eolas/zk/Handling_negative_fractions.md

---
tags:
  - prealgebra
  - fractions
---

# Negative fractions

To work with negative fractions we draw on the
[Rules for operations on like and unlike terms](Rules%20for%20operations%20on%20like%20and%20unlike%20terms.md).

## 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](Equivalent%20fractions.md):
> $$\frac{-5}{15}, \frac{5}{-15}, - \frac{5}{15}$$

## 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: $$ \frac{- 12xy^2}{ - 18xy^2} = \frac{12xy^2}{18xy^2}$$