MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C99D74.7C81FA70" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions

This presentation contains content that your browser may not be able to = show properly. This presentation was optimized for more recent versions of Micro= soft Internet Explorer.

If you would like to proceed anyway, click here.

 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/master10.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
Click to edit Master title style
Clic= k to edit Master text styles
Sec= ond level
Thi= rd level
Fou= rth level
Fif= th level
‹date/time›
‹footer›
&#= 8249;#›
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/master10.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAADygAAAAUAIQAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAEAAAALQEAAAQAAAAnAf//HAAAAPsC1P8A AAAAAACQAQAAAAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQA AAAuARgABAAAAAIBAQAFAAAACQIAAAACIQAAADIKNAA+AREAAABDb21wbGV4IEZyYWN0aW9ucwAg ABgAJgAZAAoAGAAWAAwAGwAPABgAFwAMAAoAGQAYABYABAAAAC4BAAAcAAAA+wIQAAcAAAAAALwC AAAAAAECAiJTeXN0ZW0AAAAAAAAYAAAALJ4TAAEAAADkBAAAAAAAAAQAAAAtAQQABAAAAPABAwAD AAAAAAA= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0004.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0062.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction. 
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0063.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0064.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0065.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction.
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0066.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication,
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0067.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication, i.e.
A
B
C
D
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0068.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication, i.e.
A
B
C
D
A
B
C
D
*
flip
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0069.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication, i.e.
A
B
C
D
A
B
C
D
*
flip
Example A. Simplify
4x2y
9z
xy2
6z2
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0070.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication, i.e.
A
B
C
D
A
B
C
D
*
flip
Example A. Simplify
4x2y
9z
xy2
6z2
=3D
flip
4x2y
9z
xy2
6z2
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0071.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication, i.e.
A
B
C
D
A
B
C
D
*
flip
Example A. Simplify
4x2y
9z
xy2
6z2
=3D
flip
4x2y
9z
xy2
6z2
=3D
3
2
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0046.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication, i.e.
A
B
C
D
A
B
C
D
*
flip
Example A. Simplify
4x2y
9z
xy2
6z2
=3D
flip
4x2y
9z
xy2
6z2
=3D
3
2
z
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication, i.e.
A
B
C
D
A
B
C
D
*
flip
Example A. Simplify
4x2y
9z
xy2
6z2
=3D
flip
4x2y
9z
xy2
6z2
=3D
= <= ![endif]>
3
2
z
x
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhhAAJAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACB AAYAgAAAAAAAAAIwhI+py+0Po5wn0Iuz3jf46oXiSJbmKUroyrbuCLzybEX0jZ/czvc++PkJh0RH 0FAAADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAfAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG ABoAgAAAAAAAAAIahGOHGa0OmpwQqhTXZTpj63FfB5bkOabiuhUAOx== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAC AA0AgAAAAAAAAAIEjI+pWQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhowADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACg AAIAgAAAAAAAAAIPjI+py+0Po5y02ouz3hwXADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhNAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAx AAIAgAAAAAAAAAIIjI+py+0P4yoAOy== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG AB4AgAAAAAAAAAIdBBJmqMjnoEtQ1UZXvtq+jnnbx5XkOabiGrbgexUAOx== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgAC AA0AgAAAAAAAAAIEjI+pWQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhcgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABv AAIAgAAAAAAAAAINjI+py+0Po5y02othAQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAIAgAAAAAAAAAIIjI+py+0PTQEAOw== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAO ABIAgAAAAAAAAAIbhI8XybCdHjRyVnjxVJt294FdxpBRaCIpN4YFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAW ABIAgAAAAAAAAAInhI8Wecvp4JMvTosw02rm6jVXCHAlaZrfRp5gmKKjzNK1F8OzfocFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAt ABIAgAAAAAAAAAI4hI8Xye24nomyNvqw3dNqXn2MCDokVHKnkqpe+4awTM9mbN91nqwdP8IBWbvh T+KDJZOtpRFlKQAAOw== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0047_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAO ABIAgAAAAAAAAAIbhI8XybaNHnRTVXqBnBv29oFZmJBRpo3qZSIFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication, i.e.
