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