# How do you simplify (20+4)div(-1)?

Apr 17, 2015

Recall the definition of an operation of division:
The result of division of number $X$ by number $Y$ is such a number $Z$ that, if multiplied by $Y$, produces $X$.

Based on this definition, the answer to this problem is $- 24$ because
$\left(- 24\right) \cdot \left(- 1\right) = 20 + 4$

Here are a few important logical steps to come up with this result.

1. Operations in parenthesis are performed prior to others. Therefore, $\frac{\left(20 + 4\right)}{- 1}$ can be safely replaced with $\frac{24}{- 1}$.

2. $\frac{X}{- Y} = - \frac{X}{Y}$ because $\left(- \frac{X}{Y}\right) \cdot \left(- Y\right) = \left(\frac{X}{Y}\right) \cdot Y = X$
Therefore, $\frac{24}{-} 1 = - 24$