异分母分数加法可视化演示
2016-10-30 10:42
本范例通过几何图形直观演示异分母分数的加法运算过程。利用多边形(矩形)面积模型将分数可视化,展示通分与合并的完整步骤。用户可通过交互输入不同分数,系统自动计算并显示通分后的等价分数及最终求和结果,帮助理解异分母分数加法的核心原理。
所属专题
分数
GeoGebra 画板及绘图内容加载中,请稍等……
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.286.0" id="20b47831-317f-48ba-b69d-5f7412a09c3d" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1000" height="513" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.726" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="69,54,1294,671" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="3" size="726" window="100,100,600,400" />
<view id="2" visible="false" inframe="true" stylebar="true" location="3" size="200" window="1179,23,295,724" />
<view id="16" visible="true" inframe="false" stylebar="true" location="1" size="264" window="274,52,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="24"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="725" height="510"/>
<coordSystem xZero="15.000000000000002" yZero="333.0000000000001" scale="49.99999999999998" yscale="49.999999999999986"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="2" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="0.05" distY="0.05" distTheta="0.5235987755982988"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="263" height="510"/>
<coordSystem xZero="-658.9999999999986" yZero="332.99999999999994" scale="49.999999999999815" yscale="50.00000000000002"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="2" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="0.05" distY="0.05" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="異分母分數加減" author="" date="">
<element type="numeric" label="b1">
<value val="2"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="a1 - 1" absoluteScreenLocation="true" width="200" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="pixely" exp="y(Corner[3] - Corner[1]) / y(Corner[5])" />
<element type="numeric" label="pixely">
<value val="0.020078431372549027"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="h" exp="(80 * pixely)" />
<element type="numeric" label="h">
<value val="1.6062745098039222"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Point">
<input a0="yAxis"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0" y="-1.45" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="pixelx" exp="x(Corner[3] - Corner[1]) / x(Corner[5])" />
<element type="numeric" label="pixelx">
<value val="0.02005517241379311"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="l" exp="(350 * pixelx)" />
<element type="numeric" label="l">
<value val="7.019310344827589"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Point">
<input a0="Segment[C + (0, h), C + (0, (1.85 * h))]"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelOffset x="7" y="40"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0" y="1.5216078431372562" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="a1">
<value val="3"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="2" max="30" absoluteScreenLocation="true" width="200" x="30" y="50" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="t">
<value val="0"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="1"/>
<labelMode val="1"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="200" x="454" y="155" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="0.01" speed="4" type="3" playing="false"/>
</element>
<command name="If">
<input a0="t ≤ 0.5" a1="0" a2="(2 * (t - 0.5))"/>
<output a0="t2"/>
</command>
<element type="numeric" label="t2">
<value val="0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="If">
<input a0="t ≤ 0.5" a1="(2 * t)" a2="1"/>
<output a0="t1"/>
</command>
<element type="numeric" label="t1">
<value val="0"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Point">
<input a0="Segment[B + (0, h), B + (0, (1.85 * h))]"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelOffset x="4" y="34"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0" y="4.493215686274512" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Ray">
<input a0="(0, 1.9)" a1="(0, 2.9)"/>
<output a0="f"/>
</command>
<element type="ray" label="f">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-1" y="0" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="a2">
<value val="4"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="2" max="30" absoluteScreenLocation="true" width="200" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="b2">
<value val="1"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="a2 - 1" absoluteScreenLocation="true" width="200" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="fraction1" exp=""\frac{" + (LaTeX[b1]) + "}{" + (LaTeX[a1]) + "}"" />
<element type="text" label="fraction1">
<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<absoluteScreenLocation x="97" y="16"/>
