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endif]><![endif]><p:shaperange
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.99%;
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te;
 top:0%;left:4.24%;width:95.75%;height:100.0%'><span style=3D'font-family:"=
Times New Roman"'><span
 class=3DBB style=3D'position:absolute;left:-4.43%;top:.3em'>p</span></span=
><span
 style=3D'font-family:"Times New Roman"'><b>Whole Numbers:</b></span><span
 style=3D'font-family:"Times New Roman"'><span style=3D'mso-spacerun:yes'>&=
nbsp;
 </span>{0,1,2,3&#8230;}&#13;</span></span></div>
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:5.99%;
 width:104.49%;height:12.25%;white-space:nowrap'><span style=3D'position:ab=
solute;
 top:0%;left:3.58%;width:96.41%;height:48.97%'><span style=3D'font-family:"=
Times New Roman"'><span
 class=3DBB style=3D'position:absolute;left:-3.71%;top:.3em'>p</span></span=
><span
 style=3D'font-family:"Times New Roman"'>When we encounter a number, how do=
 we
 know what </span></span><span style=3D'position:absolute;top:48.97%;left:3=
.58%;
 width:80.82%;height:48.97%'><span style=3D'font-family:"Times New Roman"'>=
it
 means?<span style=3D'mso-spacerun:yes'>&nbsp; </span>How do we know its va=
lue?</span><span
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span></div>
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solute;
 top:0%;left:3.62%;width:96.37%;height:48.97%'><span style=3D'font-family:"=
Times New Roman"'><span
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><span
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 style=3D'font-family:"Times New Roman"'><span style=3D'mso-spacerun:yes'>&=
nbsp;
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nbsp;
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5.99%;
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unique
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7%;
 left:3.59%;width:80.96%;height:48.97%'><span style=3D'font-family:"Times N=
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><span
 style=3D'font-family:"Times New Roman"'>Any subtraction problem can be
 re-written as an </span></span><span style=3D'position:absolute;top:51.02%;
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span
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:absolute;
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 each of the following as a &#8220;related sentence&#8221; </span></span><s=
pan
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%'><span
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pan></span></div>
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8.0%;
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tion:
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pan
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pan
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n:absolute;
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 style=3D'font-family:"Times New Roman"'><span class=3DB1B style=3D'positio=
n:absolute;
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4;
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ace:
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75%;
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Times New Roman";
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624;
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t:
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 <div id=3D"_x0000_s102403_0_11" class=3DB style=3D'mso-line-spacing:"90 20=
 0";
 position:absolute;top:24.0%;left:5.99%;width:88.2%;height:6.0%;white-space:
 nowrap'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio=
n:
 absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>p</span=
></span><span
 style=3D'font-family:"Times New Roman"'>5 x 9 =3D 45&#13;</span></span></d=
iv>
 <div id=3D"_x0000_s102403_11_36" class=3DB1 style=3D'mso-line-spacing:"90 =
20 0";
 position:absolute;top:30.25%;left:11.04%;width:83.14%;height:5.75%;white-s=
pace:
 nowrap'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.17%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-3.74%;top:.3em;font-family:Wingdings;font-size:75%'>n</span=
></span><span
 style=3D'font-family:"Times New Roman"'>45 </span><span style=3D'font-fami=
ly:Symbol;
 mso-ascii-font-family:"Times New Roman";mso-char-type:symbol'>&cedil;</spa=
n><span
 style=3D'font-family:"Times New Roman"'> 5 =3D 9<span style=3D'mso-tab-cou=
nt:1;
 width:10.22%'> </span>or<span style=3D'mso-tab-count:1;width:9.03%'> </spa=
n>45 </span><span
 style=3D'font-family:Symbol;mso-ascii-font-family:"Times New Roman";mso-ch=
ar-type:
 symbol'>&cedil;</span><span style=3D'font-family:"Times New Roman"'> 9 =3D=
 5&#13;</span></span></div>
 <div id=3D"_x0000_s102403_36_48" class=3DB style=3D'mso-line-spacing:"90 2=
0 0";
 position:absolute;top:36.0%;left:5.99%;width:88.2%;height:6.5%;white-space:
 nowrap'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio=
n:
 absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>p</span=
></span><span
 style=3D'font-family:"Times New Roman"'>72 </span><span style=3D'font-fami=
ly:Symbol;
 mso-ascii-font-family:"Times New Roman";mso-char-type:symbol'>&cedil;</spa=
n><span
 style=3D'font-family:"Times New Roman"'> 6 =3D 12&#13;</span></span></div>
 <div id=3D"_x0000_s102403_48_75" class=3DB1 style=3D'mso-line-spacing:"90 =
20 0";
 position:absolute;top:43.25%;left:11.04%;width:83.14%;height:5.25%;white-s=
pace:
 nowrap'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.17%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-3.74%;top:.3em;font-family:Wingdings;font-size:75%'>n</span=
></span><span
 style=3D'font-family:"Times New Roman"'>6 x 12 =3D 72<span style=3D'mso-ta=
b-count:
 1;width:8.33%'> </span>or<span style=3D'mso-tab-count:1;width:9.03%'> </sp=
an>12
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 <div id=3D"_x0000_s102403_75_86" class=3DB style=3D'mso-line-spacing:"90 2=
0 0";
 position:absolute;top:49.25%;left:5.99%;width:88.2%;height:6.0%;white-spac=
e:
 nowrap'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio=
n:
 absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>p</span=
></span><span
 style=3D'font-family:"Times New Roman"'>7 x 9 =3D 63&#13;</span></span></d=
iv>
 <div id=3D"_x0000_s102403_86_111" class=3DB1 style=3D'mso-line-spacing:"90=
 20 0";
 position:absolute;top:55.5%;left:11.04%;width:83.14%;height:5.75%;white-sp=
ace:
 nowrap'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.17%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-3.74%;top:.3em;font-family:Wingdings;font-size:75%'>n</span=
></span><span
 style=3D'font-family:"Times New Roman"'>63 </span><span style=3D'font-fami=
ly:Symbol;
 mso-ascii-font-family:"Times New Roman";mso-char-type:symbol'>&cedil;</spa=
n><span
 style=3D'font-family:"Times New Roman"'> 7 =3D 9<span style=3D'mso-tab-cou=
nt:1;
 width:10.22%'> </span>or<span style=3D'mso-tab-count:1;width:9.03%'> </spa=
n>63 </span><span
 style=3D'font-family:Symbol;mso-ascii-font-family:"Times New Roman";mso-ch=
ar-type:
 symbol'>&cedil;</span><span style=3D'font-family:"Times New Roman"'> 9 =3D=
 7&#13;</span></span></div>
 <div id=3D"_x0000_s102403_111_122" class=3DB style=3D'mso-line-spacing:"90=
 20 0";
 position:absolute;top:62.0%;left:5.99%;width:88.2%;height:6.0%;white-space:
 nowrap'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio=
n:
 absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>p</span=
></span><span
 style=3D'font-family:"Times New Roman"'>4 x 8 =3D 32&#13;</span></span></d=
iv>
 <div id=3D"_x0000_s102403_122_147" class=3DB1 style=3D'mso-line-spacing:"9=
0 20 0";
 position:absolute;top:68.25%;left:11.04%;width:83.14%;height:5.75%;white-s=
pace:
 nowrap'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.17%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-3.74%;top:.3em;font-family:Wingdings;font-size:75%'>n</span=
></span><span
 style=3D'font-family:"Times New Roman"'>32 </span><span style=3D'font-fami=
ly:Symbol;
 mso-ascii-font-family:"Times New Roman";mso-char-type:symbol'>&cedil;</spa=
n><span
 style=3D'font-family:"Times New Roman"'> 4 =3D 8<span style=3D'mso-tab-cou=
nt:1;
 width:10.22%'> </span>or<span style=3D'mso-tab-count:1;width:9.03%'> </spa=
n>32 </span><span
 style=3D'font-family:Symbol;mso-ascii-font-family:"Times New Roman";mso-ch=
ar-type:
 symbol'>&cedil;</span><span style=3D'font-family:"Times New Roman"'> 8 =3D=
 4&#13;</span></span></div>
 <div id=3D"_x0000_s102403_147_158" class=3DB style=3D'mso-line-spacing:"90=
 20 0";
 position:absolute;top:74.75%;left:5.99%;width:88.2%;height:6.0%;white-spac=
e:
 nowrap'><span style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio=
n:
 absolute;left:-4.43%;top:.3em;font-family:Wingdings;font-size:75%'>p</span=
></span><span
 style=3D'font-family:"Times New Roman"'>? x 9 =3D 54&#13;</span></span></d=
iv>
 <div id=3D"_x0000_s102403_158_182" class=3DB1 style=3D'mso-line-spacing:"9=
0 20 0";
 position:absolute;top:81.0%;left:11.04%;width:83.14%;height:5.75%;white-sp=
ace:
 nowrap'><span style=3D'position:absolute;top:0%;left:3.6%;width:96.17%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-3.74%;top:.3em;font-family:Wingdings;font-size:75%'>n</span=
></span><span
 style=3D'font-family:"Times New Roman"'>54 </span><span style=3D'font-fami=
ly:Symbol;
 mso-ascii-font-family:"Times New Roman";mso-char-type:symbol'>&cedil;</spa=
n><span
 style=3D'font-family:"Times New Roman"'> 9 =3D ?<span style=3D'mso-tab-cou=
nt:1;
 width:10.46%'> </span>&#8594;<span style=3D'mso-tab-count:1;width:8.33%'> =
</span>54
 </span><span style=3D'font-family:Symbol;mso-ascii-font-family:"Times New =
Roman";
 mso-char-type:symbol'>&cedil;</span><span style=3D'font-family:"Times New =
Roman"'>
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New Roman"'>Locate
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"Times New Roman";
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<span
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n:absolute;
 top:24.0%;left:5.99%;width:88.2%;height:6.0%;white-space:nowrap'><span
 style=3D'position:absolute;top:0%;left:4.24%;width:95.75%;height:100.0%'><=
span
 style=3D'font-family:"Times New Roman"'><span style=3D'mso-special-format:=
bullet;
 color:#666600;mso-color-index:2;position:absolute;left:-4.43%;top:.3em;
 font-family:Wingdings;font-size:75%'>p</span></span><span style=3D'font-fa=
mily:
 "Times New Roman"'>275<span style=3D'mso-tab-count:3;width:24.17%'> </span=
>Round
 to the nearest ten&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:30.75%;
 left:5.99%;width:88.2%;height:6.0%'><span style=3D'position:absolute;top:0=
%;
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ew Roman";
 visibility:hidden'><span style=3D'mso-special-format:bullet;color:#666600;
 mso-color-index:2;position:absolute;left:-4.43%;font-family:Wingdings;
 font-size:75%'>p</span></span><span style=3D'font-family:"Times New Roman";
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 <div id=3D"_x0000_s40963_32_67" style=3D'mso-line-spacing:"90 20 0";positi=
on:absolute;
 top:37.5%;left:5.99%;width:90.26%;height:6.0%;white-space:nowrap'><span
 style=3D'position:absolute;top:0%;left:4.14%;width:95.85%;height:100.0%'><=
span
 style=3D'font-family:"Times New Roman"'><span style=3D'mso-special-format:=
bullet;
 color:#666600;mso-color-index:2;position:absolute;left:-4.32%;top:.3em;
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mily:
 "Times New Roman"'>4350<span style=3D'mso-tab-count:2;width:21.35%'> </spa=
n>Round
 to the nearest hundred&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:44.5%;left:=
5.99%;
 width:88.2%;height:6.0%'><span style=3D'position:absolute;top:0%;left:4.24=
%;
 width:95.75%;height:100.0%'><span style=3D'font-family:"Times New Roman";
 visibility:hidden'><span style=3D'mso-special-format:bullet;color:#666600;
 mso-color-index:2;position:absolute;left:-4.43%;font-family:Wingdings;
 font-size:75%'>p</span></span><span style=3D'font-family:"Times New Roman";
 display:none'>&#13;</span></span></div>
 <div id=3D"_x0000_s40963_68_99" style=3D'mso-line-spacing:"90 20 0";positi=
on:absolute;
 top:51.24%;left:5.99%;width:88.2%;height:6.0%;white-space:nowrap'><span
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span
 style=3D'font-family:"Times New Roman"'><span style=3D'mso-special-format:=
bullet;
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mily:
 "Times New Roman"'>8786<span style=3D'mso-tab-count:2;width:21.87%'> </spa=
n>Round
 to the nearest ten&#13;</span></span></div>
 <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:58.25%;
 left:5.99%;width:88.2%;height:6.0%'><span style=3D'position:absolute;top:0=
%;
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ew Roman";
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endif]><![endif]><p:shaperange
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 Roman";
 color:black;mso-color-index:1'><b>Definitions</b></span></div>
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s105475"
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5.99%;
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olute;
 top:0%;left:3.84%;width:96.15%;height:48.97%'><span style=3D'font-family:"=
Times New Roman"'><span
 class=3DBB style=3D'position:absolute;left:-4.0%;top:.3em'>p</span></span>=
<span
 style=3D'font-family:"Times New Roman"'><b>Variable:</b></span><span
 style=3D'font-family:"Times New Roman"'><span style=3D'mso-spacerun:yes'>&=
nbsp;
 </span>Letter or symbol that represents one or </span></span><span
 style=3D'position:absolute;top:51.02%;left:3.84%;width:86.73%;height:48.97=
%'><span
 style=3D'font-family:"Times New Roman"'>more numbers&#13;</span></span></d=
iv>
 <div id=3D"_x0000_s105475_64_129" style=3D'position:absolute;top:38.0%;lef=
t:5.99%;
 width:88.2%;height:12.25%;white-space:nowrap'><span style=3D'position:abso=
lute;
 top:0%;left:4.24%;width:95.75%;height:48.97%'><span style=3D'font-family:"=
Times New Roman"'><span
 class=3DBB style=3D'position:absolute;left:-4.43%;top:.3em'>p</span></span=
><span
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 style=3D'font-family:"Times New Roman"'><span style=3D'mso-spacerun:yes'>&=
nbsp;
 </span>Mathematical statement that two </span></span><span style=3D'positi=
on:
 absolute;top:51.02%;left:4.24%;width:95.75%;height:48.97%'><span
 style=3D'font-family:"Times New Roman"'>expressions are equal&#13;</span><=
/span></div>
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 left:5.99%;width:93.82%;height:12.25%;white-space:nowrap'><span
 style=3D'position:absolute;top:0%;left:3.99%;width:96.0%;height:48.97%'><s=
pan
 style=3D'font-family:"Times New Roman"'><span class=3DBB style=3D'position=
:absolute;
 left:-4.15%;top:.3em'>p</span></span><span style=3D'font-family:"Times New=
 Roman"'><b>Solution:</b></span><span
 style=3D'font-family:"Times New Roman"'><span style=3D'mso-spacerun:yes'>&=
nbsp;
 </span>A number that when substituted for a </span></span><span
 style=3D'position:absolute;top:51.02%;left:3.99%;width:90.01%;height:48.97=
%'><span
 style=3D'font-family:"Times New Roman"'>variable makes the statement true<=
/span></span></div>
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 <div v:shape=3D"_x0000_s107523" class=3DB>
 <div id=3D"_x0000_s107523_0_73" style=3D'position:absolute;top:24.5%;left:=
5.99%;
 width:101.68%;height:12.25%;white-space:nowrap'><span style=3D'position:ab=
solute;
 top:0%;left:3.68%;width:96.31%;height:48.97%'><span style=3D'font-family:"=
Times New Roman"'><span
 class=3DBB style=3D'position:absolute;left:-3.82%;top:.3em'>p</span></span=
><span
 style=3D'font-family:"Times New Roman"'><b>Isolate the Variable:</b></span=
><span
 style=3D'font-family:"Times New Roman"'><span style=3D'mso-spacerun:yes'>&=
nbsp;
 </span>Get the variable alone on one </span></span><span style=3D'position=
:absolute;
 top:51.02%;left:3.68%;width:83.05%;height:48.97%'><span style=3D'font-fami=
ly:
 "Times New Roman"'>side of an equation&#13;</span></span></div>
 <div id=3D"_x0000_s107523_73_190" style=3D'position:absolute;top:38.0%;lef=
t:5.99%;
 width:100.74%;height:18.5%;white-space:nowrap'><span style=3D'position:abs=
olute;
 top:0%;left:3.71%;width:89.4%;height:32.43%'><span style=3D'font-family:"T=
imes New Roman"'><span
 class=3DBB style=3D'position:absolute;left:-4.15%;top:.3em'>p</span></span=
><span
 style=3D'font-family:"Times New Roman"'><b>Solve an Equation Using Inverse
 Operations:</b></span><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span></span></span><span style=3D'posi=
tion:
 absolute;top:33.78%;left:3.71%;width:96.28%;height:32.43%'><span
 style=3D'font-family:"Times New Roman"'>Rewrite the equation to isolate the
 variable using an </span></span><span style=3D'position:absolute;top:67.56=
%;
 left:3.71%;width:83.82%;height:32.43%'><span style=3D'font-family:"Times N=
ew Roman"'>inverse
 operation&#13;</span></span></div>
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span
 style=3D'font-family:"Times New Roman"'><span class=3DBB style=3D'position=
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 left:-4.35%;top:.3em'>p</span></span><span style=3D'font-family:"Times New=
 Roman"'><b>Check
 the Solution:</b></span><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-spacerun:yes'>&nbsp; </span>Substitute back into the </span><=
/span><span
 style=3D'position:absolute;top:51.02%;left:4.17%;width:94.15%;height:48.97=
%'><span
 style=3D'font-family:"Times New Roman"'>original equation</span></span></d=
iv>
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th:11.48%'>
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To
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div>
