The document discusses multiplying and dividing fractions. It provides the rule that to multiply fractions, multiply the numerators and denominators, cancelling terms when possible. It then gives examples of multiplying fractions by reducing or cancelling terms first before multiplying. It notes that fractional expressions like "x of y" translate to fraction multiplications.

1. Multiplication and Division of Fractions
Remember to cancel first!

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

3. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

4. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
12
25
15
8
*a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

5. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

6. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

7. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
5
3
a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

8. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
5
3
=
3*3
2*5
a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

9. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
5
3
= =
9
10
3*3
2*5
a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

10. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
5
3
= =
9
10
3*3
2*5
b.
8
9
7
8
*
10
11
9
10
**
a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

11. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
5
3
= =
9
10
3*3
2*5
7*8*9*10
8*9*10*11
b.
8
9
7
8
*
10
11
9
10
** =
a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

12. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
5
3
= =
9
10
3*3
2*5
7*8*9*10
8*9*10*11
b.
8
9
7
8
*
10
11
9
10
** =
a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

13. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
5
3
= =
9
10
3*3
2*5
7*8*9*10
8*9*10*11
b.
8
9
7
8
*
10
11
9
10
** =
a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

14. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
5
3
= =
9
10
3*3
2*5
7*8*9*10
8*9*10*11
b.
8
9
7
8
*
10
11
9
10
** =
a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

15. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
5
3
= =
9
10
3*3
2*5
7*8*9*10
8*9*10*11
b.
8
9
7
8
*
10
11
9
10
** = =
7
11
a.
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

16. c
d
=
a*c
b*d
a
b
*
Multiplication and Division of Fractions
Example A. Multiply by reducing first.
=
15 * 12
8 * 25
12
25
15
8
*
2
3
5
3
= =
9
10
3*3
2*5
7*8*9*10
8*9*10*11
b.
8
9
7
8
*
10
11
9
10
** = =
7
11
a.
Can't do this for addition and subtraction, i.e.
c
d
=
a c
b d
a
b
±
±
±
Rule for Multiplication of Fractions
To multiply fractions, multiply the numerators and multiply
the denominators, but always cancel as much as possible
first then multiply.

17. a
b
d
a
b
d
d
1
The fractional multiplications are important.
Multiplication and Division of Fractions
or* *
Often in these problems the denominator b can be cancelled
against d = .

18. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18a.
The fractional multiplications are important.
Multiplication and Division of Fractions
or* *
*
Often in these problems the denominator b can be cancelled
against d = .

19. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18a.
The fractional multiplications are important.
6
Multiplication and Division of Fractions
or* *
*
Often in these problems the denominator b can be cancelled
against d = .

20. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6a.
The fractional multiplications are important.
6
Multiplication and Division of Fractions
or* *
* *
Often in these problems the denominator b can be cancelled
against d = .

21. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
Multiplication and Division of Fractions
or* *
* *
Often in these problems the denominator b can be cancelled
against d = .

22. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
11
16
48b.
Multiplication and Division of Fractions
or* *
* *
*
Often in these problems the denominator b can be cancelled
against d = .

23. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
11
16
48b.
3
Multiplication and Division of Fractions
or* *
* *
*
Often in these problems the denominator b can be cancelled
against d = .

24. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
11
16
48b.
3
Multiplication and Division of Fractions
or* *
* *
* = 3 * 11
Often in these problems the denominator b can be cancelled
against d = .

25. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
11
16
48b.
3
Multiplication and Division of Fractions
or* *
* *
* = 3 * 11 = 33
Often in these problems the denominator b can be cancelled
against d = .

26. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
11
16
48b.
3
Multiplication and Division of Fractions
or* *
* *
* = 3 * 11 = 33
Often in these problems the denominator b can be cancelled
against d = .
The often used phrases " (fraction) of .." are translated to
multiplications correspond to this kind of problems.

27. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
11
16
48b.
3
Multiplication and Division of Fractions
or* *
* *
* = 3 * 11 = 33
Often in these problems the denominator b can be cancelled
against d = .
The often used phrases " (fraction) of .." are translated to
multiplications correspond to this kind of problems.
Example C: a. What is of $108?2
3

28. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
11
16
48b.
3
Multiplication and Division of Fractions
or* *
* *
* = 3 * 11 = 33
Often in these problems the denominator b can be cancelled
against d = .
The often used phrases " (fraction) of .." are translated to
multiplications correspond to this kind of problems.
Example C: a. What is of $108?2
3
* 108
2
3
The statement translates into

29. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
11
16
48b.
3
Multiplication and Division of Fractions
or* *
* *
* = 3 * 11 = 33
Often in these problems the denominator b can be cancelled
against d = .
The often used phrases " (fraction) of .." are translated to
multiplications correspond to this kind of problems.
Example C: a. What is of $108?2
3
* 108
2
3
36
The statement translates into

30. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
11
16
48b.
3
Multiplication and Division of Fractions
or* *
* *
* = 3 * 11 = 33
Often in these problems the denominator b can be cancelled
against d = .
The often used phrases " (fraction) of .." are translated to
multiplications correspond to this kind of problems.
Example C: a. What is of $108?2
3
* 108 = 2 * 36
2
3
36
The statement translates into

31. a
b
d
a
b
d
d
1
Example B: Multiply by cancelling first.
2
3
18 = 2 6 = 12a.
The fractional multiplications are important.
6
11
16
48b.
3
Multiplication and Division of Fractions
or* *
* *
* = 3 * 11 = 33
Often in these problems the denominator b can be cancelled
against d = .
The often used phrases " (fraction) of .." are translated to
multiplications correspond to this kind of problems.
Example C: a. What is of $108?2
3
* 108 = 2 * 36 = 72 $.
2
3
36
The statement translates into

32. b. 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?
Multiplication and Division of Fractions

33. b. 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?
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48

34. b. 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?
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12

35. b. 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?
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
so there are 12 pieces of chocolate candies.

36. b. 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?
1
3
* 48
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
For caramel, 1/3 of 48 is
so there are 12 pieces of chocolate candies.

37. b. 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?
1
3
* 48
16
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
For caramel, 1/3 of 48 is = 16,
so there are 12 pieces of chocolate candies.

38. b. 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?
1
3
* 48
16
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
For caramel, 1/3 of 48 is = 16,
so there are 16 pieces of caramel candies.
so there are 12 pieces of chocolate candies.

39. b. 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?
1
3
* 48
16
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
For caramel, 1/3 of 48 is = 16,
so there are 16 pieces of caramel candies.
The rest 48 – 12 – 16 = 20 are lemon drops.
so there are 12 pieces of chocolate candies.

40. b. 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?
1
3
* 48
16
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
For caramel, 1/3 of 48 is = 16,
so there are 16 pieces of caramel candies.
The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of
the lemon drops is 20
48
so there are 12 pieces of chocolate candies.

41. b. 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?
1
3
* 48
16
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
For caramel, 1/3 of 48 is = 16,
so there are 16 pieces of caramel candies.
The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of
the lemon drops is 20
48
=
20/4
48/4
so there are 12 pieces of chocolate candies.

42. b. 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?
1
3
* 48
16
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
For caramel, 1/3 of 48 is = 16,
so there are 16 pieces of caramel candies.
The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of
the lemon drops is 20
48
=
20/4
48/4
=
5
12
so there are 12 pieces of chocolate candies.

43. b. 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?
1
3
* 48
16
c. A class has x students, ¾ of them are girls, how many girls
are there?
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
For caramel, 1/3 of 48 is = 16,
so there are 16 pieces of caramel candies.
The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of
the lemon drops is 20
48
=
20/4
48/4
=
5
12
so there are 12 pieces of chocolate candies.