A
B
C
D
A
B
C
D
*
flip
Example A. Simplify
4x2y
9z
xy2
6z2
=3D
flip
4x2y
9z
xy2
6z2
=3D
=
3
2
z
x
y
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhhAAJAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACB AAYAgAAAAAAAAAIwhI+py+0Po5wn0Iuz3jf46oXiSJbmKUroyrbuCLzybEX0jZ/czvc++PkJh0RH 0FAAADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAfAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG ABoAgAAAAAAAAAIahGOHGa0OmpwQqhTXZTpj63FfB5bkOabiuhUAOx== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAC AA0AgAAAAAAAAAIEjI+pWQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhowADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACg AAIAgAAAAAAAAAIPjI+py+0Po5y02ouz3hwXADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhNAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAx AAIAgAAAAAAAAAIIjI+py+0P4yoAOy== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG AB4AgAAAAAAAAAIdBBJmqMjnoEtQ1UZXvtq+jnnbx5XkOabiGrbgexUAOx== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image033.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgAC AA0AgAAAAAAAAAIEjI+pWQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image034.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhcgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABv AAIAgAAAAAAAAAINjI+py+0Po5y02othAQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image035.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAIAgAAAAAAAAAIIjI+py+0PTQEAOw== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image036.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image037.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAO ABIAgAAAAAAAAAIbhI8XybCdHjRyVnjxVJt294FdxpBRaCIpN4YFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAW ABIAgAAAAAAAAAInhI8Wecvp4JMvTosw02rm6jVXCHAlaZrfRp5gmKKjzNK1F8OzfocFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image039.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOAAmAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA2 ACQAgAAAAAAAAAJihI+pEOsP42qy2kqv3ibzL3ngOJGmI55mqo5s+70wJ89XbWM5ie9R70MFY0Na kZd79YAbpc7m/CWFUigVwtREq7PtI3u7fqclLsw7tpaxZMWynXir3c+u+K5Cr894+jxeUQAAOw== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0073_image040.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAO ABIAgAAAAAAAAAIbhI8XybaNHnRTVXqBnBv29oFZmJBRpo3qZSIFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication, i.e.
A
B
C
D
A
B
C
D
*
flip
Example A. Simplify
4x2y
9z
xy2
6z2
=3D
flip
4x2y
9z
xy2
6z2
=3D
=
3
2
z
x
y
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image041.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image042.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image043.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhhAAJAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACB AAYAgAAAAAAAAAIwhI+py+0Po5wn0Iuz3jf46oXiSJbmKUroyrbuCLzybEX0jZ/czvc++PkJh0RH 0FAAADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image044.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image045.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image046.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAfAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG ABoAgAAAAAAAAAIahGOHGa0OmpwQqhTXZTpj63FfB5bkOabiuhUAOx== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image047.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAC AA0AgAAAAAAAAAIEjI+pWQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image048.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhowADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACg AAIAgAAAAAAAAAIPjI+py+0Po5y02ouz3hwXADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image049.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image050.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image051.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhNAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAx AAIAgAAAAAAAAAIIjI+py+0P4yoAOy== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image052.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG AB4AgAAAAAAAAAIdBBJmqMjnoEtQ1UZXvtq+jnnbx5XkOabiGrbgexUAOx== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image053.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgAC AA0AgAAAAAAAAAIEjI+pWQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image054.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhcgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABv AAIAgAAAAAAAAAINjI+py+0Po5y02othAQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image055.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAIAgAAAAAAAAAIIjI+py+0PTQEAOw== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image056.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image057.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAO ABIAgAAAAAAAAAIbhI8XybCdHjRyVnjxVJt294FdxpBRaCIpN4YFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image058.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAW ABIAgAAAAAAAAAInhI8Wecvp4JMvTosw02rm6jVXCHAlaZrfRp5gmKKjzNK1F8OzfocFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image059.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOAAmAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA2 ACQAgAAAAAAAAAJihI+pEOsP42qy2kqv3ibzL3ngOJGmI55mqo5s+70wJ89XbWM5ie9R70MFY0Na kZd79YAbpc7m/CWFUigVwtREq7PtI3u7fqclLsw7tpaxZMWynXir3c+u+K5Cr894+jxeUQAAOw== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0072_image060.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAO ABIAgAAAAAAAAAIbhI8XybaNHnRTVXqBnBv29oFZmJBRpo3qZSIFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
A fraction with its numerator or the denominator containing fraction(s) is called = a complex fraction.  = In other = words, a complex fraction is a fractional expression = divided by another fractional expression.
We want to simplify complex fractions to regular fractions.
The “easy” complex fractions are just regular divisions of of a frac= tion by another fraction. In this case just flip the denominat= or then simplify the multiplication, i.e.
