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------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/master29.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAADwQAAAAUAHAAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAEAAAALQEAAAQAAAAnAf//HAAAAPsC1P8A AAAAAACQAQAAAAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQA AAAuARgABAAAAAIBAQAFAAAACQIAAAACGAAAADIKNAB5AQsAAABQcm9wb3J0aW9ucwAdAA8AGAAZ ABgADwAMAAsAGQAYABYABAAAAC4BAAAcAAAA+wIQAAcAAAAAALwCAAAAAAECAiJTeXN0ZW0AAAAA AAAYAAAAHLETAAEAAADkBAAAAAAAAAQAAAAtAQQABAAAAPABAwADAAAAAAA= ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0121.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
Two related quantities stated side by side is called a ratio.
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0122.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
Two relat= ed quantities stated side by side is called a ratio= .
For example, if a recipe calls for 3 eggs for 4 cups of flour, <= span style=3D'position:absolute;top:20.0%;left:4.49%;width:91.38%;height:5.25%'= >then the = ratio of eggs to flour is 3 to 4.
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0123.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
3
4
Proportions
Two relat= ed quantities stated side by side is called a ratio= .
For example, if a recipe calls for 3 eggs for 4 cups of flour, <= span style=3D'position:absolute;top:20.0%;left:4.49%;width:107.49%;height:5.25%= '>then the = ratio of eggs to flour is 3 to 4.  We = may write it using fractional notation as:
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0123_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAT AAIAgAAAAAAAAAIFjI+py1YAO1== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0124.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
3
4
eggs
cups of flour
Proportions
Two relat= ed quantities stated side by side is called a ratio= .
For example, if a recipe calls for 3 eggs for 4 cups of flour, <= span style=3D'position:absolute;top:20.0%;left:4.49%;width:107.49%;height:5.25%= '>then the = ratio of eggs to flour is 3 to 4.  We = may write it using fractional notation as:
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0124_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAT AAIAgAAAAAAAAAIFjI+py1YAO1== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0124_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAs AAYAgAAAAAAAAAIahI+pyxcNowShmoqz3rz7D4bgREpYiULPUQAAOw== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0124_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAn AAUAgAAAAAAAAAIWhI+pqxHnopy02giu3pf5v2DgOD5HAQA7 ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0125.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
3
4
eggs
cups of flour
Proportions
This fraction is also the amount of per unit of the given ratio, in this case, &= frac34; egg / per cup of flour.
Two relat= ed quantities stated side by side is called a ratio= .
For example, if a recipe calls for 3 eggs for 4 cups of flour, <= span style=3D'position:absolute;top:20.0%;left:4.49%;width:107.49%;height:5.25%= '>then the = ratio of eggs to flour is 3 to 4.  We = may write it using fractional notation as:
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0125_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAT AAIAgAAAAAAAAAIFjI+py1YAO1== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0125_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAs AAYAgAAAAAAAAAIahI+pyxcNowShmoqz3rz7D4bgREpYiULPUQAAOw== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0125_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAn AAUAgAAAAAAAAAIWhI+pqxHnopy02giu3pf5v2DgOD5HAQA7 ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0126.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
3
4
eggs
cups of flour
Proportions
This fraction is also the amount of per unit of the given ratio, in this case, &= frac34; egg / per cup of flour.
Two ratios that are equal are said to be in proportion. =
Two relat= ed quantities stated side by side is called a ratio= .
For example, if a recipe calls for 3 eggs for 4 cups of flour, <= span style=3D'position:absolute;top:20.0%;left:4.49%;width:107.49%;height:5.25%= '>then the = ratio of eggs to flour is 3 to 4.  We = may write it using fractional notation as:
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0126_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAT AAIAgAAAAAAAAAIFjI+py1YAO1== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0126_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAs AAYAgAAAAAAAAAIahI+pyxcNowShmoqz3rz7D4bgREpYiULPUQAAOw== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0126_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAn AAUAgAAAAAAAAAIWhI+pqxHnopy02giu3pf5v2DgOD5HAQA7 ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0127.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
3
4
eggs
cups of flour
Proportions
This fraction is also the amount of per unit of the given ratio, in this case, &= frac34; egg / per cup of flour.
Two ratio= s that are equal are said to be in proportion.
Thus &quo= t;3 to 4" is proportion to "6 to 8" since
3
4
=3D
6
8
Two relat= ed quantities stated side by side is called a ratio= .
For example, if a recipe calls for 3 eggs for 4 cups of flour, <= span style=3D'position:absolute;top:20.0%;left:4.49%;width:107.49%;height:5.25%= '>then the = ratio of eggs to flour is 3 to 4.  We = may write it using fractional notation as:
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0127_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAT AAIAgAAAAAAAAAIFjI+py1YAO1== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0127_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAs AAYAgAAAAAAAAAIahI+pyxcNowShmoqz3rz7D4bgREpYiULPUQAAOw== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0127_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAn AAUAgAAAAAAAAAIWhI+pqxHnopy02giu3pf5v2DgOD5HAQA7 ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0127_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAT AAIAgAAAAAAAAAIFjI+py1YAO1== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0127_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAT AAIAgAAAAAAAAAIFjI+py1YAO1== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0128.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
3
4
eggs
cups of flour
Proportions
This fraction is also the amount of per unit of the given ratio, in this case, &= frac34; egg / per cup of flour.
