2.5 fractions w
TRANSCRIPT
![Page 2: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/2.jpg)
Numbers 1, 2, 3, 4,.. are called counting numbers, or natural numbers and they are used to track whole items.
Fractions
![Page 3: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/3.jpg)
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.)
Fractions
![Page 4: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/4.jpg)
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.)
Fractions
But in real life, we also need to measure and record fragments of a whole item.
![Page 5: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/5.jpg)
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.)
Fractions
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.
![Page 6: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/6.jpg)
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.)
7 ÷ 2 = 3 with R = 1 .
Fractions
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
![Page 7: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/7.jpg)
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.)
7 ÷ 2 = 3 with R = 1 .
2 people 3 for each 1 remains
Fractions
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
![Page 8: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/8.jpg)
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.)
7 ÷ 2 = 3 with R = 1 .
2 people 3 for each 1 remains
Fractions
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
or
![Page 9: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/9.jpg)
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.)
7 ÷ 2 = 3 with R = 1 .
2 people 3 for each 1 remains
Fractions
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
To share the remaining apple between 2 people, we cut it into two pieces of equal size and let each person takes one piece.
or
![Page 10: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/10.jpg)
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.)
7 ÷ 2 = 3 with R = 1 .
2 people 3 for each 1 remains
Fractions
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
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.
or
![Page 11: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/11.jpg)
Fractions are numbers of the form (or N/D) where N, D are whole numbers* where D ≠ 0.
ND
Fractions
* We will address fractions of other type of numbers later.
![Page 12: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/12.jpg)
Fractions are numbers of the form (or N/D) where N, D are whole numbers* where D ≠ 0.
ND
36
Fractions
* We will address fractions of other type of numbers later.
![Page 13: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/13.jpg)
Fractions are numbers of the form (or N/D) where N, D are whole numbers* where D ≠ 0.
ND
36
Fractions
Fractions are numbers that measure parts of whole items.
* We will address fractions of other type of numbers later.
![Page 14: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/14.jpg)
Fractions are numbers of the form (or N/D) where N, D are whole numbers* where D ≠ 0.
ND
36
36
Fractions
Suppose a pizza is cut into 6 equal slices and we have 3 of
of the pieces, the fraction that represents this quantity is .
Fractions are numbers that measure parts of whole items.
* We will address fractions of other type of numbers later.
![Page 15: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/15.jpg)
Fractions are numbers of the form (or N/D) where N, D are whole numbers* where D ≠ 0.
ND
36
The bottom number is the number of equal parts in the division and it is called the denominator.
36
Fractions
Suppose a pizza is cut into 6 equal slices and we have 3 of
of the pieces, the fraction that represents this quantity is .
Fractions are numbers that measure parts of whole items.
* We will address fractions of other type of numbers later.
![Page 16: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/16.jpg)
Fractions are numbers of the form (or N/D) where N, D are whole numbers* where D ≠ 0.
ND
36
The bottom number is the number of equal parts in the division and it is called the denominator.
36
Fractions
Suppose a pizza is cut into 6 equal slices and we have 3 of
of the pieces, the fraction that represents this quantity is .
Fractions are numbers that measure parts of whole items.
* We will address fractions of other type of numbers later.
![Page 17: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/17.jpg)
Fractions are numbers of the form (or N/D) where N, D are whole numbers* where D ≠ 0.
ND
36
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.
36
Fractions
Suppose a pizza is cut into 6 equal slices and we have 3 of
of the pieces, the fraction that represents this quantity is .
Fractions are numbers that measure parts of whole items.
* We will address fractions of other type of numbers later.
![Page 18: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/18.jpg)
Fractions are numbers of the form (or N/D) where N, D are whole numbers* where D ≠ 0.
ND
36
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.
Fractions
Suppose a pizza is cut into 6 equal slices and we have 3 of
of the pieces, the fraction that represents this quantity is .
Fractions are numbers that measure parts of whole items.
3/6 of a pizza
36
* We will address fractions of other type of numbers later.
![Page 19: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/19.jpg)
Fractions For larger denominators we can use a pan–pizza for pictures.
