Reduce to lowest terms:

`NEG1S` \dfrac{`N1`}{`D1`} \div `NEG2S` \dfrac{`N2`}{`D2`} = {?}

Dividing by a fraction is the same as multiplying by the reciprocal.

The reciprocal of

is `NEG2S` \dfrac{`N2`}{`D2`}

. We just flipped the numerator and denominator.
`NEG2S` \dfrac{`D2`}{`N2`}

Since multiplying by the reciprocal is the same as dividing, lets use the reciprocal to change the problem into a multiplication problem:

```
\begin{eqnarray}
```

`NEG1S` \frac{`N1`}{`D1`} \color{`GREEN`}{\div `NEG2S` \frac{`N2`}{`D2`}}
& \qquad = \qquad &
`NEG1S` \frac{`N1`}{`D1`} \color{`BLUE`}{\times `NEG2S` \frac{`D2`}{`N2`}}
\end{eqnarray}

Because we're now multiplying fractions instead of dividing them, all we have to do is multiply the numerators and the denominators:

```
\begin{eqnarray}
\hphantom{
```

`NEG1S` \frac{`N1`}{`D1`} \div \color{`GREEN`}{`NEG2S` \frac{`N2`}{`D2`}}}
& \qquad = \qquad &
\dfrac{`NEG1S` `N1` \times \color{`BLUE`}{`NEG2S` `D2`}}{`D1` \times \color{`BLUE`}{`N2`}}
\end{eqnarray}

We could just multiply everything to get `\frac{`

and then try to reduce that to get the final answer, but it's easier if we can find and reduce some common factors before we multiply.
`NEG1 * NEG2 * N1 * D2`}{`N2 * D1`}

In this case, we can divide the

in the numerator and the `NEG2 * D2`

in the denominator by `D1`

:`GCD2`

```
\begin{eqnarray}
\hphantom{
```

`NEG1S` \frac{`N1`}{`D1`} \div \color{`GREEN`}{`NEG2S` \frac{`N2`}{`D2`}}}
& \qquad = \qquad &
\dfrac{`NEG1S` `N1` \times \color{`PINK`}{\cancel{\color{`BLUE`}{`NEG2S` `D2`}}^{`NEG2S``SIMP_D2`}}}{\color{`PINK`}{\cancel{\color{black}{`D1`}}^{`SIMP_D1`}} \times \color{`BLUE`}{`N2`}} \\ \\
& \qquad = \qquad &
\dfrac{`NEG1S` `N1` \times \color{`PINK`}{`NEG2S``SIMP_D2`}}{\color{`PINK`}{`SIMP_D1`} \times \color{`BLUE`}{`N2`}}
\end{eqnarray}

After reducing the common factors, it's easier to multiply and get the simplified answer:

```
\begin{eqnarray}
\hphantom{\color{gray}{
```

`NEG1S` \frac{`N1`}{`D1`} \div `NEG2S` \frac{`N2`}{`D2`}}}
& \qquad = \qquad &
`fractionReduce(NEG1 * N1 * NEG2 * D2, D1 * N2)`
\end{eqnarray}

Just multiply to get the final answer. Double-check that it's simplified:

```
\begin{eqnarray}
\hphantom{\color{gray}{
```

`NEG1S` \frac{`N1`}{`D1`} \div `NEG2S` \frac{`N2`}{`D2`}}}
& \qquad = \qquad &
`fractionReduce(NEG1 * N1 * NEG2 * D2, D1 * N2)`
\end{eqnarray}