The document discusses fractions and how they are used to represent parts of a whole. It explains that fractions are written as two numbers separated by a slash, where the top number is the numerator and indicates the number of parts, and the bottom number is the denominator and indicates the total number of equal parts the whole was divided into. Examples using pizza slices are provided to illustrate how to represent fractions such as 3/6, 5/8, and 7/12 pictorially. The document also notes that whole numbers can be viewed as fractions with a denominator of 1.

1. Fractions
http://www.lahc.edu/math/frankma.htm

2. Fractions
Numbers 1, 2, 3, 4,.. are called counting numbers, or natural
numbers and they are used to track whole items.

3. Fractions
Numbers 1, 2, 3, 4,.. are called counting numbers, or natural
numbers and they are used to track whole items.
(Note that 0 is not a counting number because we don’t have
to count when there is nothing to count.)

4. Fractions
Numbers 1, 2, 3, 4,.. are called counting numbers, or natural
numbers and they are used to track whole items.
(Note that 0 is not a counting number because we don’t have
to count when there is nothing to count.)
But in real life, we also need to measure and record fragments
of a whole item.

5. Fractions
Numbers 1, 2, 3, 4,.. are called counting numbers, or natural
numbers and they are used to track whole items.
(Note that 0 is not a counting number because we don’t have
to count when there is nothing to count.)
But in real life, we also need to measure and record fragments
of a whole item. Many such fragments come from sharing
whole items, i.e. from the division operation.

6. Fractions
Numbers 1, 2, 3, 4,.. are called counting numbers, or natural
numbers and they are used to track whole items.
(Note that 0 is not a counting number because we don’t have
to count when there is nothing to count.)
But in real life, we also need to measure and record fragments
of a whole item. Many such fragments come from sharing
whole items, i.e. from the division operation.
For example, divide 7 apples between 2 people, we have that
7
2 = 3 with R = 1 .

7. Fractions
Numbers 1, 2, 3, 4,.. are called counting numbers, or natural
numbers and they are used to track whole items.
(Note that 0 is not a counting number because we don’t have
to count when there is nothing to count.)
But in real life, we also need to measure and record fragments
of a whole item. Many such fragments come from sharing
whole items, i.e. from the division operation.
For example, divide 7 apples between 2 people, we have that
7
2 = 3 with R = 1 .
2 people 3 for each
1 remains

8. Fractions
Numbers 1, 2, 3, 4,.. are called counting numbers, or natural
numbers and they are used to track whole items.
(Note that 0 is not a counting number because we don’t have
to count when there is nothing to count.)
But in real life, we also need to measure and record fragments
of a whole item. Many such fragments come from sharing
whole items, i.e. from the division operation.
For example, divide 7 apples between 2 people, we have that
7
2 = 3 with R = 1 .
or
2 people 3 for each
1 remains

9. Fractions
Numbers 1, 2, 3, 4,.. are called counting numbers, or natural
numbers and they are used to track whole items.
(Note that 0 is not a counting number because we don’t have
to count when there is nothing to count.)
But in real life, we also need to measure and record fragments
of a whole item. Many such fragments come from sharing
whole items, i.e. from the division operation.
For example, divide 7 apples between 2 people, we have that
7
2 = 3 with R = 1 .
or
2 people 3 for each
1 remains
To share the remaining apple between 2 people, we cut it into
two pieces of equal size and let each person takes one piece.

10. Fractions
Numbers 1, 2, 3, 4,.. are called counting numbers, or natural
numbers and they are used to track whole items.
(Note that 0 is not a counting number because we don’t have
to count when there is nothing to count.)
But in real life, we also need to measure and record fragments
of a whole item. Many such fragments come from sharing
whole items, i.e. from the division operation.
For example, divide 7 apples between 2 people, we have that
7
2 = 3 with R = 1 .
or
2 people 3 for each
1 remains
To share the remaining apple between 2 people, we cut it into
two pieces of equal size and let each person takes one piece.
Fragments obtained by cutting whole items into equal parts are
measured and recorded with fractions.

