# Do 10 divide by 0 and 0 divide by 10 have the same answer?

Jun 9, 2016

No.

$\frac{10}{0}$ is UNDEFINED

$\frac{0}{10} = 0$

#### Explanation:

Start from a definition of an operation of division.
$a$ divided by $b$ is such a number $c$ that $a = b \cdot c$.

So, $\frac{10}{0}$ must be such a number that, if multiplied by $0$, gives $10$. But any number multiplied by $0$ gives $0$, not $10$.
Therefore, $\frac{10}{0}$ is UNDEFINED.

Next, $\frac{0}{10}$ is a number that, if multiplied by $10$, gives $0$. The only number with such a property is $0$ because $0 \cdot 10 = 0$. Any other number, multiplied by $10$, will not result in $0$.
Therefore, $\frac{0}{10} = 0$.