</element>
<expression label="fraction2" exp=""\frac{" + (LaTeX[b2]) + "}{" + (LaTeX[a2]) + "}"" />
<element type="text" label="fraction2">
<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<absoluteScreenLocation x="97" y="151"/>
</element>
<command name="Polygon">
<input a0="{A, A + (l, 0), A + (l, h), A + (0, h)}"/>
<output a0="poly1"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="7" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{B, B + (l, 0), B + (l, h), B + (0, h)}"/>
<output a0="poly2"/>
</command>
<element type="polygon" label="poly2">
<lineStyle thickness="7" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="numeric" label="c1">
<value val="1"/>
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelOffset x="75" y="-28"/>
<labelMode val="3"/>
<slider min="1" max="9" absoluteScreenLocation="true" width="100" x="9" y="123" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
<caption val="擴分"/>
</element>
<element type="numeric" label="c2">
<value val="1"/>
<show object="false" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="1" max="9" absoluteScreenLocation="true" width="100" x="9" y="263" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="Segment[A + ((i * l / a1), 0), A + ((i * l / a1), h)]" a1="i" a2="1" a3="a1 - 1"/>
<output a0="list1"/>
</command>
<element type="list" label="list1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="8" type="10" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Segment[B + ((i * l / a2), 0), B + ((i * l / a2), h)]" a1="i" a2="1" a3="a2 - 1"/>
<output a0="list2"/>
</command>
<element type="list" label="list2">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="8" type="10" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Polygon">
<input a0="{A, A + ((b1 * l / a1), 0), A + ((b1 * l / a1), h), A + (0, h)}"/>
<output a0="poly3"/>
</command>
<element type="polygon" label="poly3">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.3"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{B, B + ((b2 * l / a2), 0), B + ((b2 * l / a2), h), B + (0, h)}"/>
<output a0="poly4"/>
</command>
<element type="polygon" label="poly4">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="255" b="0" alpha="0.3"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Sequence">
<input a0="Sequence[Segment[A + ((i * l / a1) + (j * l / ((a1 * c1))), 0), A + ((i * l / a1) + (j * l / ((a1 * c1))), h)], j, 1, c1 - 1]" a1="i" a2="0" a3="a1 - 1"/>
<output a0="list3"/>
</command>
<element type="list" label="list3">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="4" type="20" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Sequence[Segment[B + ((i * l / a2) + (j * l / ((a2 * c2))), 0), B + ((i * l / a2) + (j * l / ((a2 * c2))), h)], j, 1, c2 - 1]" a1="i" a2="0" a3="a2 - 1"/>
<output a0="list4"/>
</command>
<element type="list" label="list4">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="4" type="20" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<expression label="text3" exp=""擴分""/>
<element type="text" label="text3">
<show object="true" label="true" ev="40"/>
<condition showObject="t ≟ 1 ∧ (a1 ≠ a2)"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="0.7" size="-8" style="0"/>
<absoluteScreenLocation x="398" y="134"/>
</element>
<expression label="text4" exp=""擴分""/>
<element type="text" label="text4">
<show object="true" label="true" ev="40"/>
<condition showObject="t ≟ 1 ∧ (a1 ≠ a2)"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<font serif="false" sizeM="0.7" size="-8" style="0"/>
<absoluteScreenLocation x="400" y="282"/>
</element>
<expression label="text5" exp=""" + (LaTeX[If[a1 ≟ 1, "1", fraction1]]) + """ />
<element type="text" label="text5">
<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<startPoint x="5.559999999999992" y="-0.6600000000000039" z="1"/>
</element>
<expression label="text6" exp=""" + (LaTeX[If[a2 ≟ 1, "1", fraction2]]) + """ />
<element type="text" label="text6">
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<startPoint x="6.959999999999985" y="-2.7600000000000042" z="1"/>
</element>
<element type="point" label="Position1">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-1.5" y="5.3" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="Position2">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="-1.5" y="2.6" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="textheight1" exp="y(Corner[text5, 3]) - y(Corner[text5, 2])" />
<element type="numeric" label="textheight1">
<value val="1.8600000000000008"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="text7" exp=""" + (LaTeX[text5]) + """ />
<element type="text" label="text7">
<show object="false" label="true" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<startPoint x="-1.439999999999995" y="4.439999999999999" z="1"/>
