1. Fractions

2. Index What is a fraction? Equivalent Fractions Making Equivalent Fractions by multiplying Making Equivalent Fractions by dividing Simplest Form Uses of Fractions Fractions Written as a Whole Improper Fraction Mixed Number How to change from Improper Fraction to Mixed Number How to change from Mixed Number to Improper Fraction Comparing Fractions Ordering Fractions Ordering Fractions with Number Line Adding Fractions

3. What is a Fraction? I’m the NUMERATOR. I tell you the number of equal parts you are looking at or have. I’m the DENOMINATOR. I tell you the number of equal parts into which the whole is divided. A fraction is formed by dividing a whole into a number of parts

4. Uses of Fractions A fraction may represent division. Fractions can express probability. Fractions are used to compare two quantities as a ratio. Student Reference Book p. 57-58

5. Equivalent Fractions Equivalent fraction: fractions that have the same value 1 WHOLE

6. Multiply the numerator and denominator by the same number. You will get a new fraction with the same value as the original fraction. We are not changing the value of the fraction, because we are simply multiplying by a fraction that is equivalent to ONE. To Make Equivalent Fractions

7. What do you get when you multiply a fraction by 1? You get AN EQUIVALENT FRACTION that makes adding & subtracting fractions possible.

10. Make An Equivalent Fraction Find the Missing Numerator! Given the new denominator, can you find the missing numerator? x 3

11. Make An Equivalent Fraction Find the Missing Numerator! Given the new denominator, can you find the missing numerator? x 4

12. Make An Equivalent Fraction If you have larger numbers, you can make equivalent fractions using division. Divide by a common factor. In this example, we can divide both numbers by 7. ÷ 7 28 35 4 5

13. Fractions in Simplest Form Fractions are in simplest form when the numerator and denominator do not have any common factors besides 1. Examples of fractions that are in simplest form: 4 5 2 11 3 8

14. Writing Fractions in Simplest Form Find the greatest common factor (GCF) of the numerator and denominator. Divide both numbers by the GCF.

15. Example: 20 28 20 1 x 20 2 x 10 4 x 5 28 1 x 28 2 x 14 4 x 7 20: 1, 2, 4, 5, 10, 20 28: 1, 2, 4, 7, 14, 28 Common Factors: 1, 2, 4 GCF: 4 We will divide by 4. ÷ 4 = 5 7 Simplest Form

16. Fractions Written as a Whole

17. If a hexagon is worth 1, what are 5 trapezoids worth? 1 Whole Trapezoid 2 Trapezoids = 1 Hexagon 1 Whole ½ We can report this as 2 ½ or 5/2 Trapezoid

18. Improper Fraction fractions that are equal to or greater than 1 5/2 is read as – five halves

19. Mixed Number a whole number and a fraction written together 2 ½ is read as - two and one half

20. If a triangle is 1/3, what shape is ONE whole? 1/3 Remember: Numerator is what you have- 1. Denominator is how many pieces your whole is cut into - 3. How many more triangles do you need to make a whole? 1/3 What shape can we make? 1/3 + 1/3 + 1/3 = 3/3 or 1 Whole Trapezoid 1 Whole

21. If the triangle is 1/3, what is the rhombus? If the rhombus is 1/3, what shape is the WHOLE? Turn to MJ p. 124 If the rhombus is 1/3, what is the triangle? If the triangle is ½, what shape is the WHOLE? If the triangle is ½, what is the trapezoid?

22. Mixed Number A mixed number has a part that is a whole number and a part that is a fraction. = 1 3 4

23. What is the mixed number? =3 3 4

24. =4 3 4

25. =5 1 2

26. Improper Fraction A fraction in which the numerator is greater than the denominator. = 8 4

27. What is the improper fraction? = 15 4

28. What is the improper fraction? = 19 4

29. What is the improper fraction? = 11 2

30. How is the mixed number below related to the improper fraction? = 11 2 = 1 2 5

31. How to change an improper fraction to a mixed number = 5 2  Divide the numerator by the denominator.  Put your remainder over the denominator.

