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

Jun 12, 2017

See a solution process below:

#### Explanation:

First, rewrite this expression as:

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

We can now use this rule for dividing fractions to simplify the expression:

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

$\frac{\frac{\textcolor{red}{- 1}}{\textcolor{b l u e}{9}}}{\frac{\textcolor{g r e e n}{- 3}}{\textcolor{p u r p \le}{1}}} = \frac{\textcolor{red}{- 1} \times \textcolor{p u r p \le}{1}}{\textcolor{b l u e}{9} \times \textcolor{g r e e n}{- 3}} = \frac{- 1}{-} 27 = \frac{1}{27}$

Jun 12, 2017

$+ \frac{1}{27}$

#### Explanation:

$\textcolor{b l u e}{\text{Dealing with just the numbers}}$

A quick note about the short cut approach used:

It is both correct and permissible to write 3 as $\frac{3}{1}$

For divide the rule is: Turn upside down what you were dividing by and then multiply.

So you turn $\frac{3}{1}$ upside down giving $\frac{1}{3}$ and then multiply giving:

$\frac{1}{9} \div \frac{3}{1} \text{ "->" } \frac{1}{9} \times \frac{1}{3}$

So, ignoring the signs for the moment the numbers are:

$\frac{1}{9} \times \frac{1}{3} \text{ "=" "(1xx1)/(9xx3)" "=" } \frac{1}{27}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Dealing with the signs.}}$

$\textcolor{b r o w n}{\text{For multiply or divide}}$

$\text{ }$If the signs are the same the answer is positive.
$\text{ }$If the signs are different then the answer is negative

In this question the signs are the same so the answer is positive thus we have:

$+ \frac{1}{27}$