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} $$

  • Or we could apply the negative symbol to the numerator. It would stand for the same value: $$ \\frac{-5}{15} $$

Therefore:

Let \(a,b\) be 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: $$ \frac{- 12xy^2}{ - 18xy^2} = \frac{12xy^2}{18xy^2}$$

logo