11. Fractions
Fractions are numbers of the form N (or N/D) where N, D are
D
whole numbers* where D ≠ 0.
* We will address fractions of other type of numbers later.

12. Fractions
Fractions are numbers of the form N (or N/D) where N, D are
D
whole numbers* where D ≠ 0.
3
6
* We will address fractions of other type of numbers later.

13. Fractions
Fractions are numbers of the form N (or N/D) where N, D are
D
whole numbers* where D ≠ 0.
Fractions are numbers that measure parts of whole items.
3
6
* We will address fractions of other type of numbers later.

14. Fractions
Fractions are numbers of the form N (or N/D) where N, D are
D
whole numbers* where D ≠ 0.
Fractions are numbers that measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
of the pieces, the fraction that represents this quantity is 3 .
6
3
6
* We will address fractions of other type of numbers later.

15. Fractions
Fractions are numbers of the form N (or N/D) where N, D are
D
whole numbers* where D ≠ 0.
Fractions are numbers that measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
of the pieces, the fraction that represents this quantity is 3 .
6
3
6
The bottom number is the
number of equal parts in the
division and it is called the
denominator.
* We will address fractions of other type of numbers later.

16. Fractions
Fractions are numbers of the form N (or N/D) where N, D are
D
whole numbers* where D ≠ 0.
Fractions are numbers that measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
of the pieces, the fraction that represents this quantity is 3 .
6
3
6
The bottom number is the
number of equal parts in the
division and it is called the
denominator.
* We will address fractions of other type of numbers later.

17. Fractions
Fractions are numbers of the form N (or N/D) where N, D are
D
whole numbers* where D ≠ 0.
Fractions are numbers that measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
of the pieces, the fraction that represents this quantity is 3 .
6
3
6
The top number “3” is the
number of parts that we
have and it is called the
numerator.
The bottom number is the
number of equal parts in the
division and it is called the
denominator.
* We will address fractions of other type of numbers later.

18. Fractions
Fractions are numbers of the form N (or N/D) where N, D are
D
whole numbers* where D ≠ 0.
Fractions are numbers that measure parts of whole items.
Suppose a pizza is cut into 6 equal slices and we have 3 of
of the pieces, the fraction that represents this quantity is 3 .
6
3
6
The top number “3” is the
number of parts that we
have and it is called the
numerator.
The bottom number is the
number of equal parts in the
division and it is called the
denominator.
3/6 of a pizza
* We will address fractions of other type of numbers later.

19. Fractions
For larger denominators we can use a pan–pizza for
pictures.

20. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8

21. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
How many slices should we cut
the pizza into and how should
we do the cuts?

22. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
Cut the pizza into 8 pieces,
How many slices should we cut
the pizza into and how should
we do the cuts?

23. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
or
5
8
Cut the pizza into 8 pieces,
How many slices should we cut
the pizza into and how should
we do the cuts?

24. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
or
5
8
5/8 of a pizza
Cut the pizza into 8 pieces,
take 5 of them.
How many slices should we cut
the pizza into and how should
we do the cuts?

25. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
or
5/8 of a pizza
How many slices should we cut
the pizza into and how should
we do the cuts?
7
12

26. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
or
5/8 of a pizza
How many slices should we cut
the pizza into and how should
we do the cuts?
7
12
Cut the pizza into 12 pieces,

27. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
or
5/8 of a pizza
How many slices should we cut
the pizza into and how should
we do the cuts?
7
12
Cut the pizza into 12 pieces,

28. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
or
5/8 of a pizza
How many slices should we cut
the pizza into and how should
we do the cuts?
7
12
Cut the pizza into 12 pieces,
or

29. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
or
5/8 of a pizza
How many slices should we cut
the pizza into and how should
we do the cuts?
7
12
Cut the pizza into 12 pieces,
take 7 pieces.
or

30. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
or
5/8 of a pizza
How many slices should we cut
the pizza into and how should
we do the cuts?
7
12
Cut the pizza into 12 pieces,
take 7 pieces.
7/12 of a pizza
or

31. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
or
5/8 of a pizza
How many slices should we cut
the pizza into and how should
we do the cuts?
7
12
7/12 of a pizza
Cut the pizza into 12 pieces,
8
12
take 7 pieces. Note that 8 or 12 = 1,
or

32. Fractions
For larger denominators we can use a pan–pizza for
pictures. For example,
5
8
or
5/8 of a pizza
How many slices should we cut
the pizza into and how should
we do the cuts?
7
12
7/12 of a pizza
Cut the pizza into 12 pieces,
8
12
take 7 pieces. Note that 8 or 12 = 1,
and in general that x = 1.
x
or

33. Fractions
Whole numbers can be viewed as fractions with denominator 1.

34. Fractions
Whole numbers can be viewed as fractions with denominator 1.
x
5
Thus 5 =
and x = 1 .
1

35. Fractions
Whole numbers can be viewed as fractions with denominator 1.
0
x
5
Thus 5 =
and x = 1 . The fraction x = 0, where x 0.
1

36. Fractions
Whole numbers can be viewed as fractions with denominator 1.
0
x
5
Thus 5 =
and x = 1 . The fraction x = 0, where x 0.
1
However, x does not have any meaning, it is undefined.
0

37. Fractions
Whole numbers can be viewed as fractions with denominator 1.
0
x
5
Thus 5 =
and x = 1 . The fraction x = 0, where x 0.
1
However, x does not have any meaning, it is undefined.
0
The Ultimate No-No of Mathematics:
The denominator (bottom) of a fraction can't
be 0. (It's undefined if the denominator is 0.)

38. Fractions
Whole numbers can be viewed as fractions with denominator 1.
0
x
5
Thus 5 =
and x = 1 . The fraction x = 0, where x 0.
1
However, x does not have any meaning, it is undefined.
0
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.

39. Fractions
Whole numbers can be viewed as fractions with denominator 1.
0
x
5
Thus 5 =
and x = 1 . The fraction x = 0, where x 0.
1
However, x does not have any meaning, it is undefined.
0
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
3
4
=
=
=
2
4
6
8
… are equivalent fractions.

40. Fractions
Whole numbers can be viewed as fractions with denominator 1.
0
x
5
Thus 5 =
and x = 1 . The fraction x = 0, where x 0.
1
However, x does not have any meaning, it is undefined.
0
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
3
4
=
=
=
2
4
6
8
… are equivalent fractions.
The fraction with the smallest denominator of all the
equivalent Fractions s called the reduced fraction.

41. Fractions
Whole numbers can be viewed as fractions with denominator 1.
0
x
5
Thus 5 =
and x = 1 . The fraction x = 0, where x 0.
1
However, x does not have any meaning, it is undefined.
0
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
3
4
=
=
=
2
4
6
8
… are equivalent fractions.
The fraction with the smallest denominator of all the
equivalent Fractions s called the reduced fraction.
1
is the reduced fraction in the above list. It’s the easiest one
2
to execute for cutting a pizza to obtain the specified amount.

42. Fractions
We use the following fact to reduce a fraction.

43. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule

44. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a
b
b
c .
c

45. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.

46. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
Example A. Reduce the fraction 54 .
78

47. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78

48. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78
54
= 54 2
78
78 2

49. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78
27
54
= 54 2 =
78
78 2
39

50. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78
27
54
= 54 2 = 27/3
78
78 2
39/3
39

51. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78
27
54
= 54 2 = 27/3 = 9 which is reduced.
78
78 2
13
39/3
39

52. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78
27
54
= 54 2 = 27/3 = 9 which is reduced.
78
78 2
13
39/3
39
We may also divide both by 6 to obtain the answer in one step.

53. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78
27
54
= 54 2 = 27/3 = 9 which is reduced.
78
78 2
13
39/3
39
We may also divide both by 6 to obtain the answer in one step.
In other words, a factor common to both the numerator and the
denominator may be canceled as 1,

54. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78
27
54
= 54 2 = 27/3 = 9 which is reduced.
78
78 2
13
39/3
39
We may also divide both by 6 to obtain the answer in one step.
In other words, a factor common to both the numerator and the
denominator may be canceled as 1, i.e. x * c =
y *c

55. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78
27
54
= 54 2 = 27/3 = 9 which is reduced.
78
78 2
13
39/3
39
We may also divide both by 6 to obtain the answer in one step.
In other words, a factor common to both the numerator and the
denominator may be canceled as 1, i.e. x * c = x * c
y *c
y *c
1

56. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78
27
54
= 54 2 = 27/3 = 9 which is reduced.
78
78 2
13
39/3
39
We may also divide both by 6 to obtain the answer in one step.
In other words, a factor common to both the numerator and the
denominator may be canceled as 1, i.e. x * c = x * c
y *c
y *c
(We may omit writing the 1’s after the cancellation.)
1

57. Fractions
We use the following fact to reduce a fraction.
Factor-Cancellation Rule
a
Given a fraction b and c is a factor of both, then a = a c .
b
b c
that is, if the numerator and denominator are divided by the
same quantity c, the result is simpler equivalent fraction.
To reduce a fraction, we keep dividing the top and bottom by
common numbers until no more common division is possible.
Example A. Reduce the fraction 54 .
78
27
54
= 54 2 = 27/3 = 9 which is reduced.
78
78 2
13
39/3
39
We may also divide both by 6 to obtain the answer in one step.
In other words, a factor common to both the numerator and the
denominator may be canceled as 1, i.e. x * c = x * c = x
y *c
y.
y *c
(We may omit writing the 1’s after the cancellation.)
1

58. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.

59. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6

60. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6
2*3*4*5
3*4*5*6

61. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6
2*3*4*5
3*4*5*6

62. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6
2*3*4*5
3*4*5*6

63. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6
2*3*4*5 = 2
6
3*4*5*6

64. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6
2 * 3 * 4 * 5 = 2 = 1 which is reduced.
6
3
3*4*5*6

65. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6
2 * 3 * 4 * 5 = 2 = 1 which is reduced.
6
3
3*4*5*6
On Cancellations

66. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6
2 * 3 * 4 * 5 = 2 = 1 which is reduced.
6
3
3*4*5*6
On Cancellations
There are two types of cancellations.

67. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6
2 * 3 * 4 * 5 = 2 = 1 which is reduced.
6
3
3*4*5*6
On Cancellations
There are two types of cancellations.
The phrase “the 5’s cancelled each other” is used sometime to
describe “5 – 5 = 0” in the sense that they’re reduced to “0”,
i.e. the 5’s neutralized each other.

68. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6
2 * 3 * 4 * 5 = 2 = 1 which is reduced.
6
3
3*4*5*6
On Cancellations
There are two types of cancellations.
The phrase “the 5’s cancelled each other” is used sometime to
describe “5 – 5 = 0” in the sense that they’re reduced to “0”,
i.e. the 5’s neutralized each other.
We also use the phrase “the 5’s cancelled as 1” to describe
“ 5 = 1 ” in the sense that they are common factors
5
so they maybe crossed out to be 1.

69. Fractions
So if the top and bottom of a fraction are already factored, then
all we’ve to do is to scan and cross out pair(s) of common factors.
Example B. Reduce the fraction 2 * .3 * 4 * 5
3*4*5*6
2 * 3 * 4 * 5 = 2 = 1 which is reduced.
6
3
3*4*5*6
On Cancellations
There are two types of cancellations.
The phrase “the 5’s cancelled each other” is used sometime to
describe “5 – 5 = 0” in the sense that they’re reduced to “0”,
i.e. the 5’s neutralized each other.
We also use the phrase “the 5’s cancelled as 1” to describe
“ 5 = 1 ” in the sense that they are common factors
5
so they maybe crossed out to be 1.
One common mistake when simplifying Fractions s to cross
out non-factors. We address this issue next.

