46 lines
1.2 KiB
Markdown
46 lines
1.2 KiB
Markdown
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---
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tags:
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- prealgebra
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- fractions
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---
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# Negative fractions
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To work with negative fractions we draw on the
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[Rules for operations on like and unlike terms](Rules%20for%20operations%20on%20like%20and%20unlike%20terms.md).
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## Fractions with unlike terms
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- A fraction is just one number divided by another. $\frac{5}{10}$ is just ten
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divided by 5.
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- A positive integer divided by a negative or vice versa will always result in a
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negative. Thus $\frac{5}{-15}$ is equal to $-3$.
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- We can therefore express the whole fraction as a negative:
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$$
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- \frac{5}{15}
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$$
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- Or we could apply the negative symbol to the numerator. It would stand for the
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same value:
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$$
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\\frac{-5}{15}
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$$
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Therefore:
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> Let $a,b$ be any integers. The following three fractions are
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> [equivalent](Equivalent%20fractions.md):
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> $$\frac{-5}{15}, \frac{5}{-15}, - \frac{5}{15}$$
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## Fractions with like terms
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- In cases where both the numerator and denominator are both negative, the value
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that the fraction represents will be positive overall. This is because the
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quotient of a negative integer divided by a negative integer will always be
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positive.
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- Thus: $$ \frac{- 12xy^2}{ - 18xy^2} = \frac{12xy^2}{18xy^2}$$
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