2. Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers.
p
q
Fractions
3. Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers.
p
q
Fractions
3
6
4. Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers. Fractions are numbers that
measure parts of whole items.
p
q
Fractions
3
6
5. Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers. Fractions are numbers that
measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
them, the fraction that represents this quantity is .
p
q
3
6
Fractions
3
6
6. Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers. Fractions are numbers that
measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
them, the fraction that represents this quantity is .
p
q
3
6
3
6
Fractions
7. Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers. Fractions are numbers that
measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
them, the fraction that represents this quantity is .
p
q
3
6
The bottom number is the
number of equal parts in the
division and it is called the
denominator.
3
6
Fractions
8. Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers. Fractions are numbers that
measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
them, the fraction that represents this quantity is .
p
q
3
6
The bottom number is the
number of equal parts in the
division and it is called the
denominator.
3
6
Fractions
9. Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers. Fractions are numbers that
measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
them, the fraction that represents this quantity is .
p
q
3
6
The bottom number is the
number of equal parts in the
division and it is called the
denominator.
The top number “3” is the
number of parts that we
have and it is called the
numerator.
3
6
Fractions
10. Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers. Fractions are numbers that
measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
them, the fraction that represents this quantity is .
p
q
3
6
The bottom number is the
number of equal parts in the
division and it is called the
denominator.
The top number “3” is the
number of parts that we
have and it is called the
numerator.
3
6
Fractions
3/6 of a pizza
12. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
How many slices should we cut the pizza into and how do
we do this?
13. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
Cut the pizza into 8 pieces,
14. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
Cut the pizza into 8 pieces, take 5 of them.
15. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
5/8 of a pizza
Cut the pizza into 8 pieces, take 5 of them.
16. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
7
12
5/8 of a pizza
17. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
7
12
5/8 of a pizza
Cut the pizza into 12 pieces,
18. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
7
12
5/8 of a pizza
Cut the pizza into 12 pieces,
19. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
7
12
5/8 of a pizza
Cut the pizza into 12 pieces, take 7 of them.
20. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
7
12
5/8 of a pizza
Cut the pizza into 12 pieces, take 7 of them.
or
21. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
7
12
5/8 of a pizza
7/12 of a pizza
or
Cut the pizza into 12 pieces, take 7 of them.
22. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
7
12
5/8 of a pizza
Note that or is the same as 1.8
8
12
12
7/12 of a pizza
or
23. For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Fractions
7
12
5/8 of a pizza
Fact: a
a
Note that or is the same as 1.8
8
12
12
= 1 (provided that a = 0.)
7/12 of a pizza
or
25. Fractions
Example A. a. What is ¾ of $100?
We may talk about the fractional amount of a group of items.
b. Out of an audience of 72 people at a movie, 7/12 of them
like the show very much. How many people is that?
26. Fractions
Example A. a. What is ¾ of $100?
We may talk about the fractional amount of a group of items.
To calculate such amounts, we always divide the group into
parts indicated by the denominator, then retrieve the number
of parts indicated by the numerator.
b. Out of an audience of 72 people at a movie, 7/12 of them
like the show very much. How many people is that?
27. Fractions
Example A. a. What is ¾ of $100?
We may talk about the fractional amount of a group of items.
To calculate such amounts, we always divide the group into
parts indicated by the denominator, then retrieve the number
of parts indicated by the numerator.
b. Out of an audience of 72 people at a movie, 7/12 of them
like the show very much. How many people is that?
3
4 Divide $100 into
4 equal parts.
28. Fractions
Example A. a. What is ¾ of $100?
We may talk about the fractional amount of a group of items.
To calculate such amounts, we always divide the group into
parts indicated by the denominator, then retrieve the number
of parts indicated by the numerator.
b. Out of an audience of 72 people at a movie, 7/12 of them
like the show very much. How many people is that?
3
4 Divide $100 into
4 equal parts.
100 ÷ 4 = 25
so each part is $25,
29. Fractions
Example A. a. What is ¾ of $100?
We may talk about the fractional amount of a group of items.
To calculate such amounts, we always divide the group into
parts indicated by the denominator, then retrieve the number
of parts indicated by the numerator.
b. Out of an audience of 72 people at a movie, 7/12 of them
like the show very much. How many people is that?
3
4 Divide $100 into
4 equal parts.
Take 3 parts. 100 ÷ 4 = 25
so each part is $25,
30. Fractions
Example A. a. What is ¾ of $100?
We may talk about the fractional amount of a group of items.
To calculate such amounts, we always divide the group into
parts indicated by the denominator, then retrieve the number
of parts indicated by the numerator.
b. Out of an audience of 72 people at a movie, 7/12 of them
like the show very much. How many people is that?
