# Question #cd69e

Oct 14, 2016

Yes, the answer will be positive.

#### Explanation:

The quotient of any two negative real numbers will be positive. Mixed numbers, fractions, and decimals are all just different ways of writing down a given value. For example, $1 \frac{1}{2} = \frac{3}{2} = 1.5$. How you write it down does not change the rules you apply when performing operations.

Given any $a > 0$ and $b > 0$, we have

$\frac{- a}{- b} = \frac{- 1 \cdot a}{- 1 \cdot b} = \frac{- 1}{- 1} \cdot \frac{a}{b} = 1 \cdot \frac{a}{b} = \frac{a}{b} > 0$

For the given exercise of $- 2 \frac{2}{3} \div - \frac{1}{2}$, we have

$- 2 \frac{2}{3} \div - \frac{1}{2} = \frac{- 2 \frac{2}{3}}{- \frac{1}{2}}$

$= \frac{- \frac{8}{3}}{- \frac{1}{2}}$

$= \frac{- 1}{- 1} \cdot \frac{\frac{8}{3}}{\frac{1}{2}}$

$= \frac{\frac{8}{3}}{\frac{1}{2}}$

$= \frac{\frac{8}{3} \cdot 2}{\frac{1}{2} \cdot 2}$

$= \frac{16}{3}$