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- 1. HANDOUT- FRACTIONS <br />By : Mr. Ronald (PGS)<br /><ul><li>Definition of Fraction
- 2. Fraction is numbers expressed in the form :
- 3. ab, where b ≠0
- 4. a=numerator
- 5. b=denominator
- 6. Example :
- 7. what is the fraction of shaded and un-shaded from the picture below!
- 8. 18097582550
- 9. Solution :
- 10. Shaded region : 39= 13
- 11. Un-Shaded region : 1- 13= 23
- 12. Forms and Kinds of Fraction
- 13. Proper Fraction
- 14. Proper faraction is a fraction in which its numenator less than its denominator.
- 15. Example : 12, 35,67.
- 16. Improper Fraction
- 17. Improper fraction is a fraction in which its denominator less than numerator.
- 18. Example : 94, 145,267
- 19. Note :
- 20. Improper Fraction can be change to mixed number
- 21. Mixed Number ( Mixed Fraction )
- 22. Mixed number is a fraction which consist of integer and proper fraction.
- 23. Value of mixed number is :
- 24. abc, where c ≠0
- 25. Example : 212,335,467
- 26. Note:
- 27. Mixed number can be expressed as a n improper fraction.
- 28. abc=a x c+bc, where c ≠0
- 29. Equivalent Fraction
- 30. Equivalent fraction is a collection of fraction which has the same value.
- 31. Equivalent fraction can be obtained by multiplying or dividing numerator and denominator with same number.
- 32. Example :
- 33. 12= 1 x 22 x 2=24
- 34. 48= 4 : 48 :4= 12
- 35. Decimals
- 36. Decimals is a part of fraction which is expressed by using comma or point
- 37. Example : 3, 003 ; 17, 8 ; 1234,567
- 38.
- 39. Percentage
- 40. Percentage can be called as fraction per- 100.
- 41. In other words percentage is a fraction whose denominator is 100.
- 42. Percentage is symbolized by %
- 43. Example :
- 44. 50 %=50100= 12=0,5
- 45. 0,25=25100=14=25 %
- 46. Permile (Per-Thousand)
- 47. Permile is a fraction whose denominator is 1000.
- 48. We can call permile is fraction per 1000.
- 49. Permile is symbolized by %0
- 50. Example :
- 51. 5 %=51000= 1200=0,005
- 52. Simplifying Fraction
- 53. The simplest can be obtained if numerator and denominator of original fraction divided by their GCF (greatest Common factors )
- 54. Example :
- 55. Express 1218 in the simplest form!
- 56. Factors of 12 = 1, 2, 3, 4, 6, 12
- 57. Factors of 18 = 1, 2, 3, 6, 9, 18
- 58. GCF of 12 and 18 is 6
- 59. Then, 1218= 12 :618 :6=23
- 60. Sorting out Fraction
- 61. Fraction can be sorted out from the largest to the smallest or inversely as follows.
- 62. Equalizing the denominators
- 63. First, find LCM of the denominators. Express the fractions using the obtained LCM as their denominators. Then consider the numerators. The larger numerator, the larger fraction. It inversely hold.
- 64. Equalizing the numerators
- 65. First, find LCM of the numerators. Express the fractions using the obtained LCM as their numerators. Then consider the denominators. Then, the smaller the denominator is the larger fraction. It inversely hold.
- 66. Determining Fraction Having Value Between two Fraction
- 67. Among two different fraction, there must be fraction having value between the two fractions.
- 68. The denominators of two fractions are equalized first, and determine which fraction located between the two fraction.
- 69. In case no fraction is obtained, change the denominators to be twice greater of the previous one.</li></ul>Example :<br />Determine a fraction located between 58 and 34 !<br /><ul><li>Equalizing denominators
- 70. 58=58
- 71. 34=68
- 72. Since no intended fractions are obtained, each denominators is made bigger that the following is obtained.</li></ul>58=1016<br />68=1216<br />Then, between 1016 and 1216 is 1116 <br /><ul><li>Operation Of Fraction
- 73. OPERATIONPROPERTIESFORMAdditionCommutativeab+cd= cd+abAssociativeab+cd+ef= ab+cd+ efSubstractionInvers of additionab-cd= ab+-cdMultiplicationCommutativeabxcd= cdxabassociativeabxcdxef= abxcdxefDistributiveabxcd±ef= a x cb x d±a x eb xfDivisionInvers of Multiplicationab :cd= ab x dc
- 74. Standard Form (Scientific Notation)
- 75. Standard form or scientific notation is exponential number with base of 10.
- 76. In standard form :
- 77. A large numbers is written as a x 10n where 1 ≤ a < 10, n is natural number
- 78. A small number is written as a x 10-n where 1 ≤ a < 10, n is natural number</li></ul>Example:<br />Write down the following numbers in standard form<br /><ul><li>1.000.000 = 106
- 79. 123.000= 1,23 x 105
- 80. 0,0038 = 3,8 x 10-3

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