Percentage Word Problems: Comparing Two Numbers
2019-02-15 09:55
This GeoGebra example visually demonstrates comparing two numbers in percentage word problems. By utilizing geometric constructions like polygons and line segments, it translates abstract percentage ratios into visual lengths. This helps students intuitively understand percentages and master comparison methods, making it an excellent tool for math education.
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<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="12" style="0"/>
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<expression label="text2" exp=""B佔全部的：\frac{" + (LaTeX[b]) + " }{ " + (LaTeX[a]) + " +" + (LaTeX[b]) + " } × 100% = \frac{" + (LaTeX[b]) + " }{ " + (LaTeX[a + b]) + " } × 100% = " + (LaTeX[(b / (a + b) * 100)]) + "%"" />
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<show object="true" label="true" ev="8"/>
<condition showObject="B ≟ (5, 2)"/>
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<expression label="text5" exp=""A比B多佔全部的, 或B比A少佔全部的：

\frac{" + (LaTeX[a]) + "−" + (LaTeX[b]) + "}{" + (LaTeX[a]) + "+" + (LaTeX[b]) + "} × 100% = \frac{" + (LaTeX[a - b]) + "}{" + (LaTeX[a + b]) + "} × 100% = " + (LaTeX[((a - b) / (a + b) * 100)]) + "%"" />
<element type="text" label="text5">
<show object="true" label="true" ev="8"/>
<condition showObject="B ≟ (5, 2)"/>
<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="2" size="12" style="0"/>
<startPoint x="0.0600000000000005" y="-3.06" z="1"/>
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<expression label="text4" exp=""A比B多：\frac{" + (LaTeX[a]) + "−" + (LaTeX[b]) + "}{" + (LaTeX[b]) + "} × 100%= \frac{" + (LaTeX[a - b]) + "}{" + (LaTeX[b]) + "} × 100% = " + (LaTeX[((a - b) / b * 100)]) + "% "" />
<element type="text" label="text4">
<show object="true" label="true" ev="8"/>
<condition showObject="A ≟ (6, 3)"/>
<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="2" size="12" style="0"/>
<startPoint x="0.05999999999999894" y="-2.0599999999999996" z="1"/>
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<expression label="text7" exp=""A是B的：\frac{" + (LaTeX[a]) + "}{" + (LaTeX[b]) + "} × 100%=1 \frac{" + (LaTeX[a - b]) + "}{" + (LaTeX[b]) + "} × 100% = " + (LaTeX[100 + ((a - b) / b * 100)]) + "%"" />
<element type="text" label="text7">
<show object="true" label="true" ev="8"/>
<condition showObject="A ≟ (6, 3)"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="12" style="0"/>
<startPoint x="0.0600000000000005" y="-0.06000000000000005" z="1"/>
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</construction>
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