</element>
<expression label="textheight2" exp="y(Corner[text6, 3] - Corner[text6, 2])" />
<element type="numeric" label="textheight2">
<value val="1.8600000000000008"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="text8" exp=""" + (LaTeX[text6]) + """ />
<element type="text" label="text8">
<show object="false" label="true" ev="20"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<startPoint x="-4.34" y="3.54" z="1"/>
</element>
<command name="If">
<input a0="a1 ≟ a2" a1="true" a2="false"/>
<output a0="equald"/>
</command>
<element type="boolean" label="equald">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="finalintegral" exp=""" + (LaTeX[Div[(b1 * c1) + (b2 * c2), (a1 * c1)]]) + """ />
<element type="text" label="finalintegral">
<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="7.06" y="-3.16" z="1"/>
</element>
<expression label="finalfractional" exp=""\frac{" + (LaTeX[Mod[(b1 * c1) + (b2 * c2), (a1 * c1)] / GCD[(b1 * c1) + (b2 * c2), (a1 * c1)]]) + "}{" + (LaTeX[(a1 * c1 / GCD[(b1 * c1) + (b2 * c2), (a1 * c1)])]) + "}"" />
<element type="text" label="finalfractional">
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="8.16" y="-2.66" z="1"/>
</element>
<expression label="finalintegral'" exp=""" + (LaTeX[Div[b1 + b2, a1]]) + """ />
<element type="text" label="finalintegral'">
<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="8.860000000000007" y="-2.680000000000001" z="1"/>
</element>
<expression label="finalfractional'" exp=""\frac{" + (LaTeX[Mod[b1 + b2, a1] / GCD[b1 + b2, a1]]) + "}{" + (LaTeX[a1 / GCD[b1 + b2, a1]]) + "}"" />
<element type="text" label="finalfractional'">
<show object="false" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="9.040000000000006" y="-2.560000000000001" z="1"/>
</element>
<expression label="text13" exp=""" + (LaTeX[If[Div[b1 + b2, a1] > 0, finalintegral', ""]]) + "" + (LaTeX[If[Mod[b1 + b2, a1] > 0, finalfractional', ""]]) + """ />
<element type="text" label="text13">
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="6.759999999999976" y="-1.6599999999999988" z="1"/>
</element>
<expression label="text16" exp=""\frac{" + (LaTeX[b1 + b2]) + "}{" + (LaTeX[a1]) + "}"" />
<element type="text" label="text16">
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="6.759999999999995" y="-0.16000000000000014" z="1"/>
</element>
<command name="If">
<input a0="equald ∧ ((Div[b1 + b2, a1] > 0) ∨ (GCD[b1 + b2, a1] > 1))" a1="true" a2="If[(Div[(b1 * c1) + (b2 * c2), (a1 * c1)] > 0) ∨ (GCD[(b1 * c1) + (b2 * c2), (a1 * c1)] > 1), true, false]"/>
<output a0="simplify"/>
</command>
<element type="boolean" label="simplify">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<element type="button" label="button9">
<show object="true" label="true"/>
<condition showObject="t ≟ 1 ∧ (a1 ≠ a2)"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="224" g="224" b="224" alpha="255"/>
<layer val="1"/>
<labelOffset x="442" y="116"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[c1, c1-1]"/>
<font serif="false" sizeM="1" size="0" style="1"/>
<caption val="—"/>
</element>
<element type="button" label="button10">
<show object="true" label="true"/>
<condition showObject="t ≟ 1 ∧ (a1 ≠ a2)"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="224" g="224" b="224" alpha="255"/>
<layer val="1"/>
<labelOffset x="482" y="116"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[c1, c1+1]"/>
<font serif="false" sizeM="1" size="0" style="1"/>
<caption val="+"/>
</element>
<element type="button" label="button11">
<show object="true" label="true"/>
<condition showObject="t ≟ 1 ∧ (a1 ≠ a2)"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="224" g="224" b="224" alpha="255"/>
<layer val="1"/>
<labelOffset x="445" y="265"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[c2, c2-1]"/>
<font serif="false" sizeM="1" size="0" style="1"/>
<caption val="—"/>
</element>
<element type="button" label="button12">
<show object="true" label="true"/>
<condition showObject="t ≟ 1 ∧ (a1 ≠ a2)"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="224" g="224" b="224" alpha="255"/>
<layer val="1"/>
<labelOffset x="485" y="265"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[c2, c2+1]"/>
<font serif="false" sizeM="1" size="0" style="1"/>
<caption val="+"/>
</element>
<expression label="text9" exp=""\frac{\;\;\;\;\;\;\;\;}{}+\frac{\;\;\;\;\;\;\;\;}{}""/>
<element type="text" label="text9">
<show object="true" label="true" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="46" y="122"/>
</element>
<command name="Textfield">
<input a0="a1"/>
<output a0="InputBox1"/>
</command>
