44 lines
1 KiB
Markdown
44 lines
1 KiB
Markdown
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---
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tags:
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- Mathematics
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- Prealgebra
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- fractions
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---
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Two fractions are equivalent if they represent the same value.
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To begin with we can represent this visually:
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*Each shaded area is taking up the same proportion of the whole.*
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The same properties can be represented arithmetically by multiplying the numerator and denominator at each step by 2. Thus:
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$$
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\\frac{1 (\cdot 2)}{3 (\cdot 2)} = \frac{2}{6}
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$$
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Therefore the following rule obtains:
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>
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> If you start with a fraction and multiply both its numerator and denominator by the same value, the resulting fraction is equivalent to the original fraction.
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$$
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\\frac{a}{b} = \frac{a \cdot x}{b \cdot x}
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$$
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This process works in reverse when we invert the operator and use division:
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$$
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\\frac{2 (/ 2)}{6 (/ 2)} = \frac{1}{3}
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$$
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Thus:
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>
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> If you start with a fraction and divide both its numerator and denominator by the same value, the resulting fraction is equivalent to the original fraction.
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$$
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\\frac{a}{b} = \frac{a / x}{b / x}
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$$
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