70. Fractions
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)

71. Fractions
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)
A participant in a multiplication is called a factor.
The “2” is in the expression “2 * 3” is called a factor.

72. Fractions
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)
A participant in a multiplication is called a factor.
The “2” is in the expression “2 * 3” is called a factor.
One common mistake in cancelling factor is to cancel a term,
i.e. a common number that is adding (or subtracting) in the
numerator or denominator.

73. Fractions
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)
A participant in a multiplication is called a factor.
The “2” is in the expression “2 * 3” is called a factor.
One common mistake in cancelling factor is to cancel a term,
i.e. a common number that is adding (or subtracting) in the
numerator or denominator.
Terms may not be cancelled. Only factors may be canceled.

74. Fractions
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)
A participant in a multiplication is called a factor.
The “2” is in the expression “2 * 3” is called a factor.
One common mistake in cancelling factor is to cancel a term,
i.e. a common number that is adding (or subtracting) in the
numerator or denominator.
Terms may not be cancelled. Only factors may be canceled.
3 = 2+1
5
2+3

75. Fractions
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)
A participant in a multiplication is called a factor.
The “2” is in the expression “2 * 3” is called a factor.
One common mistake in cancelling factor is to cancel a term,
i.e. a common number that is adding (or subtracting) in the
numerator or denominator.
Terms may not be cancelled. Only factors may be canceled.
3 = 2+1
2 + 1 !? 1
=
=
5
2+3
2+3
3

76. Fractions
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)
A participant in a multiplication is called a factor.
The “2” is in the expression “2 * 3” is called a factor.
One common mistake in cancelling factor is to cancel a term,
i.e. a common number that is adding (or subtracting) in the
numerator or denominator.
Terms may not be cancelled. Only factors may be canceled.
3 = 2+1
2 + 1 !? 1
=
=
5
2+3
2+3
3
This is addition.
The 2 is a term.
Can’t cancel!
Cancelling them would
change the fraction.

77. Fractions
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)
A participant in a multiplication is called a factor.
The “2” is in the expression “2 * 3” is called a factor.
One common mistake in cancelling factor is to cancel a term,
i.e. a common number that is adding (or subtracting) in the
numerator or denominator.
Terms may not be cancelled. Only factors may be canceled.
2*1
3 = 2+1
2 + 1 !? 1
=
=
2*3
5
2+3
2+3
3
This is addition.
The 2 is a term.
Can’t cancel!
Cancelling them would
change the fraction.

78. Fractions
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)
A participant in a multiplication is called a factor.
The “2” is in the expression “2 * 3” is called a factor.
One common mistake in cancelling factor is to cancel a term,
i.e. a common number that is adding (or subtracting) in the
numerator or denominator.
Terms may not be cancelled. Only factors may be canceled.
2*1
3 = 2+1
2 + 1 !? 1
=
=
2*3
5
2+3
2+3
3
Yes, 2 is a common factor.
This is addition.
They may be canceled to be 1,
The 2 is a term.
which produces an equivalent
Can’t cancel!
fraction.
Cancelling them would
change the fraction.

79. Fractions
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)
A participant in a multiplication is called a factor.
The “2” is in the expression “2 * 3” is called a factor.
One common mistake in cancelling factor is to cancel a term,
i.e. a common number that is adding (or subtracting) in the
numerator or denominator.
Terms may not be cancelled. Only factors may be canceled.
2*1
3 = 2+1
2 + 1 !? 1
= 1
=
=
2*3
3
5
2+3
2+3
3
Yes, 2 is a common factor.
This is addition.
They may be canceled to be 1,
The 2 is a term.
which produces an equivalent
Can’t cancel!
fraction.
Cancelling them would
change the fraction.