I would like confirmation that my understanding of a congruence of two fractions is correct.

Suppose we have 

$$\frac{2}{3} \equiv \frac{4}{6}\mod 5$$ 

What happened was multiplying both the numerator and denominator of the left fraction by $2$. 

So $\frac{2}{3}$ is essentially the same as $3x\equiv 2 \mod 5$ and we can multiply both sides by $2$ since that is valid in modular arithmetic we get $6x \equiv 4\mod 5$ and rewriting that as a fraction we get $\frac{4}{6}$.

A fraction really represents that $x$ and since that $x$ remains unchanged via such manipulations then those fractions are essentially congruent. 

Of course I am aware this is true only for valid fractions, i.e. where the denominator is invertible mod $5$.

Is my understanding of this correct?