<element type="textfield" label="InputBox1">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="58" y="150"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[a1, round(a1)] RunClickScript[button2]"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<linkedGeo exp="a1"/>
<length val="2"/>
<caption val=" "/>
</element>
<command name="Textfield">
<input a0="b1"/>
<output a0="InputBox2"/>
</command>
<element type="textfield" label="InputBox2">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="58" y="82"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[b1, round(b1)] RunClickScript[button2]"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<linkedGeo exp="b1"/>
<length val="2"/>
<caption val=" "/>
</element>
<command name="Textfield">
<input a0="a2"/>
<output a0="InputBox3"/>
</command>
<element type="textfield" label="InputBox3">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="158" y="150"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[a2, round(a2)] RunClickScript[button2]"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<linkedGeo exp="a2"/>
<length val="2"/>
<caption val=" "/>
</element>
<command name="Textfield">
<input a0="b2"/>
<output a0="InputBox4"/>
</command>
<element type="textfield" label="InputBox4">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="159" y="82"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[b2, round(b2)] RunClickScript[button2]"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<linkedGeo exp="b2"/>
<length val="2"/>
<caption val=" "/>
</element>
<expression label="A'" exp="((1 - t1) * A) + (t1 * C)" type="point" />
<element type="point" label="A'">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0" y="4.493215686274512" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="B'" exp="((1 - t2) * B) + (t2 * (C + ((b1 / a1 * l), 0)))" type="point" />
<element type="point" label="B'">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0" y="1.5216078431372562" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="text2" exp=""=\frac{" + (LaTeX[b2]) + "\red×\red" + (LaTeX[c2]) + "}{" + (LaTeX[a2]) + "\red×\red" + (LaTeX[c2]) + "}=\frac{" + (LaTeX[(b2 * c2)]) + "}{" + (LaTeX[(a2 * c2)]) + "}"" />
<element type="text" label="text2">
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<startPoint x="8.000000000000002" y="2.9800000000000035" z="1"/>
</element>
<command name="Polygon">
<input a0="{A', A' + (l, 0), A' + (l, h), A' + (0, h)}"/>
<output a0="poly5"/>
</command>
<element type="polygon" label="poly5">
<lineStyle thickness="8" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="t1 > 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{B', B' + ((b2 / a2 * l), 0), B' + ((b2 / a2 * l), h), B' + (0, h)}"/>
<output a0="poly6"/>
</command>
<element type="polygon" label="poly6">
<lineStyle thickness="7" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
</element>
<command name="Polygon">
<input a0="{A', A' + ((b1 * l / a1), 0), A' + ((b1 * l / a1), h), A' + (0, h)}"/>
<output a0="poly7"/>
</command>
<element type="polygon" label="poly7">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="t1 > 0"/>
<objColor r="0" g="0" b="255" alpha="0.3"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Polygon">
<input a0="{B', B' + ((b2 * l / a2), 0), B' + ((b2 * l / a2), h), B' + (0, h)}"/>
<output a0="poly8"/>
</command>
<element type="polygon" label="poly8">
<lineStyle thickness="0" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<condition showObject="t2 > 0"/>
<objColor r="0" g="255" b="0" alpha="0.3"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<command name="Sequence">
<input a0="Sequence[Segment[A' + ((i * l / a1) + (j * l / ((a1 * c1))), 0), A' + ((i * l / a1) + (j * l / ((a1 * c1))), h)], j, 1, c1 - 1]" a1="i" a2="0" a3="b1 - 1"/>
<output a0="list8"/>
</command>
<element type="list" label="list8">
<show object="true" label="true" ev="4"/>
<condition showObject="t1 ≟ 1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="20" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Sequence[Segment[B' + ((i * l / a2) + (j * l / ((a2 * c2))), 0), B' + ((i * l / a2) + (j * l / ((a2 * c2))), h)], j, 1, c2 - 1]" a1="i" a2="0" a3="b2 - 1"/>
<output a0="list9"/>
</command>
<element type="list" label="list9">
<show object="true" label="true" ev="4"/>
<condition showObject="t2 ≟ 1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="20" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<expression label="text1" exp=""=\frac{" + (LaTeX[b1]) + "\red×\red" + (LaTeX[c1]) + "}{" + (LaTeX[a1]) + "\red×\red" + (LaTeX[c1]) + "}=\frac{" + (LaTeX[(b1 * c1)]) + "}{" + (LaTeX[(a1 * c1)]) + "}"" />
<element type="text" label="text1">
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<startPoint x="8.000000000000002" y="6.320000000000005" z="1"/>
</element>