 <div id=3D"_x0000_s45059_52_105" style=3D'position:absolute;top:32.0%;left=
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mat:
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s;
 font-size:75%'>p</span><span style=3D'font-family:"Times New Roman"'><span
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 style=3D'mso-tab-count:2;width:11.85%'> </span></span><span style=3D'font-=
family:
 "Times New Roman";font-size:71%'>Use the inverse operation:<span
 style=3D'mso-spacerun:yes'>&nbsp; </span>subtraction</span><span
 style=3D'font-family:"Times New Roman";display:none'>&#13;</span></div>
 <div id=3D"_x0000_s45059_105_140" style=3D'position:absolute;top:39.25%;
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s;
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 style=3D'mso-tab-count:1;width:4.25%'> </span>n =3D 8<span style=3D'mso-ta=
b-count:
 2;width:20.66%'> </span></span><span style=3D'font-family:"Times New Roman=
";
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 display:none'><b>&#13;</b></span></div>
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span
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span
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span
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amily:
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1;
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none'>&#13;</span></span></div>
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mso-tab-count:
 1;width:9.37%'> </span></span><span style=3D'font-family:"Times New Roman";
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s;
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ab-count:
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To
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mat:
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s;
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mily:
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t-family:
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s;
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25%'><span
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span
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pan
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span
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New Roman";
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family:
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1;
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one'>&#13;</span></span></div>
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s;
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o-tab-count:
 2;width:14.05%'> </span></span><span style=3D'font-family:"Times New Roman=
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&nbsp;
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n"'><span
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%'><span
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the
 exponent </span></span><span style=3D'position:absolute;top:66.21%;left:3.=
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n:
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st use
 a set order</span><span style=3D'font-family:"Times New Roman";display:non=
e'><b>&#13;</b></span></span></div>
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pan
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span
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mat:
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s;
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unt:
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nbsp;
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family:
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lute;
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span
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 the
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   dimcolor=3D"schemeShadow"/></v:shape>
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 <div class=3DB4 style=3D'mso-margin-left-alt:1392'></div>
 <div id=3D"_x0000_s129027_0_23" class=3DB style=3D'mso-margin-left-alt:384;
 position:absolute;top:24.5%;left:5.99%;width:88.2%;height:6.0%;white-space:
 nowrap'><span style=3D'position:absolute;top:0%;left:7.64%;width:92.35%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#666600;mso-color-index:2;positio=
n:
 absolute;left:-8.27%;top:.3em;font-family:Wingdings;font-size:75%'>p</span=
></span><span
 style=3D'font-family:"Times New Roman"'>Find all factors of 45&#13;</span>=
</span></div>
 <div id=3D"_x0000_s129027_23_30" class=3DB1 style=3D'mso-margin-left-alt:6=
24;
 position:absolute;top:31.5%;left:11.04%;width:83.14%;height:5.25%;white-sp=
ace:
 nowrap'><span style=3D'position:absolute;top:0%;left:6.98%;width:93.01%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-7.5%;top:.3em;font-family:Wingdings;font-size:75%'>n</span>=
</span><span
 style=3D'font-family:"Times New Roman"'>1 x 45&#13;</span></span></div>
 <div id=3D"_x0000_s129027_30_45" class=3DB1 style=3D'mso-margin-left-alt:6=
24;
 position:absolute;top:38.0%;left:11.04%;width:83.14%;height:5.25%;white-sp=
ace:
 nowrap'><span style=3D'position:absolute;top:0%;left:6.98%;width:93.01%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-7.5%;top:.3em;font-family:Wingdings;font-size:75%'>n</span>=
</span><span
 style=3D'font-family:"Times New Roman"'>2 not a factor&#13;</span></span><=
/div>
 <div id=3D"_x0000_s129027_45_52" class=3DB1 style=3D'mso-margin-left-alt:6=
24;
 position:absolute;top:44.5%;left:11.04%;width:83.14%;height:5.25%;white-sp=
ace:
 nowrap'><span style=3D'position:absolute;top:0%;left:6.98%;width:93.01%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-7.5%;top:.3em;font-family:Wingdings;font-size:75%'>n</span>=
</span><span
 style=3D'font-family:"Times New Roman"'>3 x 15&#13;</span></span></div>
 <div id=3D"_x0000_s129027_52_67" class=3DB1 style=3D'mso-margin-left-alt:6=
24;
 position:absolute;top:50.74%;left:11.04%;width:83.14%;height:5.25%;white-s=
pace:
 nowrap'><span style=3D'position:absolute;top:0%;left:6.98%;width:93.01%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-7.5%;top:.3em;font-family:Wingdings;font-size:75%'>n</span>=
</span><span
 style=3D'font-family:"Times New Roman"'>4 not a factor&#13;</span></span><=
/div>
 <div id=3D"_x0000_s129027_67_73" class=3DB1 style=3D'mso-margin-left-alt:6=
24;
 position:absolute;top:57.25%;left:11.04%;width:83.14%;height:5.25%;white-s=
pace:
 nowrap'><span style=3D'position:absolute;top:0%;left:6.98%;width:93.01%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-7.5%;top:.3em;font-family:Wingdings;font-size:75%'>n</span>=
</span><span
 style=3D'font-family:"Times New Roman"'>5 x 9&#13;</span></span></div>
 <div id=3D"_x0000_s129027_73_91" class=3DB1 style=3D'mso-margin-left-alt:6=
24;
 position:absolute;top:63.5%;left:11.04%;width:83.14%;height:5.25%;white-sp=
ace:
 nowrap'><span style=3D'position:absolute;top:0%;left:6.98%;width:93.01%;
 height:100.0%'><span style=3D'font-family:"Times New Roman"'><span
 style=3D'mso-special-format:bullet;color:#999900;mso-color-index:3;positio=
n:
 absolute;left:-7.5%;top:.3em;font-family:Wingdings;font-size:75%'>n</span>=
</span><span
 style=3D'font-family:"Times New Roman"'>6,7,8 not factors</span><span
 style=3D'font-family:"Times New Roman";mso-special-format:lastCR;display:n=
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span
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Roman"'>A
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%'><span
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lute;
 top:0%;left:8.84%;width:91.15%;height:100.0%'><span style=3D'font-family:"=
Times New Roman"'><span
 class=3DHBB style=3D'position:absolute;left:-9.7%;top:.3em'>p</span></span=
><span
 style=3D'font-family:"Times New Roman"'>Is 60 a multiple of 12? &#13;</spa=
n></span></div>
 <div style=3D'position:absolute;top:30.75%;left:5.99%;width:42.32%;height:=
5.25%'><span
 style=3D'position:absolute;top:0%;left:8.84%;width:91.15%;height:100.0%'><=
span
 style=3D'font-family:"Times New Roman";visibility:hidden'><span class=3DHBB
 style=3D'position:absolute;left:-9.7%'>p</span></span><span style=3D'font-=
family:
 "Times New Roman";display:none'>&#13;</span></span></div>
 <div style=3D'position:absolute;top:37.0%;left:5.99%;width:42.32%;height:5=
.25%'><span
 style=3D'position:absolute;top:0%;left:8.84%;width:91.15%;height:100.0%'><=
span
 style=3D'font-family:"Times New Roman";visibility:hidden'><span class=3DHBB
 style=3D'position:absolute;left:-9.7%'>p</span></span><span style=3D'font-=
family:
 "Times New Roman";display:none'>&#13;</span></span></div>
 <div style=3D'position:absolute;top:43.5%;left:5.99%;width:42.32%;height:5=
.25%'><span
 style=3D'position:absolute;top:0%;left:8.84%;width:91.15%;height:100.0%'><=
span
 style=3D'font-family:"Times New Roman";visibility:hidden'><span class=3DHBB
 style=3D'position:absolute;left:-9.7%'>p</span></span><span style=3D'font-=
family:
 "Times New Roman";display:none'>&#13;</span></span></div>
 <div id=3D"_x0000_s131075_28_52" style=3D'position:absolute;top:50.0%;left=
:5.99%;
 width:42.32%;height:5.25%;white-space:nowrap'><span style=3D'position:abso=
lute;
 top:0%;left:8.84%;width:91.15%;height:100.0%'><span style=3D'font-family:"=
Times New Roman"'><span
 class=3DHBB style=3D'position:absolute;left:-9.7%;top:.3em'>p</span></span=
><span
 style=3D'font-family:"Times New Roman"'>Is 112 a multiple of 6?</span><span
 style=3D'font-family:"Times New Roman";mso-special-format:lastCR;display:n=
one'><b>&#13;</b></span></span></div>
 </div>
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s131076"
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umber=3D"3"
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 <div id=3D"_x0000_s131076_0_23" style=3D'position:absolute;top:24.25%;left=
:51.87%;
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lute;
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Times New Roman"'><span
 class=3DHBB style=3D'position:absolute;left:-9.7%;top:.3em'>p</span></span=
><span
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</span></div>
 <div style=3D'position:absolute;top:30.75%;left:51.87%;width:42.32%;height=
:5.25%'><span
 style=3D'position:absolute;top:0%;left:8.84%;width:91.15%;height:100.0%'><=
span
 style=3D'font-family:"Times New Roman";visibility:hidden'><span class=3DHBB
 style=3D'position:absolute;left:-9.7%'>p</span></span><span style=3D'font-=
family:
 "Times New Roman";display:none'>&#13;</span></span></div>
 <div style=3D'position:absolute;top:37.0%;left:51.87%;width:42.32%;height:=
5.25%'><span
 style=3D'position:absolute;top:0%;left:8.84%;width:91.15%;height:100.0%'><=
span
 style=3D'font-family:"Times New Roman";visibility:hidden'><span class=3DHBB
 style=3D'position:absolute;left:-9.7%'>p</span></span><span style=3D'font-=
family:
 "Times New Roman";display:none'>&#13;</span></span></div>
 <div style=3D'position:absolute;top:43.5%;left:51.87%;width:42.32%;height:=
5.25%'><span
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span
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family:
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family:
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.25%'><span
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span
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family:
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.25%'><span
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span
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family:
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lute;
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Times New Roman"'><span
 class=3DHBB style=3D'position:absolute;left:-9.7%;top:.3em'>p</span></span=
><span
 style=3D'font-family:"Times New Roman"'>Is 148 divisible by 8?</span></spa=
n></div>
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span
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family:
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span
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lute;
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Times New Roman"'><span
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nbsp;
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ly:
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tion:
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n:
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</span><span
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uct of
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%;
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%;
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ew Roman";
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n:
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></span><span
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4;
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New Roman"'>&#8220;Tree
 method&#8221;</span><span style=3D'font-family:"Times New Roman";display:n=
one'><b>&#13;</b></span></span></div>
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84;
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New Roman"'>Successive
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 top:0%;left:4.24%;width:95.75%;height:100.0%'><span style=3D'font-family:"=
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the
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span
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th:5.09%'>
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:"Times New Roman";
 font-size:91%;color:black;mso-color-index:1'><b>Examples:</b></span><span
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-index:
 1'><span style=3D'mso-spacerun:yes'>&nbsp; </span>Determine if the followi=
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span
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n:absolute;
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span
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on:absolute;
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 3&#13;</span></span></div>
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7.26%;
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95%;
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den'><span
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95%;
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den'><span
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46.75%;
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span
 style=3D'font-family:"Times New Roman"'><span class=3DHBB style=3D'positio=
n:absolute;
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Roman"'>215&#13;</span></span></div>
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span
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0.5%;
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span
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den'><span
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95%;
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den'><span
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6.75%;
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span
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span
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its
 last two digits are divisible by 4</span><span style=3D'font-family:"Times=
 New Roman";
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5.99%;
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 "Times New Roman"'><span style=3D'mso-tab-count:1;width:5.09%'> </span>If =
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es New Roman";
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9</b></span><span
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th:5.09%'>
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span></div>
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10</b></span><span
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th:2.79%'>
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span
 style=3D'font-family:"Times New Roman"'><span class=3DBB style=3D'position=
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 Roman"'><b>Note:</b></span><span
 style=3D'font-family:"Times New Roman"'><span style=3D'mso-spacerun:yes'>&=
nbsp;
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ace:
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n:
 absolute;left:-7.5%;top:.3em;font-family:Wingdings;font-size:75%'>p</span>=
</span><span
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iple
 of two or </span></span><span style=3D'position:absolute;top:51.02%;left:6=
.97%;
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ore
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b>&#13;</b></span></span></div>
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n:
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624;
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pace:
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New Roman"'>Find
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New Roman"'>Create
 a product of factors, using each factor the greatest </span></span><span
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%'><span
 style=3D'font-family:"Times New Roman"'>number of times it occurs in any o=
f the
 prime </span></span><span style=3D'position:absolute;top:66.66%;left:5.97%;
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------=_NextPart_01C97571.7B224ED0
Content-Location: file:///C:/6E4BB24E/WholeNumbersPresentation_files/script.js
Content-Transfer-Encoding: quoted-printable
Content-Type: application/javascript; charset="us-ascii"

