#pk. are neither bush. nor pk.; but bush.pk. (Art. 148), and then pk. +4pk.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. I 11. Add together 1, 1, 1, 1, and . 12. Add together 7, 8, §, and . Ans. 43. 13. Add together 3, 18, 18, and **. 14. Add together 3, 12, and f }+&+f=18+48 +48 (Art. 147, Rule 2) = = 11, Ans. 15. Add together and §. 3+3=38+33 (Art. 147, Rule 1) =‡3=133, Ans. 16. Add together f, 3, and 4. A+ A+ =1+1+1=1=14, Ans. 17. Add together, 1, and §. 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.+fd.=24d.+3d.=73d.+1fd.=f3d.=577d., Ans or, fs.+fd.=fs. +18s. =3&s. + %s. =JJs., 2d Ans. = 1st Ans. 24. Add gal. to qt. 25. Add together bush. pk. and #qt. 26. Add together ton cwt. and qr. Ans. qt. or tigal. (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. (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? #+3=38+18=17=177; 3+4=7; 31. What is the sum of 54, 35, and 123? Ans. 2113. of of 63, and 4? 36. What is the sum of 38, 63, and 31 9 of ? 37. What is the sum of 3, 4, 83, and 25? 38. How many are 83+3 +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. (a) —}=}}-18, Ans. (See Art. 152, a). 告 X-X=z¬4=}}-18=11, Ans. 22. From of take of fr• 23. From of 1 take 3 of 18. 24. From & of 14 take fr of 43. 25. From 4 of 7 take of 1. 26. From off of } take ‡ of 1% of §. Ans. . 153. Rule for subtracting one fraction from another? How are the fractions prepared in addition? 30. From s. take d. (See Art. 152, b). Ans. 1. (b) s.-fd.d.-fd.=ffd.d.§3d.=138d., Ans. or, s.d.Is. — s. 5. 08.= $s., 2d Ans. 31. From qt. take pt. = Ans. qt. or 11pt. 32. From ton take cwt. 33. From acre take rod. Ans. 188a. or 673rd. 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? 39. From 8 take 271. 8-2714-27=5, Ans. In Ex. 38, take from , and 2 units from 6 units; but in Ex. 39 we cannot take from,.. reduce one of the 8 units to, and add it to the, making tf, and then take the if, and the 2 units from the remaining 7 units. 40. From 9 take 38. from 4. Add 8 to 6).. 5. Subtract 1811⁄2 from 2517. 6. Reduce 23 to an improper fraction. 7. Reduce 8 to a fraction whose denominator is 27. 3. Reduce 9 to 6 fractional forms. 9. Divide by 13. 10. Divide by 23. 11. Divide by §. 12. Reduce of a day to hours, minutes, and seconds. 13. Reduce 3pk. 5qt. 1pt. to the fraction of a bushel. 14. Multiply 83 by 10. 15. Divide 93 by 4. 16. Divide by 9. 17. Divide 18 by 3. 18. Reduce 374 to a mixed number. 19. Reduce 1 to a whole number. 20. Multiply by 1. 21. Reduce of off to a simple fraction. 22. Subtract from 3. 153. Mode of taking a mixed number from a whole or mixed nv |