![Page 20: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/20.jpg)
58
Fractions For larger denominators we can use a pan–pizza for pictures. For example,
![Page 21: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/21.jpg)
58
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
For larger denominators we can use a pan–pizza for pictures. For example,
![Page 22: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/22.jpg)
58
Cut the pizza into 8 pieces,
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
For larger denominators we can use a pan–pizza for pictures. For example,
![Page 23: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/23.jpg)
58
Cut the pizza into 8 pieces,
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
or
For larger denominators we can use a pan–pizza for pictures. For example,
![Page 24: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/24.jpg)
58
5/8 of a pizza
Cut the pizza into 8 pieces,take 5 of them.
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
or
For larger denominators we can use a pan–pizza for pictures. For example,
![Page 25: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/25.jpg)
58
712
5/8 of a pizza
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
or
For larger denominators we can use a pan–pizza for pictures. For example,
![Page 26: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/26.jpg)
58
712
5/8 of a pizza
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
or
For larger denominators we can use a pan–pizza for pictures. For example,
Cut the pizza into 12 pieces,
![Page 27: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/27.jpg)
58
712
5/8 of a pizza
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
or
For larger denominators we can use a pan–pizza for pictures. For example,
Cut the pizza into 12 pieces,
![Page 28: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/28.jpg)
58
712
5/8 of a pizza
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
or
or
For larger denominators we can use a pan–pizza for pictures. For example,
Cut the pizza into 12 pieces,
![Page 29: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/29.jpg)
58
712
5/8 of a pizza
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
or
or
For larger denominators we can use a pan–pizza for pictures. For example,
Cut the pizza into 12 pieces,
take 7 pieces.
![Page 30: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/30.jpg)
58
712
5/8 of a pizza
7/12 of a pizza
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
or
or
For larger denominators we can use a pan–pizza for pictures. For example,
Cut the pizza into 12 pieces,
take 7 pieces.
![Page 31: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/31.jpg)
58
712
5/8 of a pizza
7/12 of a pizza
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
or
or
Cut the pizza into 12 pieces,
For larger denominators we can use a pan–pizza for pictures. For example,
Note that or = 1,88
1212take 7 pieces.
![Page 32: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/32.jpg)
58
712
5/8 of a pizza
7/12 of a pizza
Fractions
How many slices should we cut the pizza into and how should we do the cuts?
or
or
Cut the pizza into 12 pieces,
For larger denominators we can use a pan–pizza for pictures. For example,
Note that or = 1,88
1212take 7 pieces.
and in general that
xx = 1.
![Page 33: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/33.jpg)
Fractions Whole numbers can be viewed as fractions with denominator 1.
![Page 34: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/34.jpg)
51
x1
Fractions Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = .
![Page 35: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/35.jpg)
51
x1
0x
Fractions Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
![Page 36: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/36.jpg)
However, does not have any meaning, it is undefined.
51
x1
0x
x0
Fractions Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
![Page 37: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/37.jpg)
However, does not have any meaning, it is undefined.
51
x1
0x
x0
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 Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
![Page 38: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/38.jpg)
However, does not have any meaning, it is undefined.
51
x1
0x
x0
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 Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
Fractions that represents the same quantity are called equivalent fractions.
![Page 39: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/39.jpg)
However, does not have any meaning, it is undefined.
51
x1
0x
x0
The Ultimate No-No of Mathematics:The denominator (bottom) of a fraction can't be 0. (It's undefined if the denominator is 0.)
12
=24
=36
=48
Fractions Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0.
Fractions that represents the same quantity are called equivalent fractions.
… are equivalent fractions.
![Page 40: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/40.jpg)
However, does not have any meaning, it is undefined.
51
x1
0x
x0
The Ultimate No-No of Mathematics:The denominator (bottom) of a fraction can't be 0. (It's undefined if the denominator is 0.)
12
=24
=36
=48
Fractions Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 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 s called the reduced fraction.
![Page 41: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/41.jpg)
However, does not have any meaning, it is undefined.
51
x1
0x
x0
The Ultimate No-No of Mathematics:The denominator (bottom) of a fraction can't be 0. (It's undefined if the denominator is 0.)
12
=24
=36
=48
is the reduced fraction in the above list. It’s the easiest one 12
Fractions Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 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 s called the reduced fraction.
to execute for cutting a pizza to obtain the specified amount.
![Page 42: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/42.jpg)
Fractions We use the following fact to reduce a fraction.
![Page 43: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/43.jpg)
Factor-Cancellation Rule
Fractions We use the following fact to reduce a fraction.
![Page 44: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/44.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
b ÷ c
Fractions We use the following fact to reduce a fraction.
