# Is the quotient 4.5 -: .9 greater or less than 4.5? Why?

$\frac{4.5}{.9} > 4.5$ because $\frac{4.5}{.9}$ is equivalent to 5.

#### Explanation:

Is $\frac{4.5}{.9} > 4.5$ or is $\frac{4.5}{.9} < 4.5$?

Let's think this way - we know that:

$\frac{4.5}{1} = 4.5$

If we split 4.5 into two pieces, that's:

$\frac{4.5}{2} = 2.25$

and if we split 4.5 into ten pieces, that's:

$\frac{4.5}{10} = .45$

So what are we saying when we have $\frac{4.5}{.9}$? It means that we don't have a complete piece - it's .1 short of a complete piece. So how big is a whole piece?

$\frac{4.5}{.9} = \frac{\frac{4.5}{1}}{\frac{9}{10}} = \left(\frac{4.5}{1}\right) \left(\frac{10}{9}\right) = \frac{45}{9} = 5$

And so $\frac{4.5}{.9} > 4.5$ because $\frac{4.5}{.9}$ is equivalent to 5.