Another Example. OK, Reduce }j; to its lowest terms. Divide by any number that (2) (4) (6) will divide both numerator and 1:3===$. denominator without a remainder. Answer, $, lowest terms. EXERCISES. 60 T 25 6. Reduce Answer, 7. Reduce 19% to its lowest terms. Answer, 8. Reduce to its lowest terms. Answer, i 9. Reduce to its lowest terms. Answer, 13 10. Reduce 1:48 to its lowest terms. Answer, 3 11. Reduce 71 to its lowest terms. Answer, 1 Case 3d. To reduce a mixed number to an improper fraction.* Example. 8 RULE. Multiply the whole number 56 5 Numerator. into the denominator of the fraction, and add the numerator 61 to the product for a new nu7 merator, under which place the given denominator. Answer, 6-2, improper fraction. EXERCISES. 12. Reduce 4; to an improper fraction. 13. Reduce 22} to an improper fraction. 14. Reduce 2915 to an improper fraction. 15. Reduce 1001% to an improper fraction. 16. Reduce 791% to an improper fraction. 17. Reduce 514,' to an improper fraction. Answer, 1 5919 59 * To express a whole number like a fraction, put 1 for the denominator, thus1 7 as 13 as 3. CASE 4th. To reduce an improper fraction to its proper terms. Example. Reduce of 8} to a simple frac- If any of the proposed quantion. tities be whole or mixed numbers, 81= first reduce them to improper then X4=$:=ts. fractions, as in Case 3d. Answer, 15. 1 2 5 IS Answer, 496 EXERCISES. 25. Reduce of į to a simple fraction. Answer, 1 26. Reduce of to a simple fraction. Answer, 27. Reduce i of off to a simple fraction. Answer, 1 28. Reduce of 81 to a simple fraction. Answer, 33 29. Reduce of į of 12} to a simple fraction. Answer, Y 30. Reduce of of 3} to a simple fraction. Answer, as 31. Reduce f of 95 of 1} to a simple fraction. CASE 6th. To find the least common multiple of any given numbers. Example. RULE. Find the least common multiple Place the given numbers in a of 4, 6, 8, and 12. line, and divide by any number 4) 4.6.8. 12 that will divide two or more of 2) 1 6 2 them without a remainder ; put 3) 1.3 1. 3 the quotients beneath, and bring down all numbers that could not 1 1 be divided. The product of all The divisors are 4, 2, and 3, the divisors is the least common consequently 4x2x3=24. multiple. Answer, 24, least com. multiple. 3 EXERCISES. 32. Required the least common inultiple of 3, 4, and 8, Answer, 24. 33. Required the least common multiple of 2, 3, 4, 5, and 6. Answer, 60. * This method of cancelling is very useful, as it shortens the work, and brings out the fraction in the lowest terms. 34. Required the least common multiple of 10, 18, 30, and 45. Answer, 90. 35. Required the least common multiple of 12, 6, 9, and 8. Answer, 72. CASE 7th. To reduce fractions of different denominators to equivalent fractions having a commion denominator. Example. RULE. Reduce }, }, and Z to fractions having Multiply each numeraa common denominator. tor into all the denomina2X8X9=144 tors, except its own, for 5X3X9=135 New numerators. new numerators; and mul7X3X8–168 tiply all the denominators 3x8x9=216 Common denominator. together for a common deAnswer, iik, já, and 118. Inominator. Should any of the pro3 & of 4 posed quantities be whole 7 13 2 The fractions are in 7, and or mixed numbers, or com 5° 7x4x5=140 pound fractions, reduce 13x1x5= 66 New numerators. them to simple fractions, 2x1 x 4= 8 and proceed as above. 1X4 X5=20 Common denominator. Answer, 40, 45, and so 2 ܪ1 are', , and EXERCISES. 36. Reduce and á to fractions having a common denominator. Answer, 36, 37 37. Reduce }, \, and to fractions having a common denominator. Answer, 44, 45, 44 38. Reduce , j, and to fractions having a common denominator. Answer, 1905, 70690's. 39. Reduce of 5, and to fractions having a common denominator. * It will appear, by reducing the new fractions into the lowest terms, that the values are not changed: thus 1=; jf=;; and 118 = 1 Answer, o, 36 40. Reduce š, }, and g to fractions having a common denominator. Answer, $59, 379, 394, 41. Reduce ì of ], 54, and to fractions having a common denominator. Answer, 1857 180', sö• 42. Reduce $, 11, 4, and 1 to fractions having a common denominator. Answer, 1357, 9936, 1388, 193'36. 14.70 200 6 93 Case 8th. To reduce fractions to others that shall have the least common denominator. Example. RULE. mon denominator. Find the least common 2) 4 . 10 . 12 multiple of all the deno minators, by Case 6th, for 5. 6 the new denominator. Divide this by each of the 2X2X5X3=60 least com. multiple. given denominators; and then =15. 15 x 3=45 multiply the quotient by New 6X 7=42 the respective numerators 5x11=55 tors. for the new numerator. 43, 6. 2) 2 5. numera il = 6. 을 = 5. Answer, 46, 4 5 4 2 89 89 EXERCISES. 43. Reduce 1, 4, and to the least common denominator. Answer, , & 44. Reduce ), s, 4, and to the least common denominator. Answer, fz, 11, i'm, & 1. 45. Reduce }, ], , and yo to the least common denominator. Answer, fó, 56, 56, & $# 46. Reduce , 1, 4, and to the least common denominator. Answer, til, h, i, & 115. 47. Reduce 1, ý, it, and it to the least common denominator. Answer, jt, f&, £, & }f. 48. Reduce 1, 15, ži, and it to the least common denominator. Answer, 44, 45, 6, & 1*. |