function LoadSld()
{
	var sld=3DGetObj("SlideObj")
	if( !g_supportsPPTHTML ) {	=09
		sld.style.visibility=3D"visible"
		return
	}

	if( MakeNotesVis() ) return

	runAnimations =3D _InitAnimations();
=09
	if( IsWin("PPTSld") )
		parent.SldUpdated(GetSldId())
	g_origSz=3DparseInt(SlideObj.style.fontSize)
	g_origH=3Dsld.style.posHeight
	g_origW=3Dsld.style.posWidth
	g_scaleHyperlinks=3D(document.all.tags("AREA").length>0)
	if( g_scaleHyperlinks )
		InitHLinkArray()
	if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) )
		document.body.scroll=3D"no"
	_RSW()
	if( IsWin("PPTSld") && parent.IsFullScrMode() )
		FullScrInit();
=09
	MakeSldVis();
	ChkAutoAdv()

	if( runAnimations )
	{
		if( document.all("NSPlay") )
			document.all("NSPlay").autoStart =3D false;

		if( sld.filters && sld.filters.revealtrans )
			setTimeout( "document.body.start()", sld.filters.revealtrans.duration * =
1000 );
		else
			document.body.start();
	}
}

function MakeSldVis()=20
{
	var fTrans=3Dg_showAnimation && SldHasTrans()
	if( fTrans )=09
	{
		if( g_bgSound ) {
			idx=3Dg_bgSound.indexOf(",");
			pptSound.src=3Dg_bgSound.substr( 0, idx );
			pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1)));
		}
		SlideObj.filters.revealtrans.Apply()=09
    }
	SlideObj.style.visibility=3D"visible"
	if( fTrans )
		SlideObj.filters.revealtrans.Play()
}
function MakeNotesVis()=20
{
	if( !IsNts() ) return false=20
	SlideObj.style.display=3D"none"
	nObj =3D document.all.item("NotesObj")
	parent.SetHasNts(0)
	if( nObj ) {=20
		nObj.style.display=3D""
		parent.SetHasNts(1)
	}
	return 1
}
function ChkAutoAdv()
{
	if(SldHasTrans())
		SlideObj.onfilterchange=3DAutoAdv
	else
		AutoAdv()
}
function AutoAdv()
{
	if(!IsWin("PPTSld") || !gUseSldTimings )return
	var sld=3DGetCurSld()
	if( (sld.mAdvDelay>0) && !parent.IsFramesMode() )
		setTimeout("parent.GoToNextSld()",sld.mAdvDelay)
}
function GetObj(id)
{
	if(g_supportsPPTHTML) return document.all(id);
	else return document.getElementById(id);
}
function SldHasTrans() { return SlideObj.style.filter !=3D ""; }
function GetSldId()=20
{
	var regExp =3D /file:\/\/\//i
	var pos =3D location.href.search(regExp)
	if (MHTMLPrefix !=3D "" && pos !=3D -1)
		sId =3D location.href.substring(pos)
	else
	{
		sId =3D RemoveFilePrefixFromHref(location.href);
		var regExp =3D /\//
		var fixedHref =3D sId
		var pos =3D -1
=09
		pos =3D fixedHref.search(regExp)
		while (pos !=3D -1)
		{
			fixedHref =3D fixedHref.replace(regExp, "\\")
			pos =3D fixedHref.search(regExp)
		}
=09
		if (g_fBaseHyperlink =3D=3D true)
			sId =3D "file:///" + fixedHref;
		else
			sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1)
	}
=09
	return sId
}
function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx=
tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl=
e.display=3D'none'; return true } return false }
function IsWin( name ) { return window.name =3D=3D name }
function IsNts() { return IsWin("PPTNts") }
function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) }
function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"=
 && navigator.appVersion.indexOf("Windows")>0 ) }
function SupportsPPTHTML()
{
	var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0
	if( msie >=3D 0 )
		ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) )
	else
		ver=3DparseInt(appVer)

	return( ver >=3D 4 && msie >=3D 0 )
}
function _RSW()
{
	if( !g_supportsPPTHTML || IsNts() ||
	  ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) )
		return

        var padding=3D0;
        if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6

	cltWidth=3Ddocument.body.clientWidth-padding
	cltHeight=3Ddocument.body.clientHeight-padding
	factor=3D(1.0*cltWidth)/g_origW
	if( cltHeight < g_origH*factor )
		factor=3D(1.0*cltHeight)/g_origH

	newSize =3D g_origSz * factor
	if( newSize < 1 ) newSize=3D1

	s=3DSlideObj.style
	s.fontSize=3DnewSize+"px"
	s.posWidth=3Dg_origW*factor
	s.posHeight=3Dg_origH*factor
	s.posLeft=3D(cltWidth-s.posWidth+padding)/2
	s.posTop=3D(cltHeight-s.posHeight+padding)/2

