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: $$frac-515$$

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: $$\frac{-12x{y}^2}{-18x{y}^2}=\frac{12x{y}^2}{18x{y}^2}$$