# Are these two equations equivalent? Thanks. (nx)/d xx x = (xn)/d xx y

Sep 6, 2017

See explanation.

#### Explanation:

First thing. There is only one equation there.

To see if the expressions are equivalent let's look at both of them.

First part is:

## $\frac{n x}{d}$ and  (xn)/d

Those expressions are equivalent because the result of multiplication does not depend on the order of multiplied values.

But on the left side the expression is multiplied by $x$, while on the right side it's multiplied by $y$, so they would be equivalent if and only if $x = y$

Sep 6, 2017

$x = y$ $: \frac{n}{d} \ne 0$

#### Explanation:

$\frac{n x}{d} \times x = \frac{x n}{d} \times y$

First, this is one equation not two.

Since $n x = x n$ and assuming $\frac{n}{d} \ne 0$

$\cancel{\frac{n x}{d}} \times x = \cancel{\frac{x n}{d}} \times y$

$\therefore x = y$