	if( g_scaleHyperlinks )
		ScaleHyperlinks( factor )
}
function _InitAnimations()
{
	animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined';
	isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode();
	g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc=
reen && parent.IsSldVisited());
	if( g_animUseRuntime ) {
		collSeq =3D document.all.tags("seq");
		if( collSeq !=3D null ) {
			for(ii=3D0;ii<collSeq.length;ii++) {
				if( collSeq[ii].getAttribute( "p:nodeType" ) =3D=3D "mainSeq" ) {
					g_animMainSequence =3D collSeq[ii];
					break;
				}
			}
		}
=09
		if( g_animItemsToHide && document.body.playAnimations !=3D false ) {
			for(jj =3D 0; jj < g_animItemsToHide.length; jj++) {
				if( hideObj =3D GetObj(g_animItemsToHide[jj]) )
					hideObj.runtimeStyle.visibility=3D"hidden";
			}
		}

		if( g_animInteractiveItems ){
			for(jj =3D 0; jj < g_animInteractiveItems.length; jj++) {
				if( triggerObj =3D GetObj(g_animInteractiveItems[jj]) )
					triggerObj.runtimeStyle.cursor=3D"hand";
			}
		}
	=09
		if( gUseSldTimings && ''+g_animSlideTime !=3D 'undefined' ) {
			adjustedTime =3D document.body.calculateAutoAdvanceTimes( g_animSlideTim=
e, g_animEffectTimings );
			if( IsWin("PPTSld") && adjustedTime !=3D g_animSlideTime ) {
			   var sld =3D GetCurSld();
			   sld.mAdvDelay =3D adjustedTime * 1000;
			}
		}
	}

	return g_animUseRuntime;
}

gSldJump =3D 0, gSldJumpTrack =3D 0, gSldJumpIdx =3D "";

function _KPH()
{=20
	if( IsNts() ) return;

	if( !parent.IsFramesMode() && event.keyCode =3D=3D 27 && !HideMenu() )
		parent.window.close( self );
	else if( event.keyCode =3D=3D 32 ) {
		if( window.name =3D=3D "PPTSld" )
			parent.PPTSld.DocumentOnClick();
		else
			parent.GoToNextSld();
	}

	CatchNumKeys( parent, event );
}

function CatchNumKeys( win, event ) {
	if( win.IsFullScrMode() && (48<=3Devent.keyCode) && (event.keyCode<=3D57) =
) {
		gSldJump =3D 1;
		gSldJumpIdx +=3D (event.keyCode-48).toString();
	}
	if( win.IsFullScrMode() && gSldJump && event.keyCode =3D=3D 13 ) {
		var numSlds =3D parent.GetSldList().mList.length
		if ( gSldJumpIdx > numSlds )
			gSldJumpIdx =3D numSlds;
		if ( gSldJumpIdx >=3D 0 ) {
			if ( gSldJumpIdx =3D=3D 0 )
				gSldJumpIdx =3D 1;
			var jumpTo =3D parseInt(gSldJumpIdx);
			gSldJump =3D 0; gSldJumpIdx =3D "";
			win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref )
		}
	}
}

function _KDH()
{
	if( event.keyCode =3D=3D 8 ) {
		event.returnValue =3D 0;
		parent.GoToPrevSld();
	}
}function DocumentOnClick()
{
	if( IsNts() || parent.HideMenu() ) return;

	if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames=
Mode() ) ||
	    (event && event.keyCode=3D=3D32) ) {
	=09
		if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex=
t )
			return;

		parent.GoToNextSld();
	}
}


var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""=
, g_bgSound=3D"",
    g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser =
=3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1;
var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w=
indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va=
r g_animManager =3D null;
var g_animUseRuntime =3D false;
var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime;
var g_animMainSequence =3D null;

var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram=
es", gIsEndShow=3D0, NUM_VIS_SLDS=3D61, SCRIPT_HREF=3D"script.js", FULLSCR_=
HREF=3D"fullscreen.htm";
var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO=
tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true
window.gPPTHTML=3DSupportsPPTHTML()
var g_fBaseHyperlink =3D false;
var gMainDoc=3Dnew Array(new hrefList("slide0093.htm",1,-1,1),new hrefList(=
"slide0001.htm",1,-1,1),new hrefList("slide0067.htm",1,-1,1),new hrefList("=
slide0068.htm",1,-1,1),new hrefList("slide0004.htm",1,-1,1),new hrefList("s=
lide0009.htm",1,-1,1),new hrefList("slide0010.htm",1,-1,1),new hrefList("sl=
ide0011.htm",1,-1,1),new hrefList("slide0069.htm",1,-1,1),new hrefList("sli=
de0016.htm",1,-1,1),new hrefList("slide0017.htm",1,-1,1),new hrefList("slid=
e0071.htm",1,-1,1),new hrefList("slide0022.htm",1,-1,1),new hrefList("slide=
0072.htm",1,-1,1),new hrefList("slide0025.htm",1,-1,1),new hrefList("slide0=
028.htm",1,-1,1),new hrefList("slide0029.htm",1,-1,1),new hrefList("slide00=
74.htm",1,-1,1),new hrefList("slide0030.htm",1,-1,1),new hrefList("slide003=
4.htm",1,-1,1),new hrefList("slide0035.htm",1,-1,1),new hrefList("slide0036=
.htm",1,-1,1),new hrefList("slide0037.htm",1,-1,1),new hrefList("slide0038.=
htm",1,-1,1),new hrefList("slide0075.htm",1,-1,1),new hrefList("slide0076.h=
tm",1,-1,1),new hrefList("slide0039.htm",1,-1,1),new hrefList("slide0040.ht=
m",1,-1,1),new hrefList("slide0041.htm",1,-1,1),new hrefList("slide0042.htm=
",1,-1,1),new hrefList("slide0065.htm",1,-1,1),new hrefList("slide0078.htm"=
,1,-1,1),new hrefList("slide0064.htm",1,-1,1),new hrefList("slide0063.htm",=
1,-1,1),new hrefList("slide0062.htm",1,-1,1),new hrefList("slide0061.htm",1=
,-1,1),new hrefList("slide0079.htm",1,-1,1),new hrefList("slide0080.htm",1,=
-1,1),new hrefList("slide0059.htm",1,-1,1),new hrefList("slide0082.htm",1,-=
1,1),new hrefList("slide0058.htm",1,-1,1),new hrefList("slide0057.htm",1,-1=
,1),new hrefList("slide0083.htm",1,-1,1),new hrefList("slide0084.htm",1,-1,=
1),new hrefList("slide0055.htm",1,-1,1),new hrefList("slide0085.htm",1,-1,1=
),new hrefList("slide0056.htm",1,-1,1),new hrefList("slide0086.htm",1,-1,1)=
,new hrefList("slide0052.htm",1,-1,1),new hrefList("slide0051.htm",1,-1,1),=
new hrefList("slide0050.htm",1,-1,1),new hrefList("slide0049.htm",1,-1,1),n=
ew hrefList("slide0087.htm",1,-1,1),new hrefList("slide0088.htm",1,-1,1),ne=
w hrefList("slide0048.htm",1,-1,1),new hrefList("slide0089.htm",1,-1,1),new=
 hrefList("slide0047.htm",1,-1,1),new hrefList("slide0046.htm",1,-1,1),new =
hrefList("slide0090.htm",1,-1,1),new hrefList("slide0044.htm",1,-1,1),new h=
refList("slide0091.htm",1,-1,1));

/*********************************************
 Frameset functions

 These functions control slide navigation
 and state of the frameset.
**********************************************/

function RemoveFilePrefixFromHref(href)
{
	var regExp =3D /^file:\/\/\//i;
	return href.replace(regExp, "")
}

function FullScrInit()
{
	g_allowAdvOnClick =3D GetCurSld().mAdvOnClk
	document.body.style.backgroundColor=3D"black"
	document.oncontextmenu=3Dparent._CM;
	document.onkeydown =3D _KDH;
	document.ondragstart=3DCancel
	document.onselectstart=3DCancel
	self.focus()
}

function Redirect( frmId )
{=09
	var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId()
	if(idx>=3D0) str=3Dstr.substr(1);
	if( window.name !=3D frmId && ( sId !=3D str) ) {
		obj =3D GetObj("Main-File")
		window.location.href=3Dobj.href+"#"+sId
		return 1
	}
	return 0
}

var MHTMLPrefix =3D CalculateMHTMLPrefix();=20
function CalculateMHTMLPrefix()
{
	if ( document.location.protocol =3D=3D 'mhtml:') {=20
		href=3Dnew String(document.location.href)=20
		Start=3Dhref.indexOf('!')+1=20
		End=3Dhref.lastIndexOf('/')+1=20
		if (End < Start)=20
			return href.substring(0, Start)=20
		else=20
		return href.substring(0, End)=20
	}
	return '';
}

function GetTags(base,tag)
{
	if(g_supportsPPTHTML) return base.all.tags(tag);
	else return base.getElementsByTagName(tag);
}


function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP=
refix+GetHrefObj( gCurSld ).mNtsHref ) }

function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() }

function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() }

function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() }

function SetHasNts( fVal )
{
	if( gHasNts !=3D fVal ) {
		gHasNts=3DfVal
		UpdNavPane()
	}
}

function ToggleOtlText()
{
	gOtlTxtExp=3D!gOtlTxtExp
	UpdOtlPane()
}

function ClearMedia()
{
	// Clear any sounds playing before launching another browser window. Other=
wise,
	// in fullscreen mode, you'll continue to hear the sound in the frames mod=
e.
	if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0;
}

function FullScreen()
{=20
	if ( PPTSld.g_animUseRuntime )
		PPTSld.document.body.pause();
	ClearMedia();
	var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF =
: FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref;
	if (MHTMLPrefix !=3D "")
		href =3D RemoveFilePrefixFromHref(href)
	if(PPTNav.event.ctrlKey) {
		var w =3D (window.screen.availWidth * 1.0) / 2.0
		var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW
		win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top=
=3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h );
		if( win.document.body && PPTSld.g_animUseRuntime )
			win.document.body.PPTSldFrameset=3Dwindow;
	}
	else
	{
		win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" );
		if( win.document.body && PPTSld.g_animUseRuntime )
			win.document.body.PPTSldFrameset=3Dwindow;
	}
}

function ToggleVNarration()
{
	rObj=3DPPTSld.document.all("NSPlay")
	if( rObj && !PPTSld.g_animUseRuntime ) {
		if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) )
			rObj.Play()
		else if( rObj.playState =3D=3D 2 )
			rObj.Pause()
		else
			return;
	}
	else if( PPTSld.g_animUseRuntime )
	{
		narObj =3D PPTSld.document.all("narrationID")
		if( narObj )
			narObj.togglePause()
	}
}

function GetCurSldNum()
{  =20
	obj=3DGetHrefObj(gCurSld)
	if( obj.mOrigVis =3D=3D 1 )
		return obj.mSldIdx
	else  =20
		return gCurSld
}

function GetNumSlds()
{  =20
	if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 )
		return GetSldList().mNumVisSlds;
	else
		return GetSldList().mList.length
}

function GetSldNum( href )
{
	for(ii=3D0; ii<GetSldList().mList.length; ii++) {
		if ( GetSldList().mList[ii].mSldHref =3D=3D href )
			return ii+1
	}
	return 1
}

function GetHrefObj( sldIdx ){ return GetSldList().mList[sldIdx-1] }

function IsFramesMode(){ return ( SCREEN_MODE =3D=3D "Frames" ) }

function IsFullScrMode(){ return ( SCREEN_MODE =3D=3D "FullScreen" ) }

function GoToNextSld()
{
	ii=3DgCurSld + 1
	if( GetHrefObj( ii-1 ).mOrigVis =3D=3D 0 ) {
		if( ii<=3DGetSldList().mList.length ) {
			obj=3DGetHrefObj(ii)
			obj.mVis=3D1
			GoToSldNum(ii)
			return
		}
	}
	else {
		obj=3DGetHrefObj( ii )
		while ( obj && ( obj.mOrigVis =3D=3D 0 ) )
			obj=3DGetHrefObj(++ii)
		if( obj && obj.mOrigVis ) {
			GoToSldNum(ii)
			return
		}
	}
	if( gSldStack.length > 1 )
		PopSldList();
	else if( !IsFramesMode() ) {
                if( gLoopCont )
			GoToFirst()
                else
			EndShow()
	}
}