<expression label="text10" exp=""" + (LaTeX[fraction1]) + "" + (LaTeX[If[c1 > 1, text1, ""]]) + """ />
<element type="text" label="text10">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<absoluteScreenLocation x="395" y="23"/>
</element>
<expression label="text11" exp=""" + (LaTeX[fraction2]) + "" + (LaTeX[If[c2 > 1, text2, ""]]) + """ />
<element type="text" label="text11">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<absoluteScreenLocation x="395" y="172"/>
</element>
<command name="Segment">
<input a0="C - (0, 0.5)" a1="C - (0, 1)"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="false" ev="4"/>
<condition showObject="t1 ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0.5000000000000002" y="0" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C + ((b1 / a1 * l), -0.5)" a1="C + ((b1 / a1 * l), -1)"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="false" ev="4"/>
<condition showObject="t1 ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0.5000000000000002" y="0" z="-2.3397701149425316"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="C + ((b1 / a1 * l) + (b2 / a2 * l), -0.5)" a1="C + ((b1 / a1 * l) + (b2 / a2 * l), -1)"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="false" ev="4"/>
<condition showObject="t2 ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0.5000000000000002" y="0" z="-3.21718390804598"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Vector">
<input a0="Midpoint[g]" a1="Midpoint[i]"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="true" label="false" ev="4"/>
<condition showObject="t1 ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="4.679540229885059" y="0" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint x="0" y="-2.2" z="1"/>
</element>
<command name="Vector">
<input a0="Midpoint[i]" a1="Midpoint[g]"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="true" label="false" ev="4"/>
<condition showObject="t1 ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-4.679540229885059" y="0" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint x="4.679540229885059" y="-2.2" z="1"/>
</element>
<command name="Vector">
<input a0="Midpoint[i]" a1="Midpoint[j]"/>
<output a0="w"/>
</command>
<element type="vector" label="w">
<show object="true" label="false" ev="4"/>
<condition showObject="t2 ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="1.754827586206897" y="0" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint x="4.679540229885059" y="-2.2" z="1"/>
</element>
<command name="Vector">
<input a0="Midpoint[j]" a1="Midpoint[i]"/>
<output a0="a"/>
</command>
<element type="vector" label="a">
<show object="true" label="false" ev="4"/>
<condition showObject="t2 ≟ 1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="-1.754827586206897" y="0" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint x="6.434367816091956" y="-2.2" z="1"/>
</element>
<expression label="text12" exp=""\frac{" + (LaTeX[(b1 * c1)]) + "}{" + (LaTeX[(a1 * c1)]) + "}"" />
<element type="text" label="text12">
<show object="true" label="true" ev="40"/>
<condition showObject="t1 ≟ 1"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint exp="E"/>
<labelOffset x="-16" y="4"/>
</element>
<expression label="text14" exp=""\frac{" + (LaTeX[(b2 * c2)]) + "}{" + (LaTeX[(a2 * c2)]) + "}"" />
<element type="text" label="text14">
<show object="true" label="true" ev="40"/>
<condition showObject="t2 ≟ 1"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint exp="D"/>
<labelOffset x="-16" y="4"/>
</element>
<expression label="D" exp="C + ((b1 / a1 * l), 0) + ((b2 / a2 * l / 2), -0.75)" type="point" />
<element type="point" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="5.556954022988507" y="-2.2" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="E" exp="C + ((b1 / ((2 * a1)) * l), -0.75)" type="point" />
<element type="point" label="E">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="2.3397701149425294" y="-2.2" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<condition showObject="t ≟ 0"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="224" g="224" b="224" alpha="255"/>
<layer val="1"/>
<labelOffset x="384" y="271"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t, 0] StartAnimation[t, true]"/>
<font serif="false" sizeM="2" size="24" style="1"/>
<caption val="相加"/>
</element>
<command name="Sequence">
<input a0="Segment[A' + ((i * l / a1), 0), A' + ((i * l / a1), h)]" a1="i" a2="0" a3="b1"/>
<output a0="list6"/>
</command>
<element type="list" label="list6">
<show object="true" label="true" ev="4"/>
<condition showObject="t1 > 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="8" type="10" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Segment[B' + ((i * l / a2), 0), B' + ((i * l / a2), h)]" a1="i" a2="0" a3="b2"/>
