# In a mall, 1/15 of the stores sell shoes. There are 180 stores in the mall. How many of the stores sell shoes?

$x = 12$

#### Explanation:

A ratio question! Let's look first at what we're trying to find.

We have a mall and the mall has 180 stores. We want to know how many of them sell shoes. What we're told is that $\frac{1}{15}$ of them do - so in essence, we're given the reduced fraction, and we're asked to find the unreduced fraction. So we can say this:

$\text{reduced fraction"="unreduced fraction}$

$\frac{1}{15} = \frac{x}{180}$

We can now proceed a few different ways. One way is to cross-multiply the fractions, so we'd get:

$15 x = 180$

$x = 12$

Another way we could go would be to multiply the fraction on the left by a form of 1 to make it equal the right:

$\frac{1}{15} = \frac{1}{15} \left(1\right) = \frac{1}{15} \left(\frac{12}{12}\right) = \frac{12}{180}$ and so we know that $x = 12$ (this method only works well if we know that x is an integer!)