3
4 Divide $100 into
4 equal parts.
Take 3 parts. 100 ÷ 4 = 25
so each part is $25,
3 parts make $75.
So ¾ of $100 is $75.
31. Fractions
Example A. a. What is ¾ of $100?
We may talk about the fractional amount of a group of items.
To calculate such amounts, we always divide the group into
parts indicated by the denominator, then retrieve the number
of parts indicated by the numerator.
b. Out of an audience of 72 people at a movie, 7/12 of them
like the show very much. How many people is that?
3
4 Divide $100 into
4 equal parts.
Take 3 parts. 100 ÷ 4 = 25
so each part is $25,
3 parts make $75.
So ¾ of $100 is $75.
7
12 Divide 72 people
into 12 equal parts.
32. Fractions
Example A. a. What is ¾ of $100?
We may talk about the fractional amount of a group of items.
To calculate such amounts, we always divide the group into
parts indicated by the denominator, then retrieve the number
of parts indicated by the numerator.
b. Out of an audience of 72 people at a movie, 7/12 of them
like the show very much. How many people is that?
3
4 Divide $100 into
4 equal parts.
Take 3 parts. 100 ÷ 4 = 25
so each part is $25,
3 parts make $75.
So ¾ of $100 is $75.
7
12 Divide 72 people
into 12 equal parts.
72 ÷ 12 = 6
so each part consists of 6 people,
33. Fractions
Example A. a. What is ¾ of $100?
We may talk about the fractional amount of a group of items.
To calculate such amounts, we always divide the group into
parts indicated by the denominator, then retrieve the number
of parts indicated by the numerator.
b. Out of an audience of 72 people at a movie, 7/12 of them
like the show very much. How many people is that?
3
4 Divide $100 into
4 equal parts.
Take 3 parts. 100 ÷ 4 = 25
so each part is $25,
3 parts make $75.
So ¾ of $100 is $75.
7
12 Divide 72 people
into 12 equal parts.
Take 7 parts.
72 ÷ 12 = 6
so each part consists of 6 people,
7 parts make 42 people.
So 7/12 of 92 people is 42 people.
34. Whole numbers can be viewed as fractions with denominator 1.
Fractions
35. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = .5
1
x
1
Fractions
36. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.5
1
x
1
0
x
Fractions
37. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
However, does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions
38. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
However, does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions
The Ultimate No-No of Mathematics:
39. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
However, does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions
The Ultimate No-No of Mathematics:
The denominator (bottom) of a fraction can't
be 0.
40. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
However, does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions
The Ultimate No-No of Mathematics:
The denominator (bottom) of a fraction can't
be 0. (It's undefined if the denominator is 0.)
41. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
However, does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions
The Ultimate No-No of Mathematics:
The denominator (bottom) of a fraction can't
be 0. (It's undefined if the denominator is 0.)
Fractions that represents the same quantity are called
equivalent fractions.
42. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
However, does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions
The Ultimate No-No of Mathematics:
The denominator (bottom) of a fraction can't
be 0. (It's undefined if the denominator is 0.)
Fractions that represents the same quantity are called
equivalent fractions.
1
2
=
2
4
43. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
However, does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions
The Ultimate No-No of Mathematics:
The denominator (bottom) of a fraction can't
be 0. (It's undefined if the denominator is 0.)
Fractions that represents the same quantity are called
equivalent fractions.
1
2
=
2
4
=
3
6
44. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
However, does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions
The Ultimate No-No of Mathematics:
The denominator (bottom) of a fraction can't
be 0. (It's undefined if the denominator is 0.)
Fractions that represents the same quantity are called
equivalent fractions.
… are equivalent fractions.1
2
=
2
4
=
3
6
=
4
8
45. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
However, does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions
The Ultimate No-No of Mathematics:
The denominator (bottom) of a fraction can't
be 0. (It's undefined if the denominator is 0.)
Fractions that represents the same quantity are called
equivalent fractions.
… are equivalent fractions.
The fraction with the smallest denominator of all the
equivalent fractions is called the reduced fraction.
1
2
=
2
4
=
3
6
=
4
8
46. Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
However, does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions
The Ultimate No-No of Mathematics:
The denominator (bottom) of a fraction can't
be 0. (It's undefined if the denominator is 0.)
Fractions that represents the same quantity are called
equivalent fractions.
… are equivalent fractions.
The fraction with the smallest denominator of all the
equivalent fractions is called the reduced fraction.
1
2
=
2
4
=
3
6
=
4
8
is the reduced one in the above list.
