Geometric Demonstration of Fraction Addition
2016-10-30 10:54
This GeoGebra applet dynamically demonstrates the calculation process and geometric intuition of fraction addition. By using polygons or segments to visually represent fractions, combined with the FractionText command, it illustrates the principles of finding a common denominator and adding numerators. It is an excellent tool for math education, helping students understand the geometric meaning an
In collections
小四_分數
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<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"/>
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<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)"/>
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<lineStyle thickness="8" type="0" typeHidden="1"/>
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<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)"/>
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<lineStyle thickness="8" type="0" typeHidden="1"/>
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<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{Input proper fractions in the \\ boxes with denominators≤30.}""/>
<element type="text" label="text15">
<show object="true" label="true" ev="43"/>
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<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<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"/>
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<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"/>
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<font serif="false" sizeM="1" size="0" style="0"/>
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<element type="boolean" label="ans1">
<value val="false"/>
<show object="true" label="false" ev="3"/>
<condition showObject="(a1 * c1) ≟ (a2 * c2)"/>
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<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"/>
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<checkbox fixed="true"/>
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<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"/>
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<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
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<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]"/>
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</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"/>
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<lineStyle thickness="3" type="20" typeHidden="1"/>
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<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)"/>
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<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="10" style="0"/>
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<element type="button" label="button2">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
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<labelMode val="3"/>
<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="Reset"/>
</element>
</construction>
</geogebra>