12 fractions
TRANSCRIPT
![Page 1: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/1.jpg)
Fractions
Back to Algebra–Ready Review Content.
![Page 2: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/2.jpg)
Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers.
pq
Fractions
![Page 3: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/3.jpg)
Fractions are numbers of the form (or p/q) where
p, q 0 are whole numbers.
pq
Fractions
36
![Page 4: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/4.jpg)
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.
pq
Fractions
36
![Page 5: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/5.jpg)
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 .
pq
36
Fractions
36
![Page 6: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/6.jpg)
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 .
pq
36
36
Fractions
![Page 7: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/7.jpg)
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 .
pq
36
The bottom number is the
number of equal parts in the
division and it is called the
denominator.
36
Fractions
![Page 8: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/8.jpg)
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 .
pq
36
The bottom number is the
number of equal parts in the
division and it is called the
denominator.
36
Fractions
![Page 9: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/9.jpg)
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 .
pq
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
![Page 10: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/10.jpg)
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 .
pq
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
3/6 of a pizza
![Page 11: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/11.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
![Page 12: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/12.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
How many slices should we cut the pizza into and how do
we do this?
![Page 13: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/13.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
Cut the pizza into 8 pieces,
![Page 14: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/14.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
Cut the pizza into 8 pieces, take 5 of them.
![Page 15: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/15.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
5/8 of a pizza
Cut the pizza into 8 pieces, take 5 of them.
![Page 16: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/16.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
712
5/8 of a pizza
![Page 17: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/17.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
712
5/8 of a pizza
Cut the pizza into 12 pieces,
![Page 18: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/18.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
712
5/8 of a pizza
Cut the pizza into 12 pieces,
![Page 19: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/19.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
712
5/8 of a pizza
Cut the pizza into 12 pieces, take 7 of them.
![Page 20: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/20.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
712
5/8 of a pizza
Cut the pizza into 12 pieces, take 7 of them.
or
![Page 21: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/21.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
712
5/8 of a pizza
7/12 of a pizza
or
Cut the pizza into 12 pieces, take 7 of them.
![Page 22: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/22.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
712
5/8 of a pizza
Note that or is the same as 1.88
1212
7/12 of a pizza
or
![Page 23: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/23.jpg)
For larger denominators we can use a pan–pizza for
pictures. For example,
58
Fractions
712
5/8 of a pizza
Fact: aa
Note that or is the same as 1.88
1212
= 1 (provided that a = 0.)
7/12 of a pizza
or
![Page 24: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/24.jpg)
FractionsWe may talk about the fractional amount of a group of items.
![Page 25: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/25.jpg)
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?
![Page 26: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/26.jpg)
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?
![Page 27: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/27.jpg)
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?
34 Divide $100 into
4 equal parts.
![Page 28: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/28.jpg)
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?
34 Divide $100 into
4 equal parts.
100 ÷ 4 = 25
so each part is $25,
![Page 29: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/29.jpg)
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?
34 Divide $100 into
4 equal parts.
Take 3 parts. 100 ÷ 4 = 25
so each part is $25,
![Page 30: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/30.jpg)
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?
34 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.
![Page 31: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/31.jpg)
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?
34 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.
712
Divide 72 people
into 12 equal parts.
![Page 32: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/32.jpg)
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?
34 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.
712
Divide 72 people
into 12 equal parts.
72 ÷ 12 = 6
so each part consists of 6 people,
![Page 33: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/33.jpg)
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?
34 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.
712
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.
![Page 34: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/34.jpg)
Whole numbers can be viewed as fractions with denominator 1.
Fractions
![Page 35: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/35.jpg)
Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . 5
1x1
Fractions
![Page 36: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/36.jpg)
Whole numbers can be viewed as fractions with denominator 1.
Thus 5 = and x = . The fraction = 0, where x 0. 5
1x1
0
x
Fractions
![Page 37: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/37.jpg)
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
1x1
0
xx0
Fractions
![Page 38: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/38.jpg)
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
1x1
0
xx0
Fractions
The Ultimate No-No of Mathematics:
![Page 39: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/39.jpg)
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
1x1
0
xx0
Fractions
The Ultimate No-No of Mathematics:
The denominator (bottom) of a fraction can't
be 0.
![Page 40: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/40.jpg)
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
1x1
0
xx0
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.)
![Page 41: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/41.jpg)
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
1x1
0
xx0
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.