1
2
47. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
a
b
a
b =
a / c
Fractions
b / c
48. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1,
a
b
a
b =
a / c
Fractions
b / c
49. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
=
a*c
b*c
a*c
b*c
1
Fractions
b / c
50. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
a
b .=
a*c
b*c =
a*c
b*c
1
Fractions
b / c
51. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
a
b .=
a*c
b*c =
a*c
b*c
1
Fractions
b / c
(Often we omit writing the 1’s after the cancellation.)
52. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
a
b .=
a*c
b*c =
a*c
b*c
1
Fractions
b / c
To reduce a fraction, we keep divide the top and bottom by
common numbers until no more division is possible.
What's left is the reduced version.
(Often we omit writing the 1’s after the cancellation.)
53. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
a
b .=
a*c
b*c =
a*c
b*c
1
Fractions
b / c
Example B. Reduce the fraction .78
54
To reduce a fraction, we keep divide the top and bottom by
common numbers until no more division is possible.
What's left is the reduced version.
(Often we omit writing the 1’s after the cancellation.)
54. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
a
b .=
a*c
b*c =
a*c
b*c
1
Fractions
b / c
Example B. Reduce the fraction .78
54
78
54
=
To reduce a fraction, we keep divide the top and bottom by
common numbers until no more division is possible.
What's left is the reduced version.
(Often we omit writing the 1’s after the cancellation.)
55. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
a
b .=
a*c
b*c =
a*c
b*c
1
Fractions
b / c
Example B. Reduce the fraction .78
54
78
54
=
78/2
54/2
To reduce a fraction, we keep divide the top and bottom by
common numbers until no more division is possible.
What's left is the reduced version.
(Often we omit writing the 1’s after the cancellation.)
56. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
a
b .=
a*c
b*c =
a*c
b*c
1
Fractions
b / c
Example B. Reduce the fraction .78
54
78
54
=
78/2
54/2
To reduce a fraction, we keep divide the top and bottom by
common numbers until no more division is possible.
What's left is the reduced version.
=
39
27
(Often we omit writing the 1’s after the cancellation.)
57. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
a
b .=
a*c
b*c =
a*c
b*c
1
Fractions
b / c
Example B. Reduce the fraction .78
54
78
54
=
78/2
54/2
To reduce a fraction, we keep divide the top and bottom by
common numbers until no more division is possible.
What's left is the reduced version.
=
39/3
27/3
39
27
(Often we omit writing the 1’s after the cancellation.)
58. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
a
b .=
a*c
b*c =
a*c
b*c
1
Fractions
b / c
Example B. Reduce the fraction .78
54
78
54
=
78/2
54/2
= 13
9 .
To reduce a fraction, we keep divide the top and bottom by
common numbers until no more division is possible.
What's left is the reduced version.
=
39/3
27/3
39
27
(Often we omit writing the 1’s after the cancellation.)
59. Factor Cancellation Rule
Given a fraction , then
that is, if the numerator and denominator are divided by the
same quantity c, the result will be an equivalent fraction.
In other words, a common factor of the numerator and the
denominator may be canceled as 1, i.e.
a
b
a
b =
a / c
a
b .=
a*c
b*c =
a*c
b*c
1
Fractions
b / c
Example B. Reduce the fraction .78
54
78
54
=
78/2
54/2
= 13
9 .
To reduce a fraction, we keep divide the top and bottom by
common numbers until no more division is possible.
What's left is the reduced version.
=
39/3
27/3
or divide both by 6 in one step.
39
27
(Often we omit writing the 1’s after the cancellation.)
60. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
61. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
A participant in a sum or a difference is called a term.
62. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
63. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
The “2” is in the expression “2 * 3” is called a factor.
64. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
The “2” is in the expression “2 * 3” is called a factor.
Terms may not be cancelled. Only factors may be canceled.
65. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
2 + 1
2 + 3
3
5
=
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
The “2” is in the expression “2 * 3” is called a factor.
Terms may not be cancelled. Only factors may be canceled.
66. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
2 + 1
2 + 3
3
5
=
This is addition. Can’t cancel!
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
The “2” is in the expression “2 * 3” is called a factor.
Terms may not be cancelled. Only factors may be canceled.
67. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
2 + 1
2 + 3
= 2 + 1
2 + 3
3
5
=
This is addition. Can’t cancel!
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
The “2” is in the expression “2 * 3” is called a factor.
Terms may not be cancelled. Only factors may be canceled.
68. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
2 + 1
2 + 3
= 2 + 1
2 + 3
= 1
3
3
5
=
This is addition. Can’t cancel!
!?
