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------=_NextPart_01C8EB1E.108A1450 Content-Location: file:///C:/0D764A33/2Fractions_files/master09.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8EB1E.108A1450 Content-Location: file:///C:/0D764A33/2Fractions_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAADwAAAAAUAHAAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwCeQChAAMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAOAAAAJAMFAP///////3gA oAB4AKAA////////CAAAAPoCAAAAAAAAAAAAAAQAAAAtAQIABAAAAC0BAAAEAAAAJwH//xwAAAD7 Avn/AAAAAAAAkAEAAAAAAEAAAEFyaWFsAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAC0B AwAEAAAALgEYAAQAAAACAQEABQAAAAkCAAAAAhUAAAAyCgkAQgAJAAAARnJhY3Rpb25zAAQAAgAE AAQAAgACAAQABAADAAQAAAAuAQAAHAAAAPsCEAAHAAAAAAC8AgAAAAABAgIiU3lzdGVtAAAAAAAA AAAAABgAAAABAAAAcDcVAOQEAAAEAAAALQEEAAQAAADwAQMAAwAAAAAA ------=_NextPart_01C8EB1E.108A1450 Content-Location: file:///C:/0D764A33/2Fractions_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8EB1E.108A1450 Content-Location: file:///C:/0D764A33/2Fractions_files/slide0055.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Fractions
Fractions=
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        = ;            &n= bsp;            = ;   
Fractions are numbers of the form       (or = p/q) where
<= /span>
p, q &sup= 1; 0 are whole numbers.
p
q
Fractions=
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        = ;            &n= bsp;            = ;   
Fractions are numbers of the form       (or = p/q) where
<= /span>
p, q &sup= 1; 0 are whole numbers. Fractions are numbers that tracks parts of whole items.
p
q
Fractions=
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        = ;            &n= bsp;            = ;   
Fractions are numbers of the form       (or = p/q) where
<= /span>
p, q &sup= 1; 0 are whole numbers. Fractions are numbers that tracks parts of whole items.= 3;
Suppose a pizza is cut into 6 e= qual slices and we have 3 of
<= /div>
them, the fraction that represe= nts this quantity is    &= nbsp; . 
p
q
3=
6=
Fractions=
------=_NextPart_01C8EB1E.108A1450 Content-Location: file:///C:/0D764A33/2Fractions_files/slide0059.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Fractions
        = ;            &n= bsp;            = ;   
Fractions are numbers of the form       (or = p/q) where
<= /span>
p, q &sup= 1; 0 are whole numbers. Fractions are numbers that tracks parts of whole items.= 3;
Suppose a pizza is cut into 6 e= qual slices and we have 3 of
<= /div>
them, the fraction that represe= nts this quantity is    &= nbsp; . 
p
q
3
6
3=
6=
Fractions=
------=_NextPart_01C8EB1E.108A1450 Content-Location: file:///C:/0D764A33/2Fractions_files/slide0060.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Fractions
        = ;            &n= bsp;            = ;   
Fractions are numbers of the form       (or = p/q) where
<= /span>
p, q &sup= 1; 0 are whole numbers. Fractions are numbers that tracks parts of whole items.= 3;
Suppose a pizza is cut into 6 e= qual slices and we have 3 of
<= /div>
them, the fraction that represe= nts this quantity is    &= nbsp; . 
p
q
3
6
The bottom number is the number of equal parts in the division and it is called the <= /span>denominator<= /i>.
3=
6=
Fractions=
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        = ;            &n= bsp;            = ;   
Fractions are numbers of the form       (or = p/q) where
<= /span>
p, q &sup= 1; 0 are whole numbers. Fractions are numbers that tracks parts of whole items.= 3;
Suppose a pizza is cut into 6 e= qual slices and we have 3 of
<= /div>
them, the fraction that represe= nts this quantity is    &= nbsp; . 
p
q
3
6
The bottom number is the number of equal parts in the division and it is called the <= /span>denominator<= /i>.
3=
6=
Fractions=
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        = ;            &n= bsp;            = ;   
Fractions are numbers of the form       (or = p/q) where
<= /span>
p, q &sup= 1; 0 are whole numbers. Fractions are numbers that tracks parts of whole items.= 3;
Suppose a pizza is cut into 6 e= qual slices and we have 3 of
<= /div>
them, the fraction that represe= nts this quantity is    &= nbsp; . 
p
q
3
6
The bottom number is the number of equal parts in the division and it is called the <= /span>denominator<= /i>.
The= top number “3” is the number of parts that we = have and it is called the= numerator.
3=
6=
Fractions=
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Whole numbers can be view= ed as fractions with denominator 1.
Fractions=
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        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     . 
5
1
x
1
Fractions=
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        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0.
5
1
x
1
0
x
Fractions=
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        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0. 
<= /div>
However,        does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions=
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        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0. 
<= /div>
However,        does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions=
The Ulti= mate No-No of Mathematics:
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        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0. 
<= /div>
However,        does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions=
The Ultimate N= o-No of Mathematics:
The denominator (bottom) of a fraction can't be 0.
------=_NextPart_01C8EB1E.108A1450 Content-Location: file:///C:/0D764A33/2Fractions_files/slide0070.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Fractions
        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0. 
<= /div>
However,        does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions=
The Ultimate N= o-No of Mathematics:
The denominator (bottom) of a fraction can't be 0. (Its undefined if the denominator is 0.)
