help with math

The area of the floor is  11.5 x 9.5  =  109.25 square feet.

The area of each tile is:  0.5 x 0.5  =  0.25 square feet.

Dividing  109.25  by  0.25  gives an answer of  437  tiles.

Here's a third explanation lol 

How many pairs of apples are there in a batch of 10 apples? 10 ÷ 2 = 5 pairs of apples

How many $\frac12\times\frac12=\frac14$ square feet tiles are there in $11\frac12\times9\frac12 = \frac{437}{4}$ square feet?

$\frac{437}{4} \div \frac14 =\frac{437}{4}\times\frac41=437$ one-fourth square feet, or tiles