A
B
C
D
A
B
C
D
*
flip
Example A. Simplify
4x2y
9z
xy2
6z2
=3D
flip
4x2y
9z
xy2
6z2
=3D
=
3
2
z
x
y
8xz
3y
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image061.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image062.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image063.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhhAAJAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACB AAYAgAAAAAAAAAIwhI+py+0Po5wn0Iuz3jf46oXiSJbmKUroyrbuCLzybEX0jZ/czvc++PkJh0RH 0FAAADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image064.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image065.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image066.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAfAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG ABoAgAAAAAAAAAIahGOHGa0OmpwQqhTXZTpj63FfB5bkOabiuhUAOx== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image067.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAC AA0AgAAAAAAAAAIEjI+pWQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image068.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhowADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACg AAIAgAAAAAAAAAIPjI+py+0Po5y02ouz3hwXADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image069.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image070.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image071.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhNAADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAx AAIAgAAAAAAAAAIIjI+py+0P4yoAOy== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image072.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG AB4AgAAAAAAAAAIdBBJmqMjnoEtQ1UZXvtq+jnnbx5XkOabiGrbgexUAOx== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image073.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgAC AA0AgAAAAAAAAAIEjI+pWQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image074.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhcgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABv AAIAgAAAAAAAAAINjI+py+0Po5y02othAQA7 ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image075.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAIAgAAAAAAAAAIIjI+py+0PTQEAOw== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image076.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image077.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAO ABIAgAAAAAAAAAIbhI8XybCdHjRyVnjxVJt294FdxpBRaCIpN4YFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image078.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAW ABIAgAAAAAAAAAInhI8Wecvp4JMvTosw02rm6jVXCHAlaZrfRp5gmKKjzNK1F8OzfocFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image079.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOAAmAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA2 ACQAgAAAAAAAAAJihI+pEOsP42qy2kqv3ibzL3ngOJGmI55mqo5s+70wJ89XbWM5ie9R70MFY0Na kZd79YAbpc7m/CWFUigVwtREq7PtI3u7fqclLsw7tpaxZMWynXir3c+u+K5Cr894+jxeUQAAOw== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image080.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAO ABIAgAAAAAAAAAIbhI8XybaNHnRTVXqBnBv29oFZmJBRpo3qZSIFADs= ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0048_image081.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAo AAIAgAAAAAAAAAIIjI+py+0PTQEAOw== ------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0050.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
We give two methods for simplifying general complex fractions.
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
We give two methods for simplifying general complex fractions. The first m= ethod is to reduce the problem to an “easy” problem. 
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0075.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Complex Fraction= s
We give two methods for simplifying general complex fractions. The first m= ethod is to reduce the problem to an “easy” problem.  We do this by combi= ning the numerator into one fraction and the denominator into one fraction. 
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0076.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Example B.  Simplify
Complex Fraction= s
We give two methods for simplifying general complex fractions. The first m= ethod is to reduce the problem to an “easy” problem.  We do this by combi= ning the numerator into one fraction and the denominator into one fraction. 
x
x + 1
+ 1
1 –
x
x – 1
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0077.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Example B.  Simplify
Put the numerator and the denominator into one fraction.
Complex Fraction= s
We give two methods for simplifying general complex fractions. The first m= ethod is to reduce the problem to an “easy” problem.  We do this by combi= ning the numerator into one fraction and the denominator into one fraction. 
x
x + 1
+ 1
1 –
x
x – 1
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0088.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Example B.  Simplify
Put the numerator and the denominator into one fraction.
Complex Fraction= s
We give two methods for simplifying general complex fractions. The first m= ethod is to reduce the problem to an “easy” problem.  We do this by combi= ning the numerator into one fraction and the denominator into one fraction. 
x
x + 1
+ 1
1 –
x
x – 1
The LCD of the numerator is (x + 1),
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0090.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Example B.  Simplify
Put the numerator and the denominator into one fraction.
Complex Fraction= s
We give two methods for simplifying general complex fractions. The first m= ethod is to reduce the problem to an “easy” problem.  We do this by combi= ning the numerator into one fraction and the denominator into one fraction. 
x
x + 1
+ 1
1 –
x
x – 1
x
x + 1
+ 1
=3D
x
x + 1
+ 1
 (
 )
(x + 1)
The LCD of the numerator is (x + 1), hence
LCD
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0091.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Example B.  Simplify
Put the numerator and the denominator into one fraction.
Complex Fraction= s
We give two methods for simplifying general complex fractions. The first m= ethod is to reduce the problem to an “easy” problem.  We do this by combi= ning the numerator into one fraction and the denominator into one fraction. 
x
x + 1
+ 1
1 –
x
x – 1
x
x + 1
+ 1
=3D
x
x + 1
+ 1
 (
 )
(x + 1)
The LCD of the numerator is (x + 1), hence
LCD
 1
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0092.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions
Example B.  Simplify
Put the numerator and the denominator into one fraction.
Complex Fraction= s
We give two methods for simplifying general complex fractions. The first m= ethod is to reduce the problem to an “easy” problem.  We do this by combi= ning the numerator into one fraction and the denominator into one fraction. 
x
x + 1
+ 1
1 –
x
x – 1
x
x + 1
+ 1
=3D
x
x + 1
+ 1
 (
 )
(x + 1)
The LCD of the numerator is (x + 1), hence
LCD
(x + 1)
 1
------=_NextPart_01C99D74.7C81FA70 Content-Location: file:///C:/0D764A33/4ComplexFractions_files/slide0093.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Complex Fractions