37 lines
1,007 B
Markdown
37 lines
1,007 B
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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- divisors
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---
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Given the equivalence between factors and divisors we can increase fractions to higher terms in a very similar way to when we reduce fractions. In the latter case we are dividing by divisors to reduce. In the former, we are multiplying by factors to increase.
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>
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> Whenever we increase a fraction, the resultant fraction will always be [equivalent](Equivalent%20fractions.md) to the fraction we started with.
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## Demonstration
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*Express $\frac{3}{4}$ as an equivalent fraction having the denominator 20*
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$$
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\\frac{3 \cdot 4}{5 \cdot 4} = \frac{12}{20}
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$$
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*Express $\frac{2}{3}$ as an equivalent fraction having the denominator 21*
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$$
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\\frac{2 \cdot 7}{3 \cdot 7} = \frac{14}{21}
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$$
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## Increasing fractions with variables to higher terms
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*Express $\frac{2}{9}$ as an equivalent fraction having the denominator 18a*
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In these cases, just append the variable to the factor:
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$$
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\\frac{2 \cdot 2a}{9 \cdot 2a} = \frac{4a}{18a}
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$$
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