# How do you simplify 2/5 div 10?

Jul 8, 2016

$\frac{1}{25}$

#### Explanation:

$\frac{2}{5} \div 10$

In reality you would solve this in 1 or 2 lines using shortcuts. I am only going to do so in part so that I can demonstrate something called the property of being 'commutative'.

The short cut bit.

Write as:$\text{ } \frac{2}{5} \div \frac{10}{1}$

Turn the $\frac{10}{1}$ upside down and multiply.

$\implies \frac{2}{5} \times \frac{1}{10}$

$= \frac{2 \times 1}{5 \times 10}$

Swap the 5 and 10 in the denominator round
(commutative$\to 5 \times 10 \text{ "=" "50" "=" } 10 \times 5$)

$= \frac{2 \times 1}{10 \times 5}$

$= \frac{{\cancel{2}}^{1}}{{\cancel{10}}^{5}} \times \frac{1}{5}$

$= \frac{1}{5} \times \frac{1}{5} = \frac{1}{25}$