Two ratio= s that are equal are said to be in proportion.
Thus &quo= t;3 to 4" is proportion to "6 to 8" since
3
4
=3D
6
8
To solve proportional equations, we cross-multiplied and change the proportions= into regular equations.  
Two relat= ed quantities stated side by side is called a ratio= .
For example, if a recipe calls for 3 eggs for 4 cups of flour, <= span style=3D'position:absolute;top:20.0%;left:4.49%;width:107.49%;height:5.25%= '>then the = ratio of eggs to flour is 3 to 4.  We = may write it using fractional notation as:
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A
B
C
D ,
=3D
If
Cross-Multiplication-Rule
Proportions
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0119_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAh AAEAgAAAAAAAAAIFjI+pmwUAOw== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0119_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAg AAEAgAAAAAAAAAIFjI+piwUAOw== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0129.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0129_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAh AAEAgAAAAAAAAAIFjI+pmwUAOw== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0129_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhPwAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwA6 ABYAgAAAAAAAAAJbjA2pyw3nomQHTVft3atyDH3iE46kZl5BgnJIm7qrHNfsPOG2rVP9XoO1MsSi kbhBwYDA14/JXEKbq+c0iJNeRUPrNmnVfjEq71gh7pwlad/abWpTeeZdnTYtAAA7 ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0130.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
Example A. Solve for x.
3
x
5
2
=3D
a.
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0130_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAh AAEAgAAAAAAAAAIFjI+pmwUAOw== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0130_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhPwAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwA6 ABYAgAAAAAAAAAJbjA2pyw3nomQHTVft3atyDH3iE46kZl5BgnJIm7qrHNfsPOG2rVP9XoO1MsSi kbhBwYDA14/JXEKbq+c0iJNeRUPrNmnVfjEq71gh7pwlad/abWpTeeZdnTYtAAA7 ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0130_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAh AAIAgAAAAAAAAAIGjI+py+1fADt= ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0130_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAh AAIAgAAAAAAAAAIGjI+py+1fADt= ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0131.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
Example A. Solve for x.
3
x
5
2
=3D
a.
 cross multiply
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0131_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAh AAEAgAAAAAAAAAIFjI+pmwUAOw== ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0131_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhPwAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwA6 ABYAgAAAAAAAAAJbjA2pyw3nomQHTVft3atyDH3iE46kZl5BgnJIm7qrHNfsPOG2rVP9XoO1MsSi kbhBwYDA14/JXEKbq+c0iJNeRUPrNmnVfjEq71gh7pwlad/abWpTeeZdnTYtAAA7 ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0131_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAh AAIAgAAAAAAAAAIGjI+py+1fADt= ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0131_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAh AAIAgAAAAAAAAAIGjI+py+1fADt= ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0117.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
Example A. Solve for x.
3
x
5
2
=3D
a.
 cross multiply
6 =3D 5x
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A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
Example A. Solve for x.
3
x
5
2
=3D
a.
 cross multiply
6 =3D 5x
=3D x
6
5
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A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
Example A. Solve for x.
3
x
5
2
=3D
a.
 cross multiply
6 =3D 5x
=3D x
6
5
2
3
(x + 2)
(x – 5)=  
=3D
b.
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A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
Example A. Solve for x.
3
x
5
2
=3D
a.
 cross multiply
6 =3D 5x
=3D x
6
5
2
3
(x + 2)
(x – 5)=  
=3D
b.
 cross multiply
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A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
Example A. Solve for x.
3
x
5
2
=3D
a.
 cross multiply
6 =3D 5x
=3D x
6
5
2
3
(x + 2)
(x – 5)=  
=3D
b.
 cross multiply
2(x – 5) =3D 3(x + 2)
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A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
Example A. Solve for x.
3
x
5
2
=3D
a.
 cross multiply
6 =3D 5x
=3D x
6
5
2
3
(x + 2)
(x – 5)=  
=3D
b.
 cross multiply
2(x – 5) =3D 3(x + 2)
2x – 10 =3D 3x + 6
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A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
Example A. Solve for x.
3
x
5
2
=3D
a.
 cross multiply
6 =3D 5x
=3D x
6
5
2
3
(x + 2)
(x – 5)=  
=3D
b.
 cross multiply
2(x – 5) =3D 3(x + 2)
2x – 10 =3D 3x + 6
–10 – 6 =3D 3x – 2x
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A
B
C
D ,
=3D
If
then AD = =3D BC.
Cross-Multiplication-Rule
Proportions
Example A. Solve for x.
