The document discusses multiplication and division of fractions. It states that to multiply fractions, one should multiply the numerators and multiply the denominators, cancelling terms when possible. Some examples are provided, such as multiplying 12/15 by 25/8, which equals 3/5. The document also discusses how phrases like "x fraction of y" can be translated into fractional multiplications.

1. Multiplication and Division of Fractions

2. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.

3. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*db

4. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.1215a.*258

5. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.15 * 121215a.=* 8 * 25258

6. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.315 * 121215a.=* 8 * 252582

7. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.3315 * 121215a.=* 8 * 2525852

8. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.3315 * 1212153*3a.=*= 8 * 252582*552

9. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.3315 * 12121593*3a.=*== 8 * 25258102*552

10. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.3315 * 12121593*3a.=*== 8 * 25258102*55287109b.***981110

11. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.3315 * 12121593*3a.=*== 8 * 25258102*5527*8*9*1087109b.***=9811108*9*10*11

12. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.3315 * 12121593*3a.=*== 8 * 25258102*5527*8*9*1087109b.***=9811108*9*10*11

13. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.3315 * 12121593*3a.=*== 8 * 25258102*5527*8*9*1087109b.***=9811108*9*10*11

14. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.3315 * 12121593*3a.=*== 8 * 25258102*5527*8*9*1087109b.***=9811108*9*10*11

15. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.3315 * 12121593*3a.=*== 8 * 25258102*5527*8*9*10871097b.***==981110118*9*10*11

16. Multiplication and Division of FractionsRule for Multiplication of FractionsTo multiply fractions, multiply the numerators and multiply the denominators, but always cancel as much as possible first then multiply.ca*ca=*db*dbExample A. Multiply by reducing first.3315 * 12121593*3a.=*== 8 * 25258102*5527*8*9*10871097b.***==981110118*9*10*11ca ca± = ±Can't do this for addition and subtraction, i.e.db db±

17. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1

18. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.2a.18 *3

19. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 *3

20. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 **3

21. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**3

22. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**311b.48 *16

23. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**3311b.48 *16

24. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**3311b.48 = 3 * 11 *16

25. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**3311b.48 = 3 * 11 = 33*16

26. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**3311b.48 = 3 * 11 = 33*16The often used phrases " (fraction) of .." are translated to multiplications correspond to this kind of problems.

27. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**3311b.48 = 3 * 11 = 33*16The often used phrases " (fraction) of .." are translated to multiplications correspond to this kind of problems.2Example C: a. What is of $108?3

28. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**3311b.48 = 3 * 11 = 33*16The often used phrases " (fraction) of .." are translated to multiplications correspond to this kind of problems.2Example C: a. What is of $108?32* 108 The statement translates into3

29. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**3311b.48 = 3 * 11 = 33*16The often used phrases " (fraction) of .." are translated to multiplications correspond to this kind of problems.2Example C: a. What is of $108?3362* 108 The statement translates into3

30. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**3311b.48 = 3 * 11 = 33*16The often used phrases " (fraction) of .." are translated to multiplications correspond to this kind of problems.2Example C: a. What is of $108?3362* 108 = 2 * 36 The statement translates into3

31. Multiplication and Division of FractionsaaThe fractional multiplications are important.ddor bb**Often in these problems the denominator b can be cancelledagainst d = . d1Example B: Multiply by cancelling first.62a.18 = 2 6 = 12**3311b.48 = 3 * 11 = 33*16The often used phrases " (fraction) of .." are translated to multiplications correspond to this kind of problems.2Example C: a. What is of $108?3362* 108 = 2 * 36 = 72 $.The statement translates into3

32. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?

33. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?1For chocolate, ¼ of 48 is* 48 4

34. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4

35. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.

36. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.1* 48 For caramel, 1/3 of 48 is3

37. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.161* 48 For caramel, 1/3 of 48 is= 16, 3

38. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.161* 48 For caramel, 1/3 of 48 is= 16, 3so there are 16 pieces of caramel candies.

39. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.161* 48 For caramel, 1/3 of 48 is= 16, 3so there are 16 pieces of caramel candies.The rest 48 – 12 – 16 = 20 are lemon drops.

40. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.161* 48 For caramel, 1/3 of 48 is= 16, 3so there are 16 pieces of caramel candies.The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of the lemon drops is 2048

41. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.161* 48 For caramel, 1/3 of 48 is= 16, 3so there are 16 pieces of caramel candies.The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of the lemon drops is 2020/4=4848/4

42. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.161* 48 For caramel, 1/3 of 48 is= 16, 3so there are 16 pieces of caramel candies.The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of the lemon drops is 2020/45==4848/412

43. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.161* 48 For caramel, 1/3 of 48 is= 16, 3so there are 16 pieces of caramel candies.The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of the lemon drops is 2020/45==4848/412c. A class has x students, ¾ of them are girls, how many girls are there?

44. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.161* 48 For caramel, 1/3 of 48 is= 16, 3so there are 16 pieces of caramel candies.The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of the lemon drops is 2020/45==4848/412c. A class has x students, ¾ of them are girls, how many girls are there?3* x. It translates into multiplication as4

45. Multiplication and Division of Fractionsb. A bag of mixed candy contains 48 pieces of chocolate, caramel and lemon drops. 1/4 of them are chocolate, 1/3 of them are caramel. How many pieces of each are there? What fraction of the candies are lemon drops?121For chocolate, ¼ of 48 is* 48 = 12,4so there are 12 pieces of chocolate candies.161* 48 For caramel, 1/3 of 48 is= 16, 3so there are 16 pieces of caramel candies.The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of the lemon drops is 2020/45==4848/412c. A class has x students, ¾ of them are girls, how many girls are there?3* x. It translates into multiplication as4

46. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba

47. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba23So the reciprocal of is , 32

48. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 325

49. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 3251the reciprocal of is 3, 3

50. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3

51. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About Reciprocals

52. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About ReciprocalsI. The product of x with its reciprocal is 1.

53. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About ReciprocalsI. The product of x with its reciprocal is 1.23= 1,*32

54. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About ReciprocalsI. The product of x with its reciprocal is 1.231= 1,5= 1,**325

55. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About ReciprocalsI. The product of x with its reciprocal is 1.2311= 1,5= 1,x= 1,x***325

56. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About ReciprocalsI. The product of x with its reciprocal is 1.2311= 1,5= 1,x= 1,x***3251II. Dividing by x is the same as multiplying by its reciprocal .x

57. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About ReciprocalsI. The product of x with its reciprocal is 1.2311= 1,5= 1,x= 1,x***3251II. Dividing by x is the same as multiplying by its reciprocal .x1For example, 10 ÷ 2 is the same as 10 , *2

58. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About ReciprocalsI. The product of x with its reciprocal is 1.2311= 1,5= 1,x= 1,x***3251II. Dividing by x is the same as multiplying by its reciprocal .x1For example, 10 ÷ 2 is the same as 10 , both yield 5. *2

59. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About ReciprocalsI. The product of x with its reciprocal is 1.2311= 1,5= 1,x= 1,x***3251II. Dividing by x is the same as multiplying by its reciprocal .x1For example, 10 ÷ 2 is the same as 10 , both yield 5. *2Rule for Division of FractionsTo divide by a fraction x, restate it as multiplying by the reciprocal 1/x , that is,

60. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About ReciprocalsI. The product of x with its reciprocal is 1.2311= 1,5= 1,x= 1,x***3251II. Dividing by x is the same as multiplying by its reciprocal .x1For example, 10 ÷ 2 is the same as 10 , both yield 5. *2Rule for Division of FractionsTo divide by a fraction x, restate it as multiplying by the reciprocal 1/x , that is, daca = ÷*cbdbreciprocate

61. Reciprocal and Division of FractionsabThe reciprocal (multiplicative inverse) of is . ba231So the reciprocal of is , the reciprocal of 5 is , 32511and the reciprocal of x is . the reciprocal of is 3, x3Two Important Facts About ReciprocalsI. The product of x with its reciprocal is 1.2311= 1,5= 1,x= 1,x***3251II. Dividing by x is the same as multiplying by its reciprocal .x1For example, 10 ÷ 2 is the same as 10 , both yield 5. *2Rule for Division of FractionsTo divide by a fraction x, restate it as multiplying by the reciprocal 1/x , that is, da*daca= = ÷*cb*cbdbreciprocate

62. Reciprocal and Division of FractionsExample D: Divide the following fractions. 812 = a.÷1525

63. Reciprocal and Division of FractionsExample D: Divide the following fractions. 1512812* = a.÷8251525

64. Reciprocal and Division of FractionsExample D: Divide the following fractions. 31512812* = a.÷82515252

65. Reciprocal and Division of FractionsExample D: Divide the following fractions. 331512812* = a.÷825152552

66. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷82515251052

67. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷8251525105296÷ =b.8

68. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷825152510521996÷ = * b.886

69. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷8251525105231996÷ = * b.8862

70. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷82515251052319396÷ = * = b.886162

71. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷82515251052319396÷ = * = b.88616215d.÷6

72. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷82515251052319396÷ = * = b.88616261* = 5d.÷516

73. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷82515251052319396÷ = * = b.88616261 = 30 * = 5d.÷516

74. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷82515251052319396÷ = * = b.88616261 = 30 * = 5d.÷516Example E: We have ¾ cups of sugar. A cookie recipe calls for 1/16 cup of sugar for each cookie. How many cookiescan we make?

75. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷82515251052319396÷ = * = b.88616261 = 30 * = 5d.÷516Example E: We have ¾ cups of sugar. A cookie recipe calls for 1/16 cup of sugar for each cookie. How many cookiescan we make?31÷We can make 416

76. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷82515251052319396÷ = * = b.88616261 = 30 * = 5d.÷516Example E: We have ¾ cups of sugar. A cookie recipe calls for 1/16 cup of sugar for each cookie. How many cookiescan we make?31316÷ = We can make *41641

77. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷82515251052319396÷ = * = b.88616261 = 30 * = 5d.÷516Example E: We have ¾ cups of sugar. A cookie recipe calls for 1/16 cup of sugar for each cookie. How many cookiescan we make?431316÷ = We can make *41641

78. Reciprocal and Division of FractionsExample D: Divide the following fractions. 3315128129 = * = a.÷82515251052319396÷ = * = b.88616261 = 30 * = 5d.÷516Example E: We have ¾ cups of sugar. A cookie recipe calls for 1/16 cup of sugar for each cookie. How many cookiescan we make?431316÷ = = 3 * 4 = 12 cookies.We can make *41641HW: Do the web homework "Multiplication of Fractions"