Lesson 1.9 b multiplication and division of rational numbers

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1. Lesson 1.7 Multiplication and Division of Rational Numbers

2. At the end of the lesson, you are expected to: multiply rational numbers d ivide rational numbers

3. Multiplication of Rational Numbers

4. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the form . Change whole numbers to rational numbers; Change mixed fractions to improper fractions 2. Multiply. If possible use cancellations. Multiply numerators with numerators ; Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible.  

5. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 1:         Rational numbers should be in the for m .   Multiply. If possible use cancellations. Simplify. Reduce answers to lowest terms if possible.

6. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 1:         Rational numbers should be in the for m .   Multiply. If possible use cancellations. Simplify. Reduce answers to lowest terms if possible.

7. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 2:         Rational numbers should be in the for m .   Multiply. If possible use cancellations. Simplify. Reduce answers to lowest terms if possible.

8. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 2:       Since the end result is an improper fraction . For a best answer. Change to mixed number .

9. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3:     Rational numbers should be in the for m .  

10. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3: Rational numbers should be in the for m .       Multiply. If possible use cancellations.

11. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3: Multiply. If possible use cancellations.          

12. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3: Multiply. If possible use cancellations.              

13. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3: Multiply. If possible use cancellations.              

14. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3:             Simplify. Reduce answers to lowest terms if possible.  

15. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3:               What if we did not use cancellations?

16. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3:                   Rational numbers should be in the for m .  

17. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3:                   Multiply. If possible use cancellations.    

18. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3:                   Multiply. If possible use cancellations.    

19. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3:                     Simplify. Reduce answers to lowest terms if possible.  

20. Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 3:                      

21.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Rational numbers should be in the form . -change whole numbers to rational numbers ; -change mixed fractions to improper fractions  

22.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Rational numbers should be in the form . -change whole numbers to rational numbers ; -change mixed fractions to improper fractions  

23.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Rational numbers should be in the form . -change whole numbers to rational numbers ; -change mixed fractions to improper fractions   Changing mixed fraction to improper fraction. Multiply the denominator and whole number      

24.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Rational numbers should be in the form . -change whole numbers to rational numbers ; -change mixed fractions to improper fractions   Changing mixed fraction to improper fraction. Add up the product to the numerator. The result will be the new numerator.      

25.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Rational numbers should be in the form . -change whole numbers to rational numbers ; -change mixed fractions to improper fractions   Changing mixed fraction to improper fraction. Copy the denominator  

26.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Rational numbers should be in the form . -change whole numbers to rational numbers ; -change mixed fractions to improper fractions   Changing mixed fraction to improper fraction. Copy the denominator  

27.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Multiply. If possible use cancellations.

28.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Multiply. If possible use cancellations.    

29.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Multiply. If possible use cancellations.      

30.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Multiply. If possible use cancellations.          

31.   Multiplication of Rational Numbers To multiply rational numbers: 1. Rational numbers should be in the for m . 2 . Multiply . If possible use cancellations. - Change whole numbers to rational numbers; - Multiply numerators with numerators ; - Change mixed fractions to improper fractions - Multiply denominators with denominators 3. Simplify. Reduce answers to lowest terms if possible .   Example 4:   Multiply. If possible use cancellations.          

32. Got questions?

33. Simplify the following. Reduce your answer into lowest terms. 1.   2.   3.   4.   5.  

34. ANSWERS!

35. Simplify the following. Reduce your answer into lowest terms. 1.   2.   3.   4.   5.            

36. Got questions?

37. Division of Rational Numbers

38. Multiplication of Rational Numbers Then proceed just like your multiplication on rational numbers .     When dividing rational numbers, multiply the dividend by the reciprocal of the divisor . Dividend Divisor

39. Multiplication of Rational Numbers Reciprocal The number by which a given number must be multiplied to get a result of one (1) .

40. Multiplication of Rational Numbers Reciprocal The number by which a given number must be multiplied to get a result of one (1) .   ?

41. Multiplication of Rational Numbers Reciprocal The number by which a given number must be multiplied to get a result of one (1) .   ?

42. Multiplication of Rational Numbers Reciprocal The number by which a given number must be multiplied to get a result of one (1) .   ?

43. Multiplication of Rational Numbers Reciprocal The number by which a given number must be multiplied to get a result of one (1) .   ?

44. Multiplication of Rational Numbers Reciprocal The number by which a given number must be multiplied to get a result of one (1) .   ?

45. Multiplication of Rational Numbers Reciprocal The number by which a given number must be multiplied to get a result of one (1) .   ?

46. Got questions?

47. Get the reciprocal of the divisors. Don’t solve. 1.   2.   3.   4.   5.   Reciprocal of the divisor: Reciprocal of the divisor: Reciprocal of the divisor: Reciprocal of the divisor: Reciprocal of the divisor: Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .  

48. ANSWERS!

49. Get the reciprocal of the divisors. Don’t solve. 1.   2.   3.   4.   5.   Reciprocal of the divisor: Reciprocal of the divisor: Reciprocal of the divisor: Reciprocal of the divisor: Reciprocal of the divisor:           Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .  

50. Got questions?

51. Multiplication of Rational Numbers Then proceed just like your multiplication on rational numbers .     When dividing rational numbers, multiply the dividend by the reciprocal of the divisor . Dividend Divisor

52.   Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 1:   Change to multiplication . Get the reciprocal of the divisor.   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .        

53. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 1:   Multiply . If possible use cancellations.   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .        

54. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 1:     Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .   Simplify. Reduce answers to lowest terms if possible.  

55.   Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 2: Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Change to multiplication . Get the reciprocal of the divisor.        

56. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 2: Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .       Multiply . If possible use cancellations.

57. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 2: Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .       Multiply . If possible use cancellations.      

58. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 2: Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .       Multiply . If possible use cancellations.          

59. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 2: Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .       Multiply . If possible use cancellations.          

60. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 2: Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .       Multiply . If possible use cancellations.        

61. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 2: Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .               Simplify. Reduce answers to lowest terms if possible.  

62. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 2: Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .               Simplify. Reduce answers to lowest terms if possible.  

63. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Since we have mixed fractions , changed first to improper fractions .

64. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Since we have mixed fractions , changed first to improper fractions .

65. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Since we have mixed fractions , changed first to improper fractions .

66. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Change to multiplication . Get the reciprocal of the divisor.  

67. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Change to multiplication . Get the reciprocal of the divisor.    

68. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Change to multiplication . Get the reciprocal of the divisor.    

69. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Multiply. If possible use cancellations.  

70. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Multiply. If possible use cancellations.      

71. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Multiply. If possible use cancellations.      

72. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Multiply. If possible use cancellations.          

73. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Multiply. If possible use cancellations.              

74. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .     Multiply. If possible use cancellations.              

75. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .                 Simplify. Reduce answers to lowest terms if possible.   Since we got an improper fraction , change it to mixed fraction for a best answer .

76. Division of Rational Numbers When dividing rational numbers , multiply the dividend by the reciprocal of the divisor . Then proceed just like your multiplication on rational numbers .   Example 3:   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .                  

77. Got questions?

78. Get the reciprocal of the divisors. Don’t solve. 1.   2.   3.   4.   5.   Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .  

79. ANSWERS!

80. Get the reciprocal of the divisors. Don’t solve. 1.   2.   3.   4.   5.           Reciprocal The number by which a given number must be multiplied to get a result of one (1 ) .    

81. Got questions?