ans. 12rd. Oft. 5in. SECTION XVIII. SUBTRACTION OF VULGAR FRACTIONS. To subtract fractions that have a common denominator. 1. If be taken from what will be left? 2. If g be taken from § what will be left? 3. If be taken from 7 what will be left? 4. What portion of a dollar will be left, if be taken from? 5. Subtract from 1. 11-5=6. 1⁄2= Ans. |