32. How to change an improper fraction to a mixed number = 5 2 2 ) 5 numerator denominator

33. How to change an improper fraction to a mixed number = 5 2 2 ) 5 numerator denominator 2r1

34. How to change an improper fraction to a mixed number = 5 2 2 ) 5 numerator denominator 2 1 Put your remainder over the Denominator. 2

35. Change this improper fraction to a mixed number. 7 3 = 3 ) 7 2 r1 Put your remainder over the denominator. = 2 1 3

36. Change this improper fraction to a mixed number. 8 3 = 3 ) 8 2 r2 Put your remainder over the denominator. = 2 2 3

37. Change this improper fraction to a mixed number. 9 2 = 2 ) 9 4 r1 Put your remainder over the denominator. = 4 1 2

38. Change this improper fraction to a mixed number. 11 5 = 5 ) 2 r1 Put your remainder over the denominator. = 2 1 5

39. Change this improper fraction to a mixed number. 10 5 = 5 ) 2 If there is no remainder your answer is a whole number. = 2

40. Change this improper fraction to a mixed number. 16 4 = 4 ) 4 If there is no remainder your answer is a whole number. = 4

41. How to change a mixed number to an improper fraction Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. 4 1 2 x + = 9 2

42. Change this mixed number to an improper fraction Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. 6 2 3 x + = 20 3

43. Change this mixed number to an improper fraction Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. 3 2 5 x + = 17 5

44. Change this mixed number to an improper fraction Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. 4 3 4 x + = 19 4

45. Change this mixed number to an improper fraction Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. 6 2 3 x + = 20 3

46. Change this mixed number to an improper fraction Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. 8 3 5 x + = 43 5

47. Use >, <, or =. 910< < Cross Multiply or “Butterfly Method” Comparing Fractions

48. Use >, <, or =. 1210 > > Cross Multiply or “Butterfly Method”

49. To order fractions you can draw a picture or use the Least Common Denominator (LCD). Ordering Fractions

50. One way to compare or order fractions is to express them with the same denominator.

51. Any common denominator could be used. But the Least Common Denominator (LCD) makes the computation easier.

52. Use LCD List the fractions in order from greatest to least.

53. Use LCD Step 1: Find a common denominator

54. 6, 12, 18, 24, 30, 36 …. LCD = 36 Find the LCD: 12, 24, 36, 48, 60 … 9, 18, 27, 36 … 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 … Put the largest denominator first and write down the first 5 multiples Then continue with the next denominator until you find a common digit…

55. Step 2: Write equivalent fractions. 36 x 6 6 36 x 3 21 36 x 4 20 36 x 12 24

56. Step 3: Compare the numerators 36 6 21 36 20 36 24 In order from greatest to least:

57. PRACTICE: Use LCD In order from greatest to least:

58. Finding Fractions on a Number Line We can use number lines to help us order fractions.

59. Finding Fractions on a Number Line This number line breaks one whole into fourths. Where would ¼ be on the number line? What about 4/4?

60. Finding Fractions on a Number Line How many sections does this number line break one whole into? Can you locate where 1/8 would be? Name a fraction in eighths that is between ½ and ¾.

61. Finding Fractions on a Number Line What does this number line show? Where would 7/9 be? What fraction is between 1/9 and 2/9?

62. Finding Fractions on a Number Line How would you explain this number line using words? Can you find 3/5? Can you mark a fraction larger than 4/5 on the number line?

63. Finding Fractions on a Number Line What type of number line is this? Can you order 5/8, 1/4, 2/3, and 3/16 on this number line?

64. Adding Fractions with common denominators

65. Add these fractions 1/5 3 5 1 5 + = 4 5

66. Add these fractions 1/4 2 4 1 4 + = 3 4

67. Adding Fractions with different denominators Problem: You can’t add fractions with different denominators without getting them ready first. They will be ready to add when they have common denominators Solution: Turn fractions into equivalent fractions with a common denominator that is find the Lowest Common Multiple (LCM) of the two denominators

68. 7, 14, 21, 28, 35… 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 We need a common denominator to add these fractions.

69. 7, 14, 21, 28, 35… 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 REMEMBER the first number IN COMMON that appears on both lists becomes the common denominator

70. x 2 X 7 x 7 7 6 7 + 6 = 13 13 14

71. We need a common denominator to add these fractions. 5, 10, 15, 20, 25, 30, 35, 40, 45 7, 14, 21, 28, 35, 42, 49, 56, 63

72. x 7 X 5 x 5 15 7 15 + 7 = 22 22 35

73. Try These A F E B C D

74. Answers On Next Slide Each click on the next slide reveals an answer. Check your papers. If you discover an incorrect answer, be able to explain your mistake.

75. Try These A F E B C D 17 27 19 20 10 9 41 28 26 21 13 12