function GoToPrevSld()
{
	ii=3DgCurSld-1
	if( ii > 0 ) {
		obj=3DGetHrefObj(ii)
		while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) )
			obj=3DGetHrefObj(--ii)
        if( ii =3D=3D 0 ) ii=3D1
		GoToSldNum(ii)
	}
}

function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) }

function GoToLast()
{
	ii=3DGetSldList().mList.length
	if( ii !=3D gCurSld )
		GoToSld( GetHrefObj(ii).mSldHref )
}

function GoToSldNum( num )
{
	if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
	obj =3D GetHrefObj( num )
	obj.mVis=3D1
	gPrevSld=3DgCurSld
	gCurSld =3D num;
=09
	if (MHTMLPrefix !=3D "")
		PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref=
))
	else
		PPTSld.location.replace(obj.mSldHref)
	=09
	if( IsFramesMode() ) {
		UpdNavPane(); UpdOtlPane(); UpdNtsPane()
	}
}

function GoToSld( href )
{
	if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
	GetHrefObj( GetSldNum(href) ).mVis=3D1
	if (MHTMLPrefix !=3D "")
		PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href))
	else
		PPTSld.location.replace(href)
}

function SldUpdated( id )
{
	if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return
	gPrevSld=3DgCurSld
	gCurSld=3DGetSldNum(id)
	if( IsFramesMode() ) {
		UpdNavPane(); UpdOtlPane(); UpdNtsPane()
	}
}

function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) }
function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO=
bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) }
function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) }

function CloseWindow() {
	if( HideMenu() ) return;
=09
	var event =3D PPTSld.event;
	if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D=
=3D32 || event.type=3D=3D"click" ) )
		window.close( self );
	CatchNumKeys( self, event );
}

function Unload() { gIsEndShow=3D0; }

function SetupEndShow() {
	gIsEndShow=3D1;
	PPTSld.document.body.scroll=3D"no";
	PPTSld.document.onkeypress=3DCloseWindow;
	PPTSld.document.onclick=3DCloseWindow;
	PPTSld.document.oncontextmenu=3D_CM;
}

function EndShow()
{
	if( IsFramesMode() ) return
	if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue

	doc=3DPPTSld.document
	var dir =3D doc.body.dir
	if( dir !=3D "rtl" ) dir =3D "ltr";
	doc.open()
	doc.writeln('<html><body dir=3D' + dir + ' bgcolor=3Dblack onload=3Dparent=
.SetupEndShow() onunload=3Dparent.Unload()><center><p><font face=3DTahoma c=
olor=3Dwhite size=3D2><br><b>' + ENDSHOW_MESG + '</b></font></p></center></=
body></html>')
	doc.close()
}

function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue }

function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited }

function hrefList( sldHref, visible, advDelay, advClk )
{
	this.mSldHref=3D this.mNtsHref =3D sldHref
	this.mOrigVis=3D this.mVis =3D visible
	this.mVisited=3D false
	this.mAdvDelay=3D advDelay
	this.mAdvOnClk=3D advClk
}

function SldList(arr,curSld,fEnd)
{
	this.mCurSld =3D curSld;
	this.mList =3D new Array();

	var idx =3D 1;
	for(ii=3D0;ii<arr.length;ii++) {
		this.mList[ii] =3D new hrefList( arr[ii].mSldHref, arr[ii].mOrigVis, arr[=
ii].mAdvDelay, arr[ii].mAdvOnClk );
		if( arr[ii].mOrigVis )
			this.mList[ii].mSldIdx =3D idx++;
	}
	this.mNumVisSlds =3D idx-1;
	this.fEndShow =3D fEnd;
}

function GetSldList() {	return gSldStack[gSldStack.length-1] }
function GetCurSld() { return parent.GetSldList().mList[parent.gCurSld - 1]=
 }

gSldStack =3D new Array();
gSldStack[0] =3D new SldList(gMainDoc,gCurSld,1)
function ToggleOtlPane()
{
	frmset=3Ddocument.all("PPTHorizAdjust")
	frm=3Ddocument.all("PPTOtl")

	if( gOtlOpen )
		frmset.cols=3D"*,100%"
	else
		frmset.cols=3D"25%,*"

	gOtlOpen=3D!gOtlOpen
	frm.noResize=3D!frm.noResize
	UpdOtNavPane()
}

function ToggleNtsPane()
{
	frmset=3Ddocument.all("PPTVertAdjust")
	frm=3Ddocument.all("PPTNts")

	if( gNtsOpen )
		frmset.rows=3D"100%,*"
	else
		frmset.rows=3D"*,20%"

	gNtsOpen=3D!gNtsOpen
	UpdNtsPane()
}

/*********************************************
Custom Shows implementation

When ViewCustomShow() is called, we create
a new array that is a subset of the slides in=20
the main doc. This list pushed on a stack so
we can return after the end of the custom
show.
*********************************************/
function ViewCustomShow(idx,fEnd)
{
	if( !IsFullScrMode() ) return;
	var sldList =3D new Array();
	var custShow =3D custShowList[idx-1];
	var jj =3D 0;
	for( ii=3D0;ii<custShow.length;ii++ ) {
		if( custShow[ii] <=3D gMainDoc.length )
			sldList[jj++] =3D gMainDoc[custShow[ii]-1];
	}
	if (sldList.length > 0) {
	PushSldList(sldList,fEnd);
	gCurSld =3D 1;
	}
	else
		if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
}

function PushSldList(arr,fEnd) {
	var ii =3D gSldStack.length;
	gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd);
	GoToSld( gSldStack[ii].mList[0].mSldHref );
}

function PopSldList() {
	if (gSldStack[gSldStack.length-1].fEndShow)
		EndShow()
	else {
	gCurSld =3D gSldStack[gSldStack.length-1].mCurSld;
	gSldStack[gSldStack.length-1] =3D null;
	gSldStack.length--;
	var sldList =3D gSldStack[gSldStack.length-1];
	GoToSld( sldList.mList[gCurSld - 1].mSldHref );
	}
}
var custShowList=3Dnew Array();

/*********************************************
 Navigation button implementation

 There are 2 types of buttons: ImgBtn, TxtBtn
 implemented as function objects. They share
 a similiar interface so the event handlers
 can call SetActive, for example, on a button=20
 object without needing to know exactly=20
 what type of button it is.
**********************************************/

//----------------------------------
function ImgBtn( oId,bId,w,action )
//----------------------------------
{
	var t=3Dthis
	t.Perform    =3D _IBP
	t.SetActive  =3D _IBSetA
	t.SetInactive=3D _IBSetI
	t.SetPressed =3D _IBSetP
	t.SetDisabled=3D _IBSetD
	t.Enabled    =3D _IBSetE
	t.ChangeIcon =3D null
	t.UserAction =3D action
	t.ChgState   =3D _IBUI
	t.mObjId   =3D oId
	t.mBorderId=3D bId
	t.mWidth   =3D w
	t.mIsOn    =3D t.mCurState =3D 0
}

function _IBSetA()
{
	if( this.mIsOn ) {
		obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
		obj.style.posTop=3D0
	}
}

function _IBSetI()
{
	if( this.mIsOn ) {
		obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
		obj.style.posTop=3D0=20
	}
}

function _IBSetP()
{
	if( this.mIsOn ) {
		obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 )
		obj.style.posLeft+=3D1; obj.style.posTop+=3D1
	}
}

function _IBSetD()
{ =20
	obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 )
	obj.style.posTop=3D0=20
}

function _IBSetE( state )
{
	var t=3Dthis
	GetObj( t.mBorderId ).style.visibility=3D"visible"
	if( state !=3D t.mIsOn ) {
		t.mIsOn=3Dstate
		if( state )
			t.SetInactive()
		else
			t.SetDisabled()
	}
}

function _IBP()
{
	var t=3Dthis
	if( t.mIsOn ) {
		if( t.UserAction !=3D null )
			t.UserAction()
		if( t.ChangeIcon ) {
			obj=3DGetObj(t.mObjId)
			if( t.ChangeIcon() )
				obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth
			else
				obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth
		}
		t.SetActive()
	} =20
}

function _IBUI( clr1,clr2,nextState )
{
	var t=3Dthis
	SetBorder( GetObj( t.mBorderId ),clr1,clr2 )
	obj=3DGetObj( t.mObjId )
	obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj=
.style.posTop
	t.mCurState=3DnextState
	return obj
}

//-----------------------------------------
function TxtBtn( oId,oeId,action,chkState )
//-----------------------------------------
{
	var t=3Dthis
	t.Perform    =3D _TBP
	t.SetActive  =3D _TBSetA
	t.SetInactive=3D _TBSetI
	t.SetPressed =3D _TBSetP
	t.SetDisabled=3D _TBSetD
	t.SetEnabled =3D _TBSetE
	t.GetState   =3D chkState
	t.UserAction =3D action
	t.ChgState   =3D _TBUI
	t.mObjId      =3D oId
	t.m_elementsId=3D oeId
	t.mIsOn       =3D 1
}

function _TBSetA()
{
	var t=3Dthis
	if( t.mIsOn && !t.GetState() )
		t.ChgState( gHiliteClr,gShadowClr,0,0 )
}

function _TBSetI()
{
	var t=3Dthis
	if( t.mIsOn && !t.GetState() )
		t.ChgState( gFaceClr,gFaceClr,0,0 )
}

function _TBSetP()
{
	if( this.mIsOn )
		this.ChgState( gShadowClr,gHiliteClr,1,1 )
}

function _TBSetD()
{  =20
	this.ChgState( gFaceClr,gFaceClr,0,0 )
	this.mIsOn =3D 0
}

function _TBSetE()
{
	var t=3Dthis
	if( !t.GetState() )
		t.ChgState( gFaceClr,gFaceClr,0,0 )
	else
		t.ChgState( gShadowClr,gHiliteClr,1,1 )
	t.mIsOn =3D 1
}

function _TBP()
{
	var t=3Dthis
	if( t.mIsOn ) {=20
		if( t.UserAction !=3D null )
			t.UserAction()
        if( !t.GetState )
            return
		if( t.GetState() )
			t.SetPressed()
		else
			t.SetActive()
	} =20
}

function _TBUI( clr1,clr2,lOffset,tOffset )
{
	SetBorder( GetObj( this.mObjId ),clr1,clr2 )
	Offset( GetObj( this.m_elementsId ),lOffset,tOffset )
}

function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle=
ft }

function SetBorder( obj, upperLeft, lowerRight )
{
	s=3Dobj.style;
	s.borderStyle      =3D "solid"
	s.borderWidth      =3D 1=20
	s.borderLeftColor  =3D s.borderTopColor =3D upperLeft
	s.borderBottomColor=3D s.borderRightColor =3D lowerRight
}

function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] }

function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() }

function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() }

function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() }

function BtnOnUp()
{
	b=3DGetBtnObj()
	if( b !=3D null )
		b.Perform()
	else
		Upd()
}
function GetNtsState(){ return parent.gNtsOpen }

function GetOtlState(){ return parent.gOtlOpen }

function GetOtlTxtState(){ return parent.gOtlTxtExp }

function NtsBtnSetFlag( fVal )
{
	s=3Ddocument.all.item( this.m_flagId ).style
	s.display=3D"none"
	if( fVal )
		s.display=3D""
	else
		s.display=3D"none"
}

function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etActive() }

function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etInactive() }

function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S=
etPressed() }

function _BSetA_BorderImg()
{=20
	b =3D gBtnArr[this.mBorderId]=20
	if( b !=3D null && this.mIsOn && !b.GetState() ) {
		obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
		obj.style.posTop=3D0
	}
}

function _BSetI_BorderImg()
{=20
	b =3D gBtnArr[this.mBorderId]
	if( b !=3D null && this.mIsOn && !b.GetState() ) {
		obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
		obj.style.posTop=3D0
	}
}


var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"=
THREEDFACE"
var gBtnArr =3D new Array()
gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan=
e,GetOtlState )
gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt=
lPane,GetOtlState )
gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN=
tsPane )
gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg;
gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg;
gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.=
ToggleNtsPane,GetNtsState )
gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To=
ggleNtsPane,GetNtsState )
gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n=
b_prevBorder",30,parent.GoToPrevSld )
gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n=
b_nextBorder",30,parent.GoToNextSld )
gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent=
.FullScreen )
gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa=
rent.FullScreen,null )
gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border;
gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border;
gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent=
.FullScreen,null )
gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border;
gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border;
gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice=
","nb_voiceBorder",18,parent.ToggleVNarration )
gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT=
xt","nb_otlTxtBorder",23,parent.ToggleOtlText )
gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts"
gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag
gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState

/*********************************************
 Context menu implementation

 _CM() is the function that's hooked up to
 the oncontextmenu event. Once we're asked to
 show the menu, we first build it by creating
 DIVs on-the-fly. Then we position it=20
 within the screen area so it doesn't get
 clipped.