![Page 42: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/42.jpg)
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
1x1
0
xx0
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
![Page 43: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/43.jpg)
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
1x1
0
xx0
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
![Page 44: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/44.jpg)
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
1x1
0
xx0
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
![Page 45: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/45.jpg)
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
1x1
0
xx0
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
![Page 46: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/46.jpg)
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
1x1
0
xx0
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
![Page 47: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/47.jpg)
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.
ab
ab =
a / c
Fractions
b / c
![Page 48: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/48.jpg)
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,
ab
ab =
a / c
Fractions
b / c
![Page 49: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/49.jpg)
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.
ab
ab =
a / c
=a*cb*c
a*cb*c
1
Fractions
b / c
![Page 50: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/50.jpg)
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.
ab
ab =
a / c
ab .
=a*cb*c
=a*cb*c
1
Fractions
b / c
![Page 51: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/51.jpg)
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.
ab
ab =
a / c
ab .
=a*cb*c
=a*cb*c
1
Fractions
b / c
(Often we omit writing the 1’s after the cancellation.)
![Page 52: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/52.jpg)
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.
ab
ab =
a / c
ab .
=a*cb*c
=a*cb*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.)
![Page 53: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/53.jpg)
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.
ab
ab =
a / c
ab .
=a*cb*c
=a*cb*c
1
Fractions
b / c
Example B. Reduce the fraction . 7854
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.)
![Page 54: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/54.jpg)
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.
ab
ab =
a / c
ab .
=a*cb*c
=a*cb*c
1
Fractions
b / c
Example B. Reduce the fraction . 7854
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.)
![Page 55: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/55.jpg)
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.
ab
ab =
a / c
ab .
=a*cb*c
=a*cb*c
1
Fractions
b / c
Example B. Reduce the fraction . 7854
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.)
![Page 56: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/56.jpg)
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.
ab
ab =
a / c
ab .
=a*cb*c
=a*cb*c
1
Fractions
b / c
Example B. Reduce the fraction . 7854
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.)
![Page 57: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/57.jpg)
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.
ab
ab =
a / c
ab .
=a*cb*c
=a*cb*c
1
Fractions
b / c
Example B. Reduce the fraction . 7854
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.)
![Page 58: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/58.jpg)
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.
ab
ab =
a / c
ab .
=a*cb*c
=a*cb*c
1
Fractions
b / c
Example B. Reduce the fraction . 7854
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.)
![Page 59: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/59.jpg)
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.
ab
ab =
a / c
ab .
=a*cb*c
=a*cb*c
1
Fractions
b / c
Example B. Reduce the fraction . 7854
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.)
![Page 60: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/60.jpg)
FractionsOne common mistake in cancellation is to cancel a common
number that is part of an addition (or subtraction) in the
numerator or denominator.
![Page 61: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/61.jpg)
FractionsOne 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.
![Page 62: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/62.jpg)
FractionsOne 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).
![Page 63: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/63.jpg)
FractionsOne 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.
![Page 64: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/64.jpg)
FractionsOne 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.
![Page 65: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/65.jpg)
FractionsOne 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.
![Page 66: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/66.jpg)
FractionsOne 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.
![Page 67: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/67.jpg)
FractionsOne 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.
![Page 68: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/68.jpg)
FractionsOne 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.
![Page 69: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/69.jpg)
FractionsOne 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 * 12 * 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.
![Page 70: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/70.jpg)
FractionsOne 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 * 12 * 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.
![Page 71: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/71.jpg)
FractionsOne 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 * 12 * 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.
![Page 72: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/72.jpg)
FractionsOne 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 * 12 * 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.
![Page 73: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/73.jpg)
23 4
Improper Fractions and Mixed Numbers
Example C. Put into mixed form.
![Page 74: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/74.jpg)
23 4
23 4 = 5 with remainder 3. ··
Improper Fractions and Mixed Numbers
Example C. Put into mixed form.
![Page 75: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/75.jpg)
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
![Page 76: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/76.jpg)
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 =
![Page 77: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/77.jpg)
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.
![Page 78: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/78.jpg)
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
![Page 79: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/79.jpg)
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
![Page 80: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/80.jpg)
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
![Page 81: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/81.jpg)
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
![Page 82: 12 fractions](https://reader031.vdocument.in/reader031/viewer/2022032022/55aec2231a28ab674d8b486c/html5/thumbnails/82.jpg)
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
1286
11
121
171. 2. 3. 4. 5. 6. 7.
Exercise. A. Reduce the following fractions.
46 ,
812 ,
159 ,
2418 ,
3042 ,
5436 ,
6048 ,
72108