44. b. 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?
1
3
* 48
16
c. A class has x students, ¾ of them are girls, how many girls
are there?
3
4
* x.
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
For caramel, 1/3 of 48 is = 16,
so there are 16 pieces of caramel candies.
The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of
the lemon drops is 20
48
=
20/4
48/4
=
5
12
It translates into multiplication as
so there are 12 pieces of chocolate candies.

45. b. 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?
1
3
* 48
16
c. A class has x students, ¾ of them are girls, how many girls
are there?
3
4
* x.
Multiplication and Division of Fractions
For chocolate, ¼ of 48 is
1
4
* 48 = 12,
12
For caramel, 1/3 of 48 is = 16,
so there are 16 pieces of caramel candies.
The rest 48 – 12 – 16 = 20 are lemon drops. The fraction of
the lemon drops is 20
48
=
20/4
48/4
=
5
12
It translates into multiplication as
so there are 12 pieces of chocolate candies.

46. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions

47. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
So the reciprocal of is ,
2
3
3
2

48. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5

49. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
the reciprocal of is 3,1
3

50. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3

51. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3

52. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3

53. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3
2
3
3
2* = 1,

54. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3
2
3
3
2* = 1, 5 1
5* = 1,

55. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3
2
3
3
2* = 1, 5 1
5* = 1, x 1
x* = 1,

56. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3
2
3
3
2*
II. Dividing by x is the same as multiplying by its reciprocal .
= 1, 5 1
5* = 1, x 1
x* = 1,
1
x

57. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3
2
3
3
2*
II. Dividing by x is the same as multiplying by its reciprocal .
= 1, 5 1
5* = 1, x 1
x* = 1,
1
x
For example, 10 ÷ 2 is the same as 10 ,*
1
2

58. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3
2
3
3
2*
II. Dividing by x is the same as multiplying by its reciprocal .
= 1, 5 1
5* = 1, x 1
x* = 1,
1
x
For example, 10 ÷ 2 is the same as 10 , both yield 5.*
1
2

59. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3
2
3
3
2*
II. Dividing by x is the same as multiplying by its reciprocal .
= 1, 5 1
5* = 1, x 1
x* = 1,
1
x
For example, 10 ÷ 2 is the same as 10 , both yield 5.*
1
2
Rule for Division of Fractions
To divide by a fraction x, restate it as multiplying by the
reciprocal 1/x , that is,

60. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3
2
3
3
2*
II. Dividing by x is the same as multiplying by its reciprocal .
= 1, 5 1
5* = 1, x 1
x* = 1,
1
x
For example, 10 ÷ 2 is the same as 10 , both yield 5.*
1
2
Rule for Division of Fractions
To divide by a fraction x, restate it as multiplying by the
reciprocal 1/x , that is, c
d
=
a
b
÷

61. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3
2
3
3
2*
II. Dividing by x is the same as multiplying by its reciprocal .
= 1, 5 1
5* = 1, x 1
x* = 1,
1
x
For example, 10 ÷ 2 is the same as 10 , both yield 5.*
1
2
Rule for Division of Fractions
To divide by a fraction x, restate it as multiplying by the
reciprocal 1/x , that is, d
c
a
b
*
c
d
=
a
b
÷
reciprocate

62. The reciprocal (multiplicative inverse) of is .
a
b
b
a
Reciprocal and Division of Fractions
Two Important Facts About Reciprocals
I. The product of x with its reciprocal is 1.
So the reciprocal of is ,
2
3
3
2
the reciprocal of 5 is ,
1
5
and the reciprocal of x is .1
xthe reciprocal of is 3,1
3
2
3
3
2*
II. Dividing by x is the same as multiplying by its reciprocal .
= 1, 5 1
5* = 1, x 1
x* = 1,
1
x
For example, 10 ÷ 2 is the same as 10 , both yield 5.*
1
2
Rule for Division of Fractions
To divide by a fraction x, restate it as multiplying by the
reciprocal 1/x , that is, d
c
=
a*d
b*c
a
b
*
c
d
=
a
b
÷
reciprocate