 Creating the DIVs using createElement() means
 we don't have to write out any extra HTML
 into the slide HTML files.
**********************************************/
var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr=
row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval"

function ShowMenu()
{
	BuildMenu();
	var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y=
=3DPPTSld.event.clientY+doc.scrollTop
	m =3D PPTSld.document.all.item("ctxtmenu")
	m.style.pixelLeft=3Dx
	if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) )
		m.style.pixelLeft=3Dx-m.scrollWidth

	m.style.pixelTop=3Dy
	if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) )
		m.style.pixelTop=3Dy-m.scrollHeight

	m.style.display=3D""
}

function _CM()
{
	if( !parent.IsFullScrMode() ) return;
	if(!PPTSld.event.ctrlKey) {
		ShowMenu()
		return false
	} else
		HideMenu()
}

function BuildMenu()
{
	if( PPTSld.document.all.item("ctxtmenu") ) return

	var mObj=3DCreateItem( PPTSld.document.body )
	mObj.id=3D"ctxtmenu"
	mObj.style.visibility=3D"hidden"
	var s=3DmObj.style
	s.position=3D"absolute"
	s.cursor=3D"default"
	s.width=3D"120px"
	SetCMBorder(mObj,"menu","black")

	var iObj=3DCreateItem( mObj )
	SetCMBorder( iObj, "threedhighlight","threedshadow" )
	iObj.style.padding=3D2
	CreateMenuItem( iObj,sNext,M_GoNextSld,M_True )
	CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld )
=09
	CreateSeparator( iObj )
	CreateMenuItem( iObj,sEnd,M_End,M_True )
	mObj.style.visibility=3D"visible"
}

function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa=
lue=3Dfalse }

function Highlight() { ChangeClr("activecaption","threedhighlight") }

function Deselect() { ChangeClr("threedface","menutext") }

function Perform()
{
	e=3DPPTSld.event.srcElement
	if( e.type=3D=3D"menuitem" && e.IsActive() )
		e.Action()
	else
		PPTSld.event.cancelBubble=3Dtrue
}
function ChangeClr( bg,clr )
{
	e=3DPPTSld.event.srcElement
	if( e.type=3D=3D"menuitem" && e.IsActive() ) {
		e.style.backgroundColor=3Dbg
		e.style.color=3Dclr
	}
}

function M_HasPrevSld() { return( parent.HasPrevSld() ) }

function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() }

function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();=
 PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() }

function M_True() { return true }

function M_End() { window.close( self ) }

function CreateMenuItem( node,text,action,eval )
{
	var e=3DCreateItem( node )
	e.type=3D"menuitem"
	e.Action=3Daction
	e.IsActive=3Deval
	e.innerHTML=3Dtext

	if( !e.IsActive() )
		e.style.color=3D"threedshadow"

	e.onclick=3DPerform
	e.onmouseover=3DHighlight
	e.onmouseout=3DDeselect
	s=3De.style;
	s.fontFamily=3DsFont
	s.fontSize=3D"9pt"
	s.paddingLeft=3D2
}

function CreateSeparator( node )
{
	var sObj=3DCreateItem( node )
	SetCMBorder(sObj,"menu","menu")
	var s=3DsObj.style
	s.borderTopColor=3D"threedshadow"
	s.borderBottomColor=3D"threedhighlight"
	s.height=3D1
	s.fontSize=3D"0px"
}

function CreateItem( node )
{
	var elem=3DPPTSld.document.createElement("DIV")
	node.insertBefore( elem )
	return elem
}