<output a0="list7"/>
</command>
<element type="list" label="list7">
<show object="true" label="true" ev="4"/>
<condition showObject="t2 > 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="8" type="10" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Polygon[{C + ((i * l), 0), C + ((i * l) + l, 0), C + ((i * l) + l, h), C + ((i * l), h)}]" a1="i" a2="1" a3="floor(b1 / a1 + b2 / a2)"/>
<output a0="list5"/>
</command>
<element type="list" label="list5">
<show object="true" label="true" ev="4"/>
<condition showObject="t2 ≟ 1 ∧ (b1 / a1 + b2 / a2 > 1)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<listType val="polygon"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Segment">
<input a0="B'" a1="B' + ((b2 / a2 * l), 0)"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="false" ev="4"/>
<condition showObject="(t2 > 0) ∧ (t2 < 1)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0" y="1.7548275862068972" z="-2.6701594185260342"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B' + ((b2 / a2 * l), h)" a1="B' + (0, h)"/>
<output a0="m"/>
</command>
<element type="segment" label="m">
<show object="true" label="false" ev="4"/>
<condition showObject="(t2 > 0) ∧ (t2 < 1)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<coords x="0" y="-1.7548275862068972" z="5.488894239350918"/>
<lineStyle thickness="8" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="If">
<input a0="b1 / a1 + b2 / a2 ≥ 1" a1="true" a2="false"/>
<output a0="improper"/>
</command>
<element type="boolean" label="improper">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="text15" exp=""\scriptsize\text{在方格中輸入分母\\ 不大於\;30\;的真分數。}""/>
<element type="text" label="text15">
<show object="true" label="true" ev="43"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="1"/>
<absoluteScreenLocation x="4" y="3"/>
</element>
<command name="FractionText">
<input a0="b1 / a1 + b2 / a2"/>
<output a0="text19"/>
</command>
<element type="text" label="text19">
<symbolic val="true" />
<show object="false" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
</element>
<command name="FractionText">
<input a0="b1 / a1 + b2 / a2 - 1"/>
<output a0="text20"/>
</command>
<element type="text" label="text20">
<symbolic val="true" />
<show object="false" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
</element>
<element type="boolean" label="ans1">
<value val="false"/>
<show object="true" label="false" ev="3"/>
<condition showObject="(a1 * c1) ≟ (a2 * c2)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="218" y="230"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[ans2, false]"/>
</element>
<element type="boolean" label="ans2">
<value val="false"/>
<show object="true" label="false" ev="3"/>
<condition showObject="(a1 * c1) ≟ (a2 * c2) ∧ ans1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="218" y="328"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="text18" exp=""=" + (LaTeX[If[improper, If[b1 / a1 + b2 / a2 > 1, ("1" * text20), "1"], text19]]) + """ />
<element type="text" label="text18">
<show object="true" label="false" ev="11"/>
<condition showObject="(a1 * c1) ≟ (a2 * c2) ∧ ans1 ∧ ans2"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<absoluteScreenLocation x="16" y="319"/>
</element>
<command name="Sequence">
<input a0="Sequence[Segment[C + ((i * l / ((a1 * c1))) + (j * l), 0), C + ((i * l / ((a1 * c1))) + (j * l), h)], i, 1, (a1 * c1) - 1]" a1="j" a2="0" a3="If[b1 / a1 + b2 / a2 ≤ 1, 0, 1]"/>
<output a0="list10"/>
</command>
<element type="list" label="list10">
<show object="false" label="true" ev="4"/>
<condition showObject="(a1 * c1) ≟ (a2 * c2) ∧ t ≟ 1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="20" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<expression label="text17" exp=""\frac{" + (LaTeX[(b1 * c1)]) + "}{" + (LaTeX[(a1 * c1)]) + "}+\frac{" + (LaTeX[(b2 * c2)]) + "}{" + (LaTeX[(a2 * c2)]) + "}"" />
<element type="text" label="text17">
<show object="false" label="false" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<absoluteScreenLocation x="14" y="216"/>
</element>
<expression label="text21" exp=""=" + (LaTeX[If[ans1, text17, ""]]) + """ />
<element type="text" label="text21">
<show object="true" label="false" ev="43"/>
<condition showObject="(a1 * c1) ≟ (a2 * c2)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
<absoluteScreenLocation x="14" y="218"/>
</element>
<element type="button" label="button2">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelOffset x="111" y="431"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[t, 0] SetValue[ans1, false] SetValue[c1, 1] SetValue[c2, 1] SetValue[B, C + (0, 1.85h)] SetValue[A, B + (0, 1.85h)]"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="重設"/>
</element>
</construction>
</geogebra>