------=_NextPart_01C8EB1E.108A1450 Content-Location: file:///C:/0D764A33/2Fractions_files/slide0071.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Fractions
        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0. 
<= /div>
However,        does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions=
The Ultimate N= o-No of Mathematics:
The denominator (bottom) of a fraction can't be 0. (Its undefined if the denominator is 0.)
Fra= ctions that represents the same quantity are called equivale= nt fractions.
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        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0. 
<= /div>
However,        does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions=
The Ultimate N= o-No of Mathematics:
The denominator (bottom) of a fraction can't be 0. (Its undefined if the denominator is 0.)
Fractions that represents the s= ame quantity are called equivalent fractions.
<= /div>
        = ;            &n= bsp;       
1
2
=3D
2
4
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        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0. 
<= /div>
However,        does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions=
The Ultimate N= o-No of Mathematics:
The denominator (bottom) of a fraction can't be 0. (Its undefined if the denominator is 0.)
Fractions that represents the s= ame quantity are called equivalent fractions.
<= /div>
        = ;            &n= bsp;
1
2
=3D
2
4
=3D
3
6
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        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0. 
<= /div>
However,        does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions=
The Ultimate N= o-No of Mathematics:
The denominator (bottom) of a fraction can't be 0. (Its undefined if the denominator is 0.)
Fractions that represents the s= ame quantity are called equivalent fractions.
<= /div>
        = ;            &n= bsp;        … are equivalent fractions.
1
2
=3D
2
4
=3D
3
6
=3D
4
8
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        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0. 
<= /div>
However,        does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions=
The Ultimate N= o-No of Mathematics:
The denominator (bottom) of a fraction can't be 0. (Its undefined if the denominator is 0.)
Fractions that represents the s= ame quantity are called equivalent fractions.
<= /div>
        = ;            &n= bsp;        … are equivalent fractions.
<= /div>
The fraction with the smallest denominator of all the equivalent fractions is called = the reduced fraction. <= /span>
1
2
=3D
2
4
=3D
3
6
=3D
4
8
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        = ;            &n= bsp;            = ;   
Whole numbers can be viewed as fractions with denominator 1. 
<= /div>
Thus 5 =3D       and= x =3D     .  The fraction       =3D= 0, where = x ¹ 0. 
<= /div>
However,        does not have any meaning, it is undefined.
5
1
x
1
0
x
x
0
Fractions=
The Ultimate N= o-No of Mathematics:
The denominator (bottom) of a fraction can't be 0. (Its undefined if the denominator is 0.)
Fractions that represents the s= ame quantity are called equivalent fractions.
<= /div>
        = ;            &n= bsp;        … are equivalent fractions.
<= /div>
The fraction with the smallest denominator of all the equivalent fractions is called = the reduced fraction. <= /span>
1
2
=3D
2
4
=3D
3
6
=3D
4
8
 is the reduced one in the above li= st.
1
2
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Cancellation Rule: <= /div>
<= /div>
Given a fraction      , then= 3;
<= /div>
that is, if the numerator and denominator are divided by the same quantity c, the result wil= l be an equivalent fraction.
a
b
a
b
=3D
a / c
Fractions=
b / c
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Cancellation Rule: <= /div>
<= /div>
Given a fraction      , then= 3;
<= /div>
that is, if the numerator and denominator are divided by the same quantity c, the result wil= l be an equivalent fraction.
In other words, a common factor of the numerator and the
<= /div>
denomiantor may be canceled as = 1,
a
b
a
b
=3D
a / c
Fractions=
b / c
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Cancellation Rule: <= /div>
<= /div>
Given a fraction      , then= 3;
<= /div>
that is, if the numerator and denominator are divided by the same quantity c, the result wil= l be an equivalent fraction.
In other words, a common factor of the numerator and the
<= /div>
denomiantor may be canceled as = 1, i.e.
a
b
a
b
=3D
a / c
=3D
a*c
b*c  
a*c
b*c  
Fractions=
b / c
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Cancellation Rule: <= /div>
<= /div>
Given a fraction      , then= 3;
<= /div>
that is, if the numerator and denominator are divided by the same quantity c, the result wil= l be an equivalent fraction.
In other words, a common factor of the numerator and the
<= /div>
denomiantor may be canceled as = 1, i.e.
a
b
a
b
=3D
a / c
a
b .
=3D
a*c
b*c  
=3D
a*c
b*c  
Fractions=
b / c
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Cancellation Rule: <= /div>
<= /div>
Given a fraction      , then= 3;
<= /div>
that is, if the numerator and denominator are divided by the same quantity c, the result wil= l be an equivalent fraction.
In other words, a common factor of the numerator and the
<= /div>
denomiantor may be canceled as = 1, i.e.
a
b
a
b
=3D
a / c
a
b .
=3D
a*c
b*c  
=3D
a*c
b*c  
Fractions=
b / c
To reduce a fraction, we keep divide the top and bottom by  common numbers until no more division is possible. 
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Cancellation Rule: <= /div>
<= /div>
Given a fraction      , then= 3;
<= /div>
that is, if the numerator and denominator are divided by the same quantity c, the result wil= l be an equivalent fraction.
In other words, a common factor of the numerator and the
<= /div>
denomiantor may be canceled as = 1, i.e.
a
b
a
b
=3D
a / c
a
b .
=3D
a*c
b*c  
=3D
a*c
b*c