3
x
5
2
=3D
a.
 cross multiply
6 =3D 5x
=3D x
6
5
2
3
(x + 2)
(x – 5)=  
=3D
b.
 cross multiply
2(x – 5) =3D 3(x + 2)
2x – 10 =3D 3x + 6
–10 – 6 =3D 3x – 2x
–16 =3D x
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Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0138.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions i.e. both must be in numerator, or both must be in the numerator.
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0139.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions i.e. both must be in numerator, or both must be in the numerator.
Example = B. A recipe for a cake calls for 3 eggs for 4 cups of flour. How many eggs are need if we have 10 cups of flour?
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0140.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions i.e. both must be in numerator, or both must be in the numerator.
Let x be the number of eggs need= ed.
Example = B. A recipe for a cake calls for 3 eggs for 4 cups of flour. How many eggs are need if we have 10 cups of flour?
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0141.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions i.e. both must be in numerator, or both must be in the numerator.
Let x be= the number of eggs needed. Write the two types of measurements, the number of eggs and the number of cups of flour, in a column as shown.
Example = B. A recipe for a cake calls for 3 eggs for 4 cups of flour. How many eggs are need if we have 10 cups of flour?
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0150.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions i.e. both must be in numerator, or both must be in the numerator.
Let x be= the number of eggs needed. Write the two types of measurements, the number of eggs and the number of cups of flour, in a column as shown.
number of eggs
cups of flour
Example = B. A recipe for a cake calls for 3 eggs for 4 cups of flour. How many eggs are need if we have 10 cups of flour?
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0142.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions i.e. both must be in numerator, or both must be in the numerator.
Let x be= the number of eggs needed. Write the two types of measurements, the number of eggs and the number of cups of flour, in a column as shown. Then write down the ratios.
number of eggs
cups of flour
Example = B. A recipe for a cake calls for 3 eggs for 4 cups of flour. How many eggs are need if we have 10 cups of flour?
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0143.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions i.e. both must be in numerator, or both must be in the numerator.
Let x be= the number of eggs needed. Write the two types of measurements, the number of eggs and the number of cups of flour, in a column as shown. Then write down the ratios.
number of eggs
cups of flour
x
10
Example = B. A recipe for a cake calls for 3 eggs for 4 cups of flour. How many eggs are need if we have 10 cups of flour?
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0143_image089.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhPAAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA6 ABcAgQAAAAAAAPMXNgECAwJDhI+py73hopwx2GOz3rz7D2bUSDJbiaJiyo5QC8fyTNf2jef6zvf+ DwwKh8QiSSAwSpBIA/MJjUqn1GpUuXhiGc1DAQA7 ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0143_image090.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0144.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions i.e. both must be in numerator, or both must be in the numerator.
Let x be= the number of eggs needed. Write the two types of measurements, the number of eggs and the number of cups of flour, in a column as shown. Then write down the ratios.
number of eggs
cups of flour
3
4
x
10
Example = B. A recipe for a cake calls for 3 eggs for 4 cups of flour. How many eggs are need if we have 10 cups of flour?
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0144_image091.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhPAAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA6 ABcAgQAAAAAAAPMXNgECAwJDhI+py73hopwx2GOz3rz7D2bUSDJbiaJiyo5QC8fyTNf2jef6zvf+ DwwKh8QiSSAwSpBIA/MJjUqn1GpUuXhiGc1DAQA7 ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0144_image092.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA3 AAEAgAAAAAAAAAIJjI8Iy+3/kjwFADs= ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0145.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions i.e. both must be in numerator, or both must be in the numerator.
Let x be= the number of eggs needed. Write the two types of measurements, the number of eggs and the number of cups of flour, in a column as shown. Then write down the ratios.
number of eggs
cups of flour
3
4
x
10
=3D
Set them equal, we get
x
10
3
4
Example = B. A recipe for a cake calls for 3 eggs for 4 cups of flour. How many eggs are need if we have 10 cups of flour?
------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0145_image093.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhPAAZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA6 ABcAgQAAAAAAAPMXNgECAwJDhI+py73hopwx2GOz3rz7D2bUSDJbiaJiyo5QC8fyTNf2jef6zvf+ DwwKh8QiSSAwSpBIA/MJjUqn1GpUuXhiGc1DAQA7 ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0145_image094.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA3 AAEAgAAAAAAAAAIJjI8Iy+3/kjwFADs= ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0145_image095.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhNwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAA1 AAEAgAAAAAAAAAIJjI8Iy+3vkjQFADs= ------=_NextPart_01C9A1B9.86114430 Content-Location: file:///C:/AB764A33/8Proportions_files/slide0146.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rational Expressions
Proportions
When setting up a proportional equation for a word problem, = the two quantities for the same type of measurement must occupy the same position in the fractions i.e. both must be in numerator, or both must be in the numerator.
Let x be= the number of eggs needed. Write the two types of measurements, the number of eggs and the number of cups of