# Practice with the Form $\,a\cdot\frac{b}{c}$

One pattern that arises frequently in working with fractions is: $$a\cdot \frac{b}{c}$$

It's important to realize that this expression can be written in many different ways:

Note that a factor in the numerator
can optionally be centered next to the fraction.
If *everything* is moved out of the
numerator, then a $\,1\,$ is inserted as a ‘placeholder’.

A factor centered next to the fraction can be moved into the numerator. A factor in the denominator must stay in the denominator.

## Examples

*do*exist

*choices*for which these two expressions give the same value: when $\,a = 0\,,$ or $\,b = 1\,,$ or $\,b = -1\,.$ However, for all other values of $\,b\,$ (and $\,a\ne 0\,$), they are not equal.

## Practice

Assume that all variables are nonzero, so there's no concern about division by zero.