# How do you simplify  [6 div (-3)]div [-1/9]?

Jan 7, 2017

Rewrite as a fraction over a fraction and then use the rule for dividing fractions. See full explanation below:

#### Explanation:

We can rewrite this expression as:

$\frac{\frac{6}{- 3}}{\frac{- 1}{9}}$

Next, we can simplify this expresion by using the rule for dividing fractions which states:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

Substituting this for our expression gives:

$\frac{\textcolor{red}{6} \times \textcolor{p u r p \le}{9}}{\textcolor{b l u e}{- 3} \times \textcolor{g r e e n}{- 1}}$

$\frac{54}{3}$

$18$

Jan 7, 2017

18

#### Explanation:

Shortcut method for divide is turn the divisor upside down and then multiply instead.

When multiplying or dividing (for two numbers), if the signs are the same then the answer is positive. If not the same then the answer is negative.

Given:$\text{ } \left[6 \div \left(- 3\right)\right] \div \left[- \frac{1}{9}\right]$

Write as:$\text{ } \left[+ \frac{6}{1} \div \left(- \frac{3}{1}\right)\right] \div \left[- \frac{1}{9}\right]$
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$\textcolor{b l u e}{\text{Dealing with the first brackets}}$

Consider the part $\text{ } \left[+ \frac{6}{1} \div \left(- \frac{3}{1}\right)\right]$

The signs are different so the answer for this part is negative. Turn the $\frac{3}{1}$ upside down and multiply. Giving:

$- \left[\frac{6}{1} \times \frac{1}{3}\right] = - \left[\frac{6 \times 1}{1 \times 3}\right] = - \frac{6}{3} = - 2$
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$\textcolor{b l u e}{\text{Putting it all back together}}$

$- 2 \div \left[- \frac{1}{9}\right]$
The signs are the same so the answer for this bit is positive.
Turn the $\frac{1}{9}$ upside down and multiply.

$+ \left(\frac{2}{1} \times \frac{9}{1}\right) = + \left(\frac{2 \times 9}{1 \times 1}\right) = + \frac{18}{1} = + 18$

$\textcolor{b l u e}{\text{The final answer is } + 18}$