.
![Page 45: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/45.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
b ÷ c
Fractions We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
![Page 46: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/46.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
b ÷ c
Example A. Reduce the fraction . 7854
Fractions We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
![Page 47: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/47.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
b ÷ c
Example A. Reduce the fraction . 7854
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
Fractions We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
![Page 48: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/48.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
b ÷ c
Example A. Reduce the fraction . 7854
7854 = 54 ÷ 2
78 ÷ 2
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
Fractions We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
![Page 49: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/49.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
b ÷ c
Example A. Reduce the fraction . 7854
7854 = 54 ÷ 2
78 ÷ 2
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
=39
27
Fractions We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
![Page 50: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/50.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
b ÷ c
Example A. Reduce the fraction . 7854
7854 = 54 ÷ 2
78 ÷ 2
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
= 27/339/3
39
27
Fractions We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
![Page 51: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/51.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
b ÷ c
Example A. Reduce the fraction . 7854
7854 = 54 ÷ 2
78 ÷ 2= 9
13
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
= 27/339/3
which is reduced. 39
27
Fractions We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
![Page 52: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/52.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
b ÷ c
Example A. Reduce the fraction . 7854
7854 = 54 ÷ 2
78 ÷ 2= 9
13
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
= 27/339/3
which is reduced. 39
27
Fractions We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
We may also divide both by 6 to obtain the answer in one step.
![Page 53: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/53.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
b ÷ c
Example A. Reduce the fraction . 7854
7854 = 54 ÷ 2
78 ÷ 2= 9
13
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
= 27/339/3
which is reduced. 39
27
Fractions
In other words, a factor common to both the numerator and the
denominator may be canceled as 1,
We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
We may also divide both by 6 to obtain the answer in one step.
![Page 54: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/54.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
=x * cy * c
b ÷ c
Example A. Reduce the fraction . 7854
7854 = 54 ÷ 2
78 ÷ 2= 9
13
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
= 27/339/3
which is reduced. 39
27
Fractions
In other words, a factor common to both the numerator and the
denominator may be canceled as 1,
We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
i.e.
We may also divide both by 6 to obtain the answer in one step.
![Page 55: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/55.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
=x * cy * c
x * cy * c
b ÷ c
Example A. Reduce the fraction . 7854
7854 = 54 ÷ 2
78 ÷ 2= 9
13
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
= 27/339/3
which is reduced. 39
27
Fractions
In other words, a factor common to both the numerator and the
denominator may be canceled as 1,
We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
i.e.
We may also divide both by 6 to obtain the answer in one step.
1
![Page 56: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/56.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
=x * cy * c
x * cy * c 1
b ÷ c
Example A. Reduce the fraction . 7854
7854 = 54 ÷ 2
78 ÷ 2= 9
13
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
= 27/339/3
which is reduced. 39
27
(We may omit writing the 1’s after the cancellation.)
Fractions
In other words, a factor common to both the numerator and the
denominator may be canceled as 1,
We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
i.e.
We may also divide both by 6 to obtain the answer in one step.
![Page 57: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/57.jpg)
Factor-Cancellation Rule
Given a fraction and c is a factor of both, thenab
ab = a ÷ c
xy .=x * c
y * c =x * cy * c 1
b ÷ c
Example A. Reduce the fraction . 7854
7854 = 54 ÷ 2
78 ÷ 2= 9
13
To reduce a fraction, we keep dividing the top and bottom by common numbers until no more common division is possible.
= 27/339/3
which is reduced. 39
27
(We may omit writing the 1’s after the cancellation.)
Fractions
In other words, a factor common to both the numerator and the
denominator may be canceled as 1,
We use the following fact to reduce a fraction.
.
that is, if the numerator and denominator are divided by the same quantity c, the result is simpler equivalent fraction.
i.e.
We may also divide both by 6 to obtain the answer in one step.
![Page 58: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/58.jpg)
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.
![Page 59: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/59.jpg)
Fractions
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 6
![Page 60: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/60.jpg)
Fractions
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 62 * 3 * 4 * 53 * 4 * 5 * 6
![Page 61: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/61.jpg)
Fractions
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 62 * 3 * 4 * 53 * 4 * 5 * 6
![Page 62: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/62.jpg)
Fractions
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 62 * 3 * 4 * 53 * 4 * 5 * 6
![Page 63: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/63.jpg)
Fractions
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 62 * 3 * 4 * 53 * 4 * 5 * 6 =
26
![Page 64: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/64.jpg)
Fractions
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 62 * 3 * 4 * 53 * 4 * 5 * 6 =
26 =
13 which is reduced.
