6. What part of a £. is 5s. 5d. 1qr.? RULE. 2880 2880 10560 = Ans. Reduce the given number to the lowest denomination it contains for a numerator; and then reduce the integer to the same denomination, for the denominator of the fraction required. Ans. 7. Reduce 31d. to the fraction of a shilling. Ans. 7. 9. Reduce 2qr. 15lb. 4oz. 5dr. to the fraction of a cwt. Ans. T 10. What part of a pound are 7oz. 17dr.? Ans. . Ans. . 12. What part of a pound apothecaries' weight are 33 53 19 124gr.? Ans.. Ans. 13 13. What part of a yard are 2qr. Ona. 15in.? Ans. §. 15. What part of a mile are 6fur. 30rd. 12ft. 8in. 013br. ? Ans. 1. 16. Reduce 35rd. 9ft. 2in. to the fraction of a furlong. 17. What part of an acre are 2R. 6rd. 4yd. 5ft. 18. What part of a square rod are 144ft. 19 19. What part of a cord are 9ft. 1462in.? 20. What part of a hogshead of wine are 01gi.? 21. What part of a hhd. of beer are 42gal. ? sec. ? Ans. §. 127 in. ? Ans. 13. 3+5+7+11=2§=&=2} Ans. In this question, we add the numerators, and divide their sum by the denominator. RULE. Write the sum of the numerators over the common denom inator, and reduce the fraction if necessary. 11 13 6. Add 7, 17, 17, 14, 14, and 19 together. 29 4 29 87 8. Add 7, 17, 19, 19, and 37 together. 9. Add,, 2, and 117 together. 10. Add 619 491, 267, and together. 631 631 631 631 Ans. 2435. together. 3000 3370 Ans. 2141. 1 together. Ans. 2. 83 CASE II. 888 and 777 To add fractions that have not a common denominator. 1. What is the sum of 7, 12, 1, and 18 ? 4×2×3×2×5=240 common denominator. Having found a common denominator by Case VIII., we proceed as in the last Case. 8 30X 7210 12 20x 5=100 16 15x11=165 20 12×13=156 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. 11. Add 1,7, and 8 together. 349 Ans. 92. Ans. 6. Ans. 172. Ans. 92. 5 Ans. 18. Ans. 1. Ans. 318. Ans. 1 140. Ans. 62. 83 12. Add 7, 31, and 5 together. 13. Add 63, 78, and 4 together. 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 119, 19, and 235? 16. What is the sum of 184, 2770, and 491 ? 17. What is the sum of 213, 183, and 26§ ? 69 24=27 Ans. 54293. 18. What is the sum of 173, 14, and 132? Ans. 456. 19. What is the sum of 163, 87, 93, 31, and 17? Ans. 40. 20. What is the sum of 37113, 61418, and 81§ ? 21. Add of 183, and 11 of of 6 Ans. 106837. 22. Add § of 18, and of 11 of 7 together. Ans. 13. 23. Add § of 151, and ₫ of 1074 together. Ans. 93. to 3391 105 Ans. 6. and together. Ans. 31127831. 9471 3143 CASE III. To add any two fractions, whose numerators are a unit. - 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, to, 7 to 1, To to, To to , 1 to 4. 6. Add 7. Add to,to,to,to,to,to,to. 8. Add to,to,to,to,to,to,to. 9. Add to,to,to,to,to,to,to. to,to,to,to,to,to,to . - 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 3. 4 × 5=20 4+5=9x3=27 = 1 Ans. 11. Add 12. Add to, to, to, to 4, & to §, & to 1, 3 to 3. to fr, & to %, & to §, & to §, § to §, & to T 13. Add 897 6 to §, & to 11, 9 to 13, fi to fз, fi to 17, 11 to 19. 14. Add to, to fr, fr to 3, 13 to 15, fs to fr, to . 8 т 8 8 8 8 3 17 18. Add 1 to 18, 11 to 19, 11 to 19, 18 to 19, 19 to 19. 19. Add 1 to 11, 11 to 1,1 to 15, 11 to 1, 11 to 1. NOTE.The preceding rule may be found very useful, because all similar questions may be readily performed mentally. and are added by Case II. XI., Sec. XVI. The fractions 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£.+1£. = £. = 1£. 7s. 1d. 2qr. Ans. 2. Add together § of a £., † of a £., and 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. |