38 lines
1.2 KiB
Markdown
38 lines
1.2 KiB
Markdown
---
|
|
categories:
|
|
- Mathematics
|
|
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: $$ \frac{- 12xy^2}{ - 18xy^2} = \frac{12xy^2}{18xy^2}$$
|