![Page 65: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/65.jpg)
Fractions
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 62 * 3 * 4 * 53 * 4 * 5 * 6 =
26 =
13 which is reduced.
On Cancellations
![Page 66: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/66.jpg)
Fractions
There are two types of cancellations.
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 62 * 3 * 4 * 53 * 4 * 5 * 6 =
26 =
13 which is reduced.
On Cancellations
![Page 67: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/67.jpg)
Fractions
There are two types of cancellations.
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 62 * 3 * 4 * 53 * 4 * 5 * 6 =
26 =
13 which is reduced.
On 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.
![Page 68: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/68.jpg)
Fractions
There are two types of cancellations.
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 62 * 3 * 4 * 53 * 4 * 5 * 6 =
26 =
13 which is reduced.
On 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
55
= 1“ ” in the sense that they are common factors
so they maybe crossed out to be 1.
![Page 69: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/69.jpg)
One common mistake when simplifying Fractions s to cross out non-factors.
Fractions
There are two types of cancellations.
Example B. Reduce the fraction . 2 * 3 * 4 * 5
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.
3 * 4 * 5 * 62 * 3 * 4 * 53 * 4 * 5 * 6 =
26 =
13 which is reduced.
On 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
55
= 1“ ” in the sense that they are common factors
so they maybe crossed out to be 1.
We address this issue next.
![Page 70: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/70.jpg)
A participant in a sum or a difference is called a term.Fractions
The “2” in the expression “2 + 3” is a term (of the expression)
![Page 71: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/71.jpg)
A participant in a sum or a difference is called a term.Fractions
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. A participant in a multiplication is called a factor.
![Page 72: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/72.jpg)
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.
A participant in a sum or a difference is called a term.Fractions
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. A participant in a multiplication is called a factor.
![Page 73: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/73.jpg)
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.
A participant in a sum or a difference is called a term.Fractions
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.
A participant in a multiplication is called a factor.
![Page 74: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/74.jpg)
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.
2 + 12 + 3
35
=
A participant in a sum or a difference is called a term.Fractions
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.
A participant in a multiplication is called a factor.
![Page 75: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/75.jpg)
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.
2 + 12 + 3
= 2 + 1 2 + 3
= 13
35
= !?
A participant in a sum or a difference is called a term.Fractions
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.
A participant in a multiplication is called a factor.
![Page 76: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/76.jpg)
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.
2 + 12 + 3
= 2 + 1 2 + 3
= 13
35
=
This is addition. The 2 is a term.Can’t cancel!Cancelling them wouldchange the fraction.
!?
A participant in a sum or a difference is called a term.Fractions
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.
A participant in a multiplication is called a factor.
![Page 77: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/77.jpg)
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.
2 + 12 + 3
= 2 + 1 2 + 3
= 13
35
= !? 2 * 1
2 * 3
A participant in a sum or a difference is called a term.Fractions
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.
A participant in a multiplication is called a factor.
This is addition. The 2 is a term.Can’t cancel!Cancelling them wouldchange the fraction.
![Page 78: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/78.jpg)
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.
2 + 12 + 3
= 2 + 1 2 + 3
= 13
35
= !? 2 * 1
2 * 3
A participant in a sum or a difference is called a term.Fractions
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.
A participant in a multiplication is called a factor.
This is addition. The 2 is a term.Can’t cancel!Cancelling them wouldchange the fraction.
Yes, 2 is a common factor. They may be canceled to be 1, which produces an equivalent fraction.
![Page 79: 2.5 fractions w](https://reader034.vdocuments.mx/reader034/viewer/2022051515/5562944fd8b42abb398b4ae5/html5/thumbnails/79.jpg)
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.
2 + 12 + 3
= 2 + 1 2 + 3
= 13
35
= !? 2 * 1
2 * 3 = 13
A participant in a sum or a difference is called a term.Fractions
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.
A participant in a multiplication is called a factor.
This is addition. The 2 is a term.Can’t cancel!Cancelling them wouldchange the fraction.
Yes, 2 is a common factor. They may be canceled to be 1, which produces an equivalent fraction.