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
The “2” is in the expression “2 * 3” is called a factor.
Terms may not be cancelled. Only factors may be canceled.
69. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
2 + 1
2 + 3
= 2 + 1
2 + 3
= 1
3
3
5
=
This is addition. Can’t cancel!
!? 2 * 1
2 * 3
=
1
3
Yes
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
The “2” is in the expression “2 * 3” is called a factor.
Terms may not be cancelled. Only factors may be canceled.
70. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
2 + 1
2 + 3
= 2 + 1
2 + 3
= 1
3
3
5
=
This is addition. Can’t cancel!
!?
Improper Fractions and Mixed Numbers
2 * 1
2 * 3
=
1
3
Yes
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
The “2” is in the expression “2 * 3” is called a factor.
Terms may not be cancelled. Only factors may be canceled.
71. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
2 + 1
2 + 3
= 2 + 1
2 + 3
= 1
3
3
5
=
This is addition. Can’t cancel!
!?
A fraction whose numerator is the same or more than its
denominator (e.g. ) is said to be improper .
Improper Fractions and Mixed Numbers
3
2
2 * 1
2 * 3
=
1
3
Yes
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
The “2” is in the expression “2 * 3” is called a factor.
Terms may not be cancelled. Only factors may be canceled.
72. Fractions
One common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
2 + 1
2 + 3
= 2 + 1
2 + 3
= 1
3
3
5
=
This is addition. Can’t cancel!
!?
A fraction whose numerator is the same or more than its
denominator (e.g. ) is said to be improper .
We may put an improper fraction into mixed form by division.
Improper Fractions and Mixed Numbers
3
2
2 * 1
2 * 3
=
1
3
Yes
A participant in a sum or a difference is called a term.
The “2” in the expression “2 + 3” is a term (of the expression).
The “2” is in the expression “2 * 3” is called a factor.
Terms may not be cancelled. Only factors may be canceled.
74. 23
4
23 4 = 5 with remainder 3.·
·
Improper Fractions and Mixed Numbers
Example C. Put into mixed form.
75. 23
4
23 4 = 5 with remainder 3. Hence,·
·
23
4
= 5 +
Improper Fractions and Mixed Numbers
Example C. Put into mixed form.
3
4
76. 23
4
23 4 = 5 with remainder 3. Hence,·
·
23
4
= 5 + 5 3
4 .
Improper Fractions and Mixed Numbers
Example C. Put into mixed form.
3
4
=
77. 23
4
23 4 = 5 with remainder 3. Hence,·
·
23
4
= 5 + 5 3
4 .
Improper Fractions and Mixed Numbers
Example C. Put into mixed form.
3
4
=
We may put a mixed number into improper fraction by doing
the reverse via multiplication.
78. 23
4
23 4 = 5 with remainder 3. Hence,·
·
23
4
= 5 + 5 3
4 .
Improper Fractions and Mixed Numbers
Example C. Put into mixed form.
3
4
=
We may put a mixed number into improper fraction by doing
the reverse via multiplication.
Example C: Put into improper form.5 3
4
79. 23
4
23 4 = 5 with remainder 3. Hence,·
·
23
4
= 5 + 5 3
4 .
5 3
4
= 4*5 + 3
4
Improper Fractions and Mixed Numbers
Example C. Put into mixed form.
3
4
=
We may put a mixed number into improper fraction by doing
the reverse via multiplication.
Example C: Put into improper form.5 3
4
80. 23
4
23 4 = 5 with remainder 3. Hence,·
·
23
4
= 5 + 5 3
4 .
5 3
4
= 4*5 + 3
4
23
4
=
Improper Fractions and Mixed Numbers
Example C. Put into mixed form.
3
4
=
We may put a mixed number into improper fraction by doing
the reverse via multiplication.
Example C: Put into improper form.5 3
4
81. 23
4
23 4 = 5 with remainder 3. Hence,·
·
23
4
= 5 + 5 3
4 .
5 3
4
= 4*5 + 3
4
23
4
=
Improper Fractions and Mixed Numbers
Example C. Put into mixed form.
3
4
=
We may put a mixed number into improper fraction by doing
the reverse via multiplication.
Example C: Put into improper form.5 3
4
82. Improper Fractions and Mixed Numbers
B. Convert the following improper fractions into mixed
numbers then convert the mixed numbers back to the
improper form.
9
2
11
3
9
4
13
5
37
12
86
11
121
17
1. 2. 3. 4. 5. 6. 7.
Exercise. A. Reduce the following fractions.
4
6 ,
8
12 ,
15
9 ,
24
18 ,
30
42 ,
54
36 ,
60
48 ,
72
108
