How do you evaluate 4,009\div 5?

Apr 12, 2017

$801.8$

Explanation:

$\textcolor{b l u e}{\text{Method 1 - a traditional approach}}$

Really this is long division but perhaps in a different format to what you are used to seeing.

Starting point: Note that $5 \times 8 = 40$ and 4 is the first digit on the left.

$\text{ } 4009$
$\textcolor{m a \ge n t a}{800} \left(5\right) \to \underline{4000} \leftarrow \text{ subtract}$
$\text{ } 9$
$\textcolor{m a \ge n t a}{\textcolor{w h i t e}{. .} 1} \left(5\right) \to \textcolor{w h i t e}{000} \underline{5} \leftarrow \text{ subtract}$
$\text{ } 4$
$\textcolor{m a \ge n t a}{\textcolor{w h i t e}{.} \frac{4}{5}} \left(5\right) \to \text{ "ul(4) larr" subtract}$
$\text{ "0 larr" as this is 0 we stop. No remainder}$

So the answer is: color(magenta)(800+1+4/5 = 801 4/5

But $\frac{4}{5} \to \frac{8}{10} = 0.8 \text{ }$ giving: $\text{ } \textcolor{m a \ge n t a}{801.8}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Method 2 -A sort of non calculator cheat method}}$

$\div 5$ is the same as $\times \frac{1}{5}$

But $\frac{1}{5}$ is the same as $\text{ } 2 \times \frac{1}{10}$

So write $4009 \times \frac{1}{5} \text{ }$ as $\text{ } 4009 \times 2 \times \frac{1}{10}$

$= 8018 \times \frac{1}{10} = 801.8$