# How do you simplify 5.2-2.09?

Dec 16, 2016

I got $3.11$

#### Explanation:

I would write it as:

$\frac{520}{100} - \frac{209}{100} = \frac{520 - 209}{100} = \frac{311}{100} =$

dividing by $100$ we get (moving the point from right to left):

$\frac{311}{100} = 3.11$

Dec 16, 2016

$3.11$

#### Explanation:

Consider the 0.2 from 5.2

But this is the same as $\frac{2}{10}$ and can be written as:

$0.2 = \frac{1}{10} + \left[\frac{1}{10} \textcolor{g r e e n}{\times 1}\right]$

$0.2 = \frac{1}{10} + \left[\frac{1}{10} \textcolor{g r e e n}{\times \frac{10}{10}}\right]$

$0.2 = \frac{\textcolor{m a \ge n t a}{1}}{10} + \left[\frac{\textcolor{m a \ge n t a}{10}}{100}\right]$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
How is this translated into something we can use? Do this:

$5.20$
$\underline{2.09} \leftarrow \text{ subtract}$

$5. {\cancel{2}}^{\textcolor{m a \ge n t a}{1}} {\cancel{0}}^{\textcolor{m a \ge n t a}{10}}$
$\underline{2. \textcolor{w h i t e}{.} 0 \textcolor{w h i t e}{.} 9} \leftarrow \text{ subtract}$
$3. \textcolor{w h i t e}{.} 1 \textcolor{w h i t e}{.} 1$