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

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.

70. 58=58

71. 34=68

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

79. 123.000= 1,23 x 105

80. 0,0038 = 3,8 x 10-3