1. Copyright 2014 Scott Storla Rational Numbers

2. Copyright 2014 Scott Storla Vocabulary Rational number Proper fraction Improper fraction Mixed number Prime number Composite number Prime factorization Reciprocal

3. Reduce Copyright 2014 Scott Storla

4. The Rational Numbers Copyright 2014 Scott Storla

6. Irrational Numbers The real numbers which are not rational. Copyright 2014 Scott Storla Trying to find a rational number that’s equal to pi.

7. Fractions Copyright 2014 Scott Storla

8. Proper Fraction In a proper fraction the numerator (top) is less than the denominator (bottom). The value of a proper fraction will always be between 0 (inclusive) and 1 (exclusive). Copyright 2014 Scott Storla

9. Improper Fraction In an improper fraction the numerator (top) is greater than or equal to the denominator (bottom). The value of an improper fraction is greater than or equal to 1. Copyright 2014 Scott Storla

10. Mixed Number A mixed number is the sum of a positive integer and a proper fraction. Copyright 2014 Scott Storla

11. Writing a mixed number as an improper fraction The new numerator is the product of the denominator and natural number added to the numerator. The denominator remains the same. Copyright 2014 Scott Storla

12. Writing an improper fraction as a mixed number 1.Divide the numerator by the denominator. 2.The natural number is to the left of the decimal. 3.Subtract the product of the natural number and original denominator from the original numerator. This is the numerator of the proper faction. 4.The denominator of the proper fraction is the same as the original denominator. Copyright 2014 Scott Storla

13. Prime Factorization Copyright 2014 Scott Storla

14. Prime Number A natural number, greater than 1, which has unique natural number factors 1 and itself. Ex: 2, 3, 5, 7, 11, 13 Copyright 2014 Scott Storla

15. Composite Number A natural number, greater than 1, which is not prime. Ex: 4, 6, 8, 9, 10 Copyright 2014 Scott Storla

16. Prime Factorization Copyright 2014 Scott Storla

17. Prime Factorization To write a natural number as the product of prime factors. Ex: 12 = 2 x 2 x 3 Copyright 2014 Scott Storla

18. Factor Rules Copyright 2014 Scott Storla

19. Decide if 2, 3, and/or 5 is a factor of 42 310 987 4950 Copyright 2014 Scott Storla

20. List all positive integers between 51 and 61 inclusive. List all prime numbers between 51 and 61 inclusive. List all rational numbers with denominators of 1 between 110 and 120 inclusive. List all prime numbers between 110 and 120 inclusive. List all natural numbers between 31 and 40 inclusive. List all prime numbers between 31 and 40 inclusive. Copyright 2014 Scott Storla

21. Building a factor tree for 20 The prime factorization of 20 is 2 x 2 x 5. 20 45 2 2 Copyright 2014 Scott Storla

25. The prime factorization of 24 is 2 x 2 x 2 x 3. 24 2 12 Find the prime factorization of 24 2 6 2 3 Copyright 2014 Scott Storla

26. The prime factorization of 315 is 3 x 3 x 5 x 7. 315 5 63 Find the prime factorization of 315 3 21 7 3 Copyright 2014 Scott Storla

27. The prime factorization of 119 is 7 x 17. 119 7 17 Find the prime factorization of 119 Copyright 2014 Scott Storla

28. The prime factorization of 495 is 3 x 3 x 5 x 11. 495 5 99 Find the prime factorization of 495 9 11 3 Copyright 2014 Scott Storla

29. Prime Factorization Copyright 2014 Scott Storla

30. Reducing Fractions Copyright 2014 Scott Storla

32. Reducing Fractions A fraction is reduced when the numerator and denominator have no common factors other than 1. Copyright 2014 Scott Storla

33. Reducing Fractions A fraction is reduced when the numerator and denominator have no common factors other than 1. Copyright 2014 Scott Storla

34. No “Gozinta” method allowed Copyright 2014 Scott Storla

35. No “Gozinta” (Goes into) method allowed Copyright 2014 Scott Storla

36. No “Gozinta” (Goes into) method allowed Copyright 2014 Scott Storla

37. Simplify using prime factorization Copyright 2014 Scott Storla

38. Simplify using prime factorization Copyright 2014 Scott Storla

39. Simplify using prime factorization Copyright 2014 Scott Storla

40. Reduce using prime factorization Copyright 2014 Scott Storla

41. Reduce using prime factorization Copyright 2014 Scott Storla

42. Reduce using prime factorization Copyright 2014 Scott Storla

43. Reducing Fractions Copyright 2014 Scott Storla

44. Multiplying Fractions Copyright 2014 Scott Storla

45. No “Gozinta” method allowed Copyright 2014 Scott Storla

46. using prime factorizationMultiply Copyright 2014 Scott Storla

47. Procedure – Multiplying Fractions 1. Combine all the numerators, in prime factored form, in a single numerator. 2. Combine all the denominators, in prime factored form, in a single denominator. 3. Reduce common factors 4. Multiply the remaining factors in the numerator together and the remaining factors in the denominator together. Copyright 2014 Scott Storla

48. Multiply using prime factorization Copyright 2014 Scott Storla

49. Multiply using prime factorization Copyright 2014 Scott Storla

50. Multiply using prime factorization Copyright 2014 Scott Storla

51. Multiply using prime factorization Copyright 2014 Scott Storla

52. Multiplying Fractions Copyright 2014 Scott Storla

53. Dividing Fractions Copyright 2014 Scott Storla

54. Reciprocal The reciprocal of a number is a second number which when multiplied to the first gives a product of 1. Copyright 2014 Scott Storla

55. Procedure – Dividing Fractions 1.To divide two fractions multiply the fraction in the numerator by the reciprocal of the fraction in the denominator. Copyright 2014 Scott Storla

56. Procedure – Dividing Fractions 1.To divide two fractions multiply the fraction in the numerator by the reciprocal of the fraction in the denominator. Copyright 2014 Scott Storla

57. Divide using prime factorization Copyright 2014 Scott Storla

58. Divide using prime factorization Copyright 2014 Scott Storla

59. Divide using prime factorization Copyright 2014 Scott Storla

60. Divide using prime factorization Copyright 2014 Scott Storla

61. Dividing Fractions Copyright 2014 Scott Storla