How can we prove that $\frac{a}{b }\times\frac{c}{d} =\frac{ac}{bd}$ I am slowly reading calculus by michael spivak and it is one of the problems in first chapter.
however I cant prove it please help me with it...

To see that equality holds, we will write the elements $\frac1b$ and $\frac1d$ as $b^{-1}$ and $d^{-1}$, respectively. Thus
\begin{align*}
\frac ab\cdot\frac cd&=(a\cdot b^{-1})\cdot(c\cdot d^{-1})\\
&=(a\cdot c)\cdot(b^{-1}\cdot d^{-1})\\
&=(a\cdot c)\cdot(b\cdot d)^{-1}\\
&=\frac{ac}{bd}.
\end{align*}
The second line uses the associative and commutative properties of multiplication.
