integration - Justification for $u$-substitution method

I am currently learning how to find antiderivatives using the "$u$-substitution" or "integration by substitution" method. A key component of this is setting some expression in the indefinite integral as "$u$", and then also finding $du/dx$.

How can we then write $du = dx \cdot$ (some expression)? Isn't $du/dx$ defined as the derivative of $u$ and is not a fraction?