# What is 50 divided by 18?

Dec 13, 2016

In whole number arithmetic:

$\frac{50}{18} = 2$ with remainder $14$

Otherwise:

$\frac{25}{9}$, $\text{ "2 7/9" }$ or $\text{ } 2.777 \ldots = 2. \overline{7}$

#### Explanation:

If you are talking about whole number arithmetic then:

$\frac{50}{18} = 2 \text{ }$ with remainder $14$

As an "improper" fraction:

$\frac{50}{18} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 25}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 9} = \frac{25}{9}$

As a mixed fraction:

$\frac{50}{18} = \frac{36 + 14}{18} = \frac{36}{18} + \frac{14}{18} = 2 + \frac{7}{9} = 2 \frac{7}{9}$

To find a decimal representation, use long division:

$\textcolor{w h i t e}{1080 \text{)}} \underline{\textcolor{w h i t e}{000} 2 \textcolor{b l a c k}{.} 7 \textcolor{w h i t e}{0} 7 \textcolor{w h i t e}{0} 7 \textcolor{w h i t e}{0} \ldots}$
$1 \textcolor{w h i t e}{0} 8 \textcolor{w h i t e}{0} \text{)} \textcolor{w h i t e}{0} 5 \textcolor{w h i t e}{0} 0 \textcolor{b l a c k}{.} 0 \textcolor{w h i t e}{0} 0 \textcolor{w h i t e}{0} 0 \textcolor{w h i t e}{0} \ldots$
color(white)(1080")"0)underline(3color(white)(0)6
$\textcolor{w h i t e}{1080 \text{)} 0} 1 \textcolor{w h i t e}{0} 4 \textcolor{w h i t e}{.} 0$
$\textcolor{w h i t e}{1080 \text{)} 0} \underline{1 \textcolor{w h i t e}{0} 2 \textcolor{w h i t e}{.} 6}$
$\textcolor{w h i t e}{1080 \text{)} 000} 1 \textcolor{w h i t e}{.} 4 \textcolor{w h i t e}{0} 0$
$\textcolor{w h i t e}{1080 \text{)} 000} \underline{1 \textcolor{w h i t e}{.} 2 \textcolor{w h i t e}{0} 6}$
$\textcolor{w h i t e}{1080 \text{)} 0000} \textcolor{w h i t e}{.} 1 \textcolor{w h i t e}{0} 4 \textcolor{w h i t e}{0} 0$
$\textcolor{w h i t e}{1080 \text{)} 0000} \textcolor{w h i t e}{.} \underline{1 \textcolor{w h i t e}{0} 2 \textcolor{w h i t e}{0} 6}$
$\textcolor{w h i t e}{1080 \text{)} 0000} \textcolor{w h i t e}{.} \textcolor{w h i t e}{00} 1 \textcolor{w h i t e}{0} 4$

The remainder starts to repeat, and so does the quotient.

So:

$\frac{50}{18} = 2.777 \ldots = 2. \overline{7}$