function SetCMBorder( o,ltClr,rbClr )
{
	var s=3Do.style
	s.backgroundColor=3D"menu"
	s.borderStyle=3D"solid"
	s.borderWidth=3D1
	s.borderColor=3DltClr+" "+rbClr+" "+rbClr+" "+ltClr
}
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  <td align=3Dright valign=3Dtop>
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  href=3D"javascript:GoToSld('slide0001.htm');" id=3DPPTL2>Standard Notatio=
n, Order</a></font></div>
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this)"
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       </span>{0,1,2,3&#8230;}</li>
   <li>When we encounter a number, how do we know what it means?<span
       style=3D'mso-spacerun:yes'>&nbsp; </span>How do we know its value?</=
li>
   <li>Digits:<span style=3D'mso-spacerun:yes'>&nbsp; </span>The symbols
       0,1,2,3,4,5,6,7,8,9 that are used to name a place-value</li>
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t</a></font></div>
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   <li>The place-value of each digit in a number tells us the value of the
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lue is
       10 times the place value to its right</li>
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this)"
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   <li>Used to compare unequal numbers</li>
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ed to
       show order</li>
   <ul>
    <li>&lt;<span style=3D'mso-spacerun:yes'>&nbsp; </span>less than</li>
    <li>&gt;<span style=3D'mso-spacerun:yes'>&nbsp; </span>greater than</li>
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   <li>For any whole numbers a and b:</li>
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    <li>a &lt; b is true when a is left of b on the number line</li>
    <li>a &gt; b is true when a is right of b on the number line</li>
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nt></div>
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   <li>Insert the correct inequality symbol to create a true statement</li>
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  <div id=3DPPTP8 class=3DPTxt><font size=3D2><a
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traction</a></font></div>
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nt></div>
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   <li>Addends:<span style=3D'mso-spacerun:yes'>&nbsp; </span>Numbers being=
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   <li>Sum:<span style=3D'mso-spacerun:yes'>&nbsp; </span>Result of adding
       numbers</li>
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   <li>Inverse operation of addition</li>
   <li>The difference a &#8211; b is the unique number c for which a =3D c =
+ b</li>
   <li>Any subtraction problem can be re-written as an addition problem and
       vice-versa</li>
  </ul>
  </font></div>
  </td>
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ont></div>
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  <ul>
   <li>Write each of the following as a &#8220;related sentence&#8221; usin=
g an
       inverse operation</li>
   <li>11 &#8211; 7 =3D 4</li>
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    <li>11 =3D 4 + 7	or	11 =3D 7 + 4</li>
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   <li>2 + 6 =3D 8</li>
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    <li>8 &#8211; 2 =3D 6	or	8 &#8211; 6 =3D 2</li>
   </ul>
   <li>12 + ? =3D 17</li>
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    <li>17 &#8211; 12 =3D ?	or	17 &#8211; 12 =3D 5</li>
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  <div id=3DPPTP12 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0071.htm');" id=3DPPTL12>Examples (cont.=
)</a></font></div>
  <div id=3DPPTC12 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>9 &#8211; 3 =3D 6</li>
   <ul>
    <li>9 =3D 3 + 6	or	9 =3D 6 + 3</li>
   </ul>
   <li>13 &#8211; 11 =3D 2</li>
   <ul>
    <li>13 =3D 11 + 2	or	13 =3D 2 + 11</li>
   </ul>
   <li>8 + 3 =3D 11</li>
   <ul>
    <li>11 &#8211; 8 =3D 3	or	11 &#8211; 3 =3D 8</li>
   </ul>
   <li>15 + 7 =3D 22</li>
   <ul>
    <li>22 &#8211; 15 =3D 7	or	22 &#8211; 7 =3D 15</li>
   </ul>
   <li>? + 5 =3D 9</li>
   <ul>
    <li>9 &#8211; 5 =3D ?	or	9 &#8211; 5 =3D 4</li>
   </ul>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>13</font></div>
  </td>
  <td>
  <div id=3DPPTP13 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0022.htm');" id=3DPPTL13>Multiplication =
&amp;
  Division;<span style=3D'mso-spacerun:yes'>&nbsp; </span>Rounding &amp;
  Estimating</a></font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>14</font></div>
  </td>
  <td>
  <div id=3DPPTP14 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0072.htm');" id=3DPPTL14>Multiplication<=
/a></font></div>
  <div id=3DPPTC14 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Two different ways to think of multiplication:</li>
   <ul>
    <li>Repeated addition</li>
    <ul>
     <li>4 x 6	&#8594;	4 sets of 6 added</li>
    </ul>
    <li>The number of cells in a rectangular array</li>
    <br>
    <br>
    <li>	4 x 6	&#8594;</li>
   </ul>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>15</font></div>
  </td>
  <td>
  <div id=3DPPTP15 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0025.htm');" id=3DPPTL15>Multiplication
  Properties</a></font></div>
  <div id=3DPPTC15 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Multiplicative Identity:<span style=3D'mso-spacerun:yes'>&nbsp; </sp=
an>1
       &#8729; a =3D a &#8729; 1 =3D a</li>
   <li>Multiplication by Zero:<span style=3D'mso-spacerun:yes'>&nbsp; </spa=
n>0
       &#8729; a =3D a &#8729; 0 =3D 0</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>16</font></div>
  </td>
  <td>
  <div id=3DPPTP16 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0028.htm');" id=3DPPTL16>Division</a></f=
ont></div>
  <div id=3DPPTC16 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Inverse operation of multiplication</li>
   <li>Any division problem can be written as a multiplication problem and
       vice-versa</li>
   <li>Dividend:<span style=3D'mso-spacerun:yes'>&nbsp; </span>The number b=
eing
       divided</li>
   <li>Divisor:<span style=3D'mso-spacerun:yes'>&nbsp; </span>The number by=
 which
       the dividend is being divided</li>
   <li>Quotient:<span style=3D'mso-spacerun:yes'>&nbsp; </span>The answer i=
n a
       division problem</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>17</font></div>
  </td>
  <td>
  <div id=3DPPTP17 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0029.htm');" id=3DPPTL17>Examples</a></f=
ont></div>
  <div id=3DPPTC17 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Write each of the following as a &#8220;related sentence&#8221; usin=
g an
       inverse operation</li>
   <li>3 x 8 =3D 24</li>
   <ul>
    <li>24 <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman"=
> 3 =3D
        8	or	24 </font><font face=3DSymbol>&cedil;</font><font
        face=3D"Times New Roman"> 8 =3D 3</font></li>
   </ul>
   <li>18 <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman">=
 6 =3D 3</font></li>
   <ul>
    <li>3 x 6 =3D 18	or	6 x 3 =3D 18</li>
   </ul>
   <li>28 <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman">=
 ? =3D 7</font></li>
   <ul>
    <li>? x 7 =3D 28	&#8594;	4 x 7 =3D 28</li>
   </ul>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>18</font></div>
  </td>
  <td>
  <div id=3DPPTP18 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0074.htm');" id=3DPPTL18>Examples (cont.=
)</a></font></div>
  <div id=3DPPTC18 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>5 x 9 =3D 45</li>
   <ul>
    <li>45 <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman"=
> 5 =3D
        9	or	45 </font><font face=3DSymbol>&cedil;</font><font
        face=3D"Times New Roman"> 9 =3D 5</font></li>
   </ul>
   <li>72 <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman">=
 6 =3D 12</font></li>
   <ul>
    <li>6 x 12 =3D 72	or	12 x 6 =3D 72</li>
   </ul>
   <li>7 x 9 =3D 63</li>
   <ul>
    <li>63 <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman"=
> 7 =3D
        9	or	63 </font><font face=3DSymbol>&cedil;</font><font
        face=3D"Times New Roman"> 9 =3D 7</font></li>
   </ul>
   <li>4 x 8 =3D 32</li>
   <ul>
    <li>32 <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman"=
> 4 =3D
        8	or	32 </font><font face=3DSymbol>&cedil;</font><font
        face=3D"Times New Roman"> 8 =3D 4</font></li>
   </ul>
   <li>? x 9 =3D 54</li>
   <ul>
    <li>54 <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman"=
> 9 =3D
        ?	&#8594;	54 </font><font face=3DSymbol>&cedil;</font><font
        face=3D"Times New Roman"> 9 =3D 6</font></li>
   </ul>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>19</font></div>
  </td>
  <td>
  <div id=3DPPTP19 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0030.htm');" id=3DPPTL19>Division Proper=
ties</a></font></div>
  <div id=3DPPTC19 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Dividing a Number by Itself:<br>
              a <font face=3DSymbol>&cedil;</font><font face=3D"Times New R=
oman"> a
       =3D 1, a </font><font face=3DSymbol>&sup1;</font><font face=3D"Times=
 New Roman">
       0</font></li>
   <li>The Dividend is Zero:<br>
              0 <font face=3DSymbol>&cedil;</font><font face=3D"Times New R=
oman"> a
       =3D 0</font></li>
   <li>Division by Zero:<br>
              a <font face=3DSymbol>&cedil;</font><font face=3D"Times New R=
oman"> 0
       is not defined</font></li>
   <ul>
    <li>a <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman">=
 0 =3D ?</font></li>
    <li>? x 0 =3D a</li>
    <li>No such number exists</li>
   </ul>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>20</font></div>
  </td>
  <td>
  <div id=3DPPTP20 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0034.htm');" id=3DPPTL20>Rounding</a></f=
ont></div>
  <div id=3DPPTC20 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Locate (circle) the appropriate digit</li>
   <li>Consider the digit to the right:<span style=3D'mso-spacerun:yes'>&nb=
sp;
       </span>If 5 or higher, round circled digit up.<span
       style=3D'mso-spacerun:yes'>&nbsp; </span>If 4 or lower, leave circled
       digit unchanged.</li>
   <li>Change all digits to right of circled digit to zeros</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>21</font></div>
  </td>
  <td>
  <div id=3DPPTP21 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0035.htm');" id=3DPPTL21>Examples:<span
  style=3D'mso-spacerun:yes'>&nbsp; </span>Round to desired place value</a>=
</font></div>
  <div id=3DPPTC21 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>275			Round to the nearest ten</li>
   <br>
   <br>
   <li>4350		Round to the nearest hundred</li>
   <br>
   <br>
   <li>8786		Round to the nearest ten</li>
   <br>
   <br>
   <li>18,440		Round to the nearest thousand</li>
   <br>
   <br>
   <li>79,286		Round to the nearest ten-thousand</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>22</font></div>
  </td>
  <td>
  <div id=3DPPTP22 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0036.htm');" id=3DPPTL22>Estimating</a><=
/font></div>
  <div id=3DPPTC22 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Gives an approximation when an exact answer is not needed</li>
   <li><span style=3D'mso-spacerun:yes'>&nbsp;</span>Helpful to determine i=
f your
       calculated answer is &#8220;in the ballpark&#8221;</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>23</font></div>
  </td>
  <td>
  <div id=3DPPTP23 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0037.htm');" id=3DPPTL23>Examples</a></f=
ont></div>
  <div id=3DPPTC23 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Round given numbers appropriately to estimate an answer</li>
   <br>
   <br>
   <li>9 classrooms each contain 42 students.<span
       style=3D'mso-spacerun:yes'>&nbsp; </span>Estimate the total number of
       students.</li>
   <ul>
    <li>Estimate 10 classrooms of 40 students</li>
   </ul>
   <br>
   <li>93 rows each contain 62 tomato plants.<span
       style=3D'mso-spacerun:yes'>&nbsp; </span>Estimate the total number of
       tomato plants.</li>
   <ul>
    <li>Estimate 90 rows of 60 plants</li>
   </ul>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>24</font></div>
  </td>
  <td>
  <div id=3DPPTP24 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0038.htm');" id=3DPPTL24>Solving Equatio=
ns</a></font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>25</font></div>
  </td>
  <td>
  <div id=3DPPTP25 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0075.htm');" id=3DPPTL25>Definitions</a>=
</font></div>
  <div id=3DPPTC25 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Variable:<span style=3D'mso-spacerun:yes'>&nbsp; </span>Letter or sy=
mbol
       that represents one or more numbers</li>
   <li>Equation:<span style=3D'mso-spacerun:yes'>&nbsp; </span>Mathematical
       statement that two expressions are equal</li>
   <li>Solution:<span style=3D'mso-spacerun:yes'>&nbsp; </span>A number tha=
t when
       substituted for a variable makes the statement true</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>26</font></div>
  </td>
  <td>
  <div id=3DPPTP26 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0076.htm');" id=3DPPTL26>Solving Equatio=
ns</a></font></div>
  <div id=3DPPTC26 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Isolate the Variable:<span style=3D'mso-spacerun:yes'>&nbsp; </span>=
Get
       the variable alone on one side of an equation</li>
   <li>Solve an Equation Using Inverse Operations:<span
       style=3D'mso-spacerun:yes'>&nbsp; </span>Rewrite the equation to iso=
late
       the variable using an inverse operation</li>
   <li>Check the Solution:<span style=3D'mso-spacerun:yes'>&nbsp;
       </span>Substitute back into the original equation</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>27</font></div>
  </td>
  <td>
  <div id=3DPPTP27 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0039.htm');" id=3DPPTL27>Examples</a></f=
ont></div>
  <div id=3DPPTC27 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>n + 6 =3D 14	To isolate n, we need to &#8220;undo&#8221; adding 6</l=
i>
   <li>	n =3D 14 &#8211; 6		Use the inverse operation:<span
       style=3D'mso-spacerun:yes'>&nbsp; </span>subtraction</li>
   <li>	n =3D 8		Subtract 6 from both sides</li>
   <br>
   <br>
   <li>18 =3D x &#8211; 13	To isolate x, we need to &#8220;undo&#8221;
       subtracting 13</li>
   <li>	18 + 13 =3D x	Use the inverse operation:<span
       style=3D'mso-spacerun:yes'>&nbsp; </span>addition</li>
   <li>	31 =3D x		Add 13 to both sides</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>28</font></div>
  </td>
  <td>
  <div id=3DPPTP28 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0040.htm');" id=3DPPTL28>Addition/Subtra=
ction
  Examples</a></font></div>
  <div id=3DPPTC28 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>y &#8211; 3 =3D 12</li>
   <br>
   <br>
   <br>
   <li>21 =3D x &#8211; 12</li>
   <br>
   <br>
   <br>
   <li>41 =3D 14 + z</li>
   <li>7 + m =3D 9</li>
   <br>
   <br>
   <br>
   <li>y + 15 =3D 36</li>
   <br>
   <br>
   <br>
   <li>a &#8211; 5 =3D 16</li>
   <br>
   <br>
   <br>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>29</font></div>
  </td>
  <td>
  <div id=3DPPTP29 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0041.htm');" id=3DPPTL29>Multiplication/=
Division
  Examples</a></font></div>
  <div id=3DPPTC29 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>4 &#8729; x =3D 24	To isolate x, we need to &#8220;undo&#8221; multi=
plying
       by 4</li>
   <li>	x =3D 24 &divide; 4	Use the inverse operation:<span
       style=3D'mso-spacerun:yes'>&nbsp; </span>division</li>
   <li>	x =3D 6		Divide both sides by 4</li>
   <br>
   <br>
   <li>y <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman"> =
7 =3D 9		To