63. Example D: Divide the following fractions.
8
15
=
12
25
a. ÷
Reciprocal and Division of Fractions

64. Example D: Divide the following fractions.
15
8
12
25
*
8
15
=
12
25
a. ÷
Reciprocal and Division of Fractions

65. Example D: Divide the following fractions.
15
8
12
25
*
8
15
=
12
25 2
3
a. ÷
Reciprocal and Division of Fractions

66. Example D: Divide the following fractions.
15
8
12
25
*
8
15
=
12
25 5
3
2
3
a. ÷
Reciprocal and Division of Fractions

67. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a. ÷
Reciprocal and Division of Fractions

68. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
÷
÷ =b.
Reciprocal and Division of Fractions

69. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
÷
÷ = *b.
Reciprocal and Division of Fractions

70. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
3
2
÷
÷ = *b.
Reciprocal and Division of Fractions

71. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
3
2
3
16
÷
÷ = * =b.
Reciprocal and Division of Fractions

72. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
3
2
3
16
÷
÷ = * =b.
Reciprocal and Division of Fractions
1
65d. ÷

73. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
3
2
3
16
÷
÷ = * =b.
Reciprocal and Division of Fractions
6
1*1
6 =5d. ÷ 5

74. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
3
2
3
16
÷
÷ = * =b.
Reciprocal and Division of Fractions
6
1 = 30*1
6 =5d. ÷ 5

75. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
3
2
3
16
÷
÷ = * =b.
Reciprocal and Division of Fractions
6
1 = 30*1
6 =5d. ÷ 5
Example E: We have ¾ cups of sugar. A cookie recipe calls
for 1/16 cup of sugar for each cookie. How many cookies
can we make?

76. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
3
2
3
16
÷
÷ = * =b.
Reciprocal and Division of Fractions
6
1 = 30*1
6 =5d. ÷ 5
Example E: We have ¾ cups of sugar. A cookie recipe calls
for 1/16 cup of sugar for each cookie. How many cookies
can we make?
We can make
3
4
÷ 1
16

77. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
3
2
3
16
÷
÷ = * =b.
Reciprocal and Division of Fractions
6
1 = 30*1
6 =5d. ÷ 5
Example E: We have ¾ cups of sugar. A cookie recipe calls
for 1/16 cup of sugar for each cookie. How many cookies
can we make?
We can make
3
4
÷ 1
16
= 3
4
*
16
1

78. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
3
2
3
16
÷
÷ = * =b.
Reciprocal and Division of Fractions
6
1 = 30*1
6 =5d. ÷ 5
Example E: We have ¾ cups of sugar. A cookie recipe calls
for 1/16 cup of sugar for each cookie. How many cookies
can we make?
We can make
3
4
÷ 1
16
= 3
4
*
16
1
4

79. Example D: Divide the following fractions.
15
8
=
12
25
*
8
15
=
12
25 5
3
2
3
9
10
a.
6
9
8
19
8 6
3
2
3
16
÷
÷ = * =b.
Reciprocal and Division of Fractions
6
1 = 30*1
6 =5d. ÷ 5
Example E: We have ¾ cups of sugar. A cookie recipe calls
for 1/16 cup of sugar for each cookie. How many cookies
can we make?
We can make
3
4
÷ 1
16
= 3
4
*
16
1
= 3 * 4 = 12 cookies.
4
HW: Do the web homework "Multiplication of Fractions"

80. Multiplication and Division of Fractions
Factor completely and write the answer using the
exponential notation
a. 360 b. 756
In room of 120 people, 1/4 are male children, 3/8 are
female adults. There are 83 adults. Complete the table.
Male Female
Adults
Children
1
3
8
ft 22ft
How many are there?