       isolate y, we need to &#8220;undo&#8221; dividing by 7</font></li>
   <li>	y =3D 7 x 9		Use the inverse operation:<span
       style=3D'mso-spacerun:yes'>&nbsp; </span>multiplication</li>
   <li>	y =3D 63		Mulitply both sides by 7</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>30</font></div>
  </td>
  <td>
  <div id=3DPPTP30 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0042.htm');" id=3DPPTL30>Examples</a></f=
ont></div>
  <div id=3DPPTC30 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>3n =3D 15</li>
   <br>
   <br>
   <br>
   <li>5 =3D x <font face=3DSymbol>&cedil;</font><font face=3D"Times New Ro=
man"> 7</font></li>
   <br>
   <br>
   <br>
   <li>11m =3D 55</li>
   <li>45 <font face=3DSymbol>&cedil;</font><font face=3D"Times New Roman">=
 y =3D 9</font></li>
   <br>
   <br>
   <br>
   <li>9t =3D 63</li>
   <br>
   <br>
   <br>
   <li>15 &divide; x =3D 5</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>31</font></div>
  </td>
  <td>
  <div id=3DPPTP31 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0065.htm');" id=3DPPTL31>Exponents and O=
rder of
  Operations</a></font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>32</font></div>
  </td>
  <td>
  <div id=3DPPTP32 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0078.htm');" id=3DPPTL32>Exponential Not=
ation</a></font></div>
  <div id=3DPPTC32 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Exponential Notation:<span style=3D'mso-spacerun:yes'>&nbsp;
       </span>Expresses repeated multiplication</li>
   <br>
   <br>
   <li>5<sup>2</sup></li>
   <br>
   <br>
   <li>Evaluating Exponential Notation:<span style=3D'mso-spacerun:yes'>&nb=
sp;
       </span>Multiply the base together the number of times the exponent
       indicates</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>33</font></div>
  </td>
  <td>
  <div id=3DPPTP33 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0064.htm');" id=3DPPTL33>Examples</a></f=
ont></div>
  <div id=3DPPTC33 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>4<sup>2</sup> =3D 4 &#8729; 4 =3D 16</li>
   <br>
   <br>
   <li>6<sup>3</sup> =3D 6 &#8729; 6 &#8729; 6 =3D 216</li>
   <br>
   <br>
   <li>4<sup>3</sup></li>
   <br>
   <br>
   <li>2<sup>4</sup></li>
   <br>
   <br>
   <li>11<sup>2</sup></li>
   <li>3<sup>4</sup> =3D 3 &#8729; 3 &#8729; 3 &#8729; 3 =3D 81</li>
   <br>
   <br>
   <li>5<sup>2</sup></li>
   <br>
   <br>
   <li>8<sup>2</sup></li>
   <br>
   <br>
   <li>2<sup>5</sup></li>
   <br>
   <br>
   <li>5<sup>3</sup></li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>34</font></div>
  </td>
  <td>
  <div id=3DPPTP34 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0063.htm');" id=3DPPTL34>Order of Operat=
ions</a></font></div>
  <div id=3DPPTC34 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>When evaluating expressions, we must use a set order</li>
   <br>
   <br>
   <li>Consider:</li>
   <li>		2 + 4 &#8729; 3	2 + 4 &#8729; 3</li>
   <li>		6 &#8729; 3	2 + 12</li>
   <li>		18	14</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>35</font></div>
  </td>
  <td>
  <div id=3DPPTP35 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0062.htm');" id=3DPPTL35>Order of Operat=
ions</a></font></div>
  <div id=3DPPTC35 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Simplify all calculations within grouping symbols first (P)</li>
   <li>Simplify exponents (E)</li>
   <li>Simplify multiplication and division from left to right (MD)</li>
   <li>Simplify addition and subtraction from left to right (AS)</li>
   <li>Note:<span style=3D'mso-spacerun:yes'>&nbsp; </span>When grouping sy=
mbols
       are within grouping symbols, simplify innermost first</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>36</font></div>
  </td>
  <td>
  <div id=3DPPTP36 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0061.htm');" id=3DPPTL36>Examples</a></f=
ont></div>
  <div id=3DPPTC36 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>6 &#8211; 2 &#8211; 4 + 3</li>
   <br>
   <br>
   <br>
   <br>
   <li>3<sup>2</sup> + 4<sup>2</sup></li>
   <li>18 &divide; 3 &divide; 2 &#8729; 4</li>
   <br>
   <br>
   <br>
   <br>
   <li>7<sup>2</sup> &#8211; 5(6 &#8211; {2 &#8729; 2})</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>37</font></div>
  </td>
  <td>
  <div id=3DPPTP37 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0079.htm');" id=3DPPTL37>Examples (cont.=
)</a></font></div>
  <div id=3DPPTC37 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>20 &#8211; 3 &#8729; 5</li>
   <br>
   <br>
   <br>
   <br>
   <li>18 &divide; 3 &#8729; 5 &#8211; 10</li>
   <li>16 + 2(6 + 2)</li>
   <br>
   <br>
   <br>
   <br>
   <li>36 &divide; 6 &divide; 3 + 10 &#8729; 2</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>38</font></div>
  </td>
  <td>
  <div id=3DPPTP38 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0080.htm');" id=3DPPTL38>Examples (cont.=
)</a></font></div>
  <div id=3DPPTC38 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>10<sup>2</sup> &#8211; 8<sup>2</sup></li>
   <li>{7 &#8211; 10 &divide; [8 &#8211; 3]}(12)</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>39</font></div>
  </td>
  <td>
  <div id=3DPPTP39 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0059.htm');" id=3DPPTL39>Factorizations<=
/a></font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>40</font></div>
  </td>
  <td>
  <div id=3DPPTP40 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0082.htm');" id=3DPPTL40>Factor</a></fon=
t></div>
  <div id=3DPPTC40 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Numbers or variables that are multiplied together</li>
   <li>OR</li>
   <li>Any number that divides evenly (no remainder) into a given number</l=
i>
   <br>
   <br>
   <li>Test for Factors:<span style=3D'mso-spacerun:yes'>&nbsp; </span>Use
       division</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>41</font></div>
  </td>
  <td>
  <div id=3DPPTP41 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0058.htm');" id=3DPPTL41>Examples</a></f=
ont></div>
  <div id=3DPPTC41 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Is 8 a factor of 96?</li>
   <br>
   <br>
   <br>
   <li>Is 14 a factor of 88?</li>
   <br>
   <br>
   <br>
   <li>Is 7 a factor of 149?</li>
   <li>Is 6 a factor of 76?</li>
   <br>
   <br>
   <br>
   <li>Is 9 a factor of 144?</li>
   <br>
   <br>
   <br>
   <li>Is 11 a factor of 143?</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>42</font></div>
  </td>
  <td>
  <div id=3DPPTP42 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0057.htm');" id=3DPPTL42>Factorization</=
a></font></div>
  <div id=3DPPTC42 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Factors that when multiplied equal the given number</li>
   <li>To find all factors, look for factorization pairs</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>43</font></div>
  </td>
  <td>
  <div id=3DPPTP43 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0083.htm');" id=3DPPTL43>Examples</a></f=
ont></div>
  <div id=3DPPTC43 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Find all factors of 45</li>
   <ul>
    <li>1 x 45</li>
    <li>2 not a factor</li>
    <li>3 x 15</li>
    <li>4 not a factor</li>
    <li>5 x 9</li>
    <li>6,7,8 not factors</li>
   </ul>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>44</font></div>
  </td>
  <td>
  <div id=3DPPTP44 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0084.htm');" id=3DPPTL44>Examples (cont.=
)</a></font></div>
  <div id=3DPPTC44 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Find all factors of 60</li>
   <br>
   <br>
   <br>
   <li>Find all factors of 84</li>
   <br>
   <br>
   <br>
   <li>Find all factors of 75</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>45</font></div>
  </td>
  <td>
  <div id=3DPPTP45 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0055.htm');" id=3DPPTL45>Multiple Of</a>=
</font></div>
  <div id=3DPPTC45 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>A number into which a given number divides evenly (with no remainder=
)</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>46</font></div>
  </td>
  <td>
  <div id=3DPPTP46 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0085.htm');" id=3DPPTL46>Examples</a></f=
ont></div>
  <div id=3DPPTC46 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Is 60 a multiple of 12?</li>
   <br>
   <br>
   <br>
   <br>
   <li>Is 112 a multiple of 6?</li>
   <li>Is 48 a multiple of 8?</li>
   <br>
   <br>
   <br>
   <br>
   <li>Is 112 a multiple of 4?</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>47</font></div>
  </td>
  <td>
  <div id=3DPPTP47 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0056.htm');" id=3DPPTL47>Divisible By</a=
></font></div>
  <div id=3DPPTC47 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Same as multiple of</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>48</font></div>
  </td>
  <td>
  <div id=3DPPTP48 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0086.htm');" id=3DPPTL48>Examples</a></f=
ont></div>
  <div id=3DPPTC48 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Is 78 divisible by 8?</li>
   <br>
   <br>
   <br>
   <br>
   <li>Is 148 divisible by 8?</li>
   <li>Is 78 divisible by 4?</li>
   <br>
   <br>
   <br>
   <br>
   <li>Is 148 divisible by 4?</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>49</font></div>
  </td>
  <td>
  <div id=3DPPTP49 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0052.htm');" id=3DPPTL49>Definitions</a>=
</font></div>
  <div id=3DPPTC49 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Prime Number:<span style=3D'mso-spacerun:yes'>&nbsp; </span>A number=
 with
       only two factors, one and itself</li>
   <li>Composite Number:<span style=3D'mso-spacerun:yes'>&nbsp; </span>A nu=
mber
       with factors other than one and itself</li>
   <li>Note:<span style=3D'mso-spacerun:yes'>&nbsp; </span>One is neither p=
rime
       nor composite</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>50</font></div>
  </td>
  <td>
  <div id=3DPPTP50 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0051.htm');" id=3DPPTL50>Examples:<span
  style=3D'mso-spacerun:yes'>&nbsp; </span>Prime or Composite?</a></font></=
div>
  <div id=3DPPTC50 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>14</li>
   <br>
   <br>
   <br>
   <li>19</li>
   <br>
   <br>
   <br>
   <li>21</li>
   <li>67</li>
   <br>
   <br>
   <br>
   <li>33</li>
   <br>
   <br>
   <br>
   <li>29</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>51</font></div>
  </td>
  <td>
  <div id=3DPPTP51 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0050.htm');" id=3DPPTL51>Prime Factoriza=
tion</a></font></div>
  <div id=3DPPTC51 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>Write a composite number as a product of primes</li>
   <br>
   <br>
   <li>Two Methods for Finding a Prime Factorization:</li>
   <li>&#8220;Tree method&#8221;</li>
   <li>Successive divisions</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>52</font></div>
  </td>
  <td>
  <div id=3DPPTP52 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0049.htm');" id=3DPPTL52>Examples:<span
  style=3D'mso-spacerun:yes'>&nbsp; </span>Find the Prime Factorizations</a=
></font></div>
  <div id=3DPPTC52 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>		30</li>
   <br>
   <br>
   <br>
   <br>
   <li>		72</li>
   <li>		30</li>
   <br>
   <br>
   <br>
   <br>
   <li>		72</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>53</font></div>
  </td>
  <td>
  <div id=3DPPTP53 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0087.htm');" id=3DPPTL53>Examples (cont.=
)</a></font></div>
  <div id=3DPPTC53 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>		28</li>
   <br>
   <br>
   <br>
   <br>
   <li>		96</li>
   <li>		28</li>
   <br>
   <br>
   <br>
   <br>
   <li>		96</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>54</font></div>
  </td>
  <td>
  <div id=3DPPTP54 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0088.htm');" id=3DPPTL54>Examples (cont.=
)</a></font></div>
  <div id=3DPPTC54 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>		104</li>
   <br>
   <br>
   <br>
   <br>
   <li>		42</li>
   <li>		104</li>
   <br>
   <br>
   <br>
   <br>
   <li>		42</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>55</font></div>
  </td>
  <td>
  <div id=3DPPTP55 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0048.htm');" id=3DPPTL55>Rules for Divis=
ibility</a></font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>56</font></div>
  </td>
  <td>
  <div id=3DPPTP56 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0089.htm');" id=3DPPTL56>A Number is Div=
isible
  By</a></font></div>
  <div id=3DPPTC56 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>2	If its ones digit is 0,2,4,6,8 (an even number)</li>
   <li>3	If the sum of its digits is divisible by 3</li>
   <li>5	If its ones digit is 0 or 5</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>57</font></div>
  </td>
  <td>
  <div id=3DPPTP57 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0047.htm');" id=3DPPTL57>Examples:<span
  style=3D'mso-spacerun:yes'>&nbsp; </span>Determine if the following numbe=
rs are
  divisible by 2, 3, and/or 5</a></font></div>
  <div id=3DPPTC57 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>168</li>
   <ul>
    <li>2, 3</li>
    <br>
    <br>
    <br>
   </ul>
   <li>215</li>
   <ul>
    <li>5</li>
   </ul>
   <li>235</li>
   <ul>
    <li>5</li>
    <br>
    <br>
    <br>
   </ul>
   <li>270</li>
   <ul>
    <li>2, 3, 5</li>
   </ul>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>58</font></div>
  </td>
  <td>
  <div id=3DPPTP58 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0046.htm');" id=3DPPTL58>A Number is Div=
isible
  By:</a></font></div>
  <div id=3DPPTC58 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>4	If its last two digits are divisible by 4</li>
   <li>6	If it is divisible by 3 and even</li>
   <li>8	If its last three digits are divisible by 8</li>
   <li>9	If the sum of its digits is divisible by 9</li>
   <li>10	If its ones digit is 0</li>
   <li>Note:<span style=3D'mso-spacerun:yes'>&nbsp; </span>We are mainly
       concerned with 2,3,5 because they are primes</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>59</font></div>
  </td>
  <td>
  <div id=3DPPTP59 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0090.htm');" id=3DPPTL59>Least Common Mu=
ltiple
  (LCM)</a></font></div>
  <div id=3DPPTC59 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>The smallest number that is a multiple of two or more numbers</li>
   <li>Finding the LCM:</li>
   <ul>
    <li>Find the prime factorization of each number</li>
    <li>Create a product of factors, using each factor the greatest number =
of
        times it occurs in any of the prime factorizations</li>
   </ul>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>60</font></div>
  </td>
  <td>
  <div id=3DPPTP60 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0044.htm');" id=3DPPTL60>Examples</a></f=
ont></div>
  <div id=3DPPTC60 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>12 &amp; 18</li>
   <br>
   <br>
   <br>
   <br>
   <li>14 &amp; 70</li>
  </ul>
  </font></div>
  </td>
 </tr>
 <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(=
this)"
  style=3D'cursor:hand'>
  <td align=3Dright valign=3Dtop>
  <div class=3DsldNum><font size=3D2>61</font></div>
  </td>
  <td>
  <div id=3DPPTP61 class=3DPTxt><font size=3D2><a
  href=3D"javascript:GoToSld('slide0091.htm');" id=3DPPTL61>Examples (cont.=
)</a></font></div>
  <div id=3DPPTC61 class=3DCTxt style=3D'display:none'><font size=3D2>
  <ul>
   <li>15 &amp; 20</li>
   <br>
   <br>
   <br>
   <br>
   <li>25 &amp; 45</li>
  </ul>
  </font></div>
  </td>
 </tr>
</table>



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------=_NextPart_01C97571.7B224ED0
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