Calculating equilibrium constants: adding two or more equations
This is a direct result from the law of mass action.

When you have an equilibrium

$$\ce{A &lt;=&gt; B}$$  

with the equilibrium constant 

$$K_1=\frac {[\ce{B}]}{[\ce{A}]}\tag1$$

and a second equilibrium

$$\ce{B &lt;=&gt; C}$$  

with the equilibrium constant 

$$K_2=\frac {[\ce{C}]}{[\ce{B}]}\tag2$$

you can combine both chemical equations:

$$\begin{align}
\ce{A \;&amp;&lt;=&gt; B}\\
\ce{B \;&amp;&lt;=&gt; C}\\
\hline
\ce{A \;&amp;&lt;=&gt; C}
\end{align}$$

Then you can rearrange Equation $\text(1)$

$$\begin{align}
K_1&amp;=\frac {[\ce{B}]}{[\ce{A}]}\tag1\\[6pt]
\Leftrightarrow [\ce{B}]&amp;=K_1\cdot[\ce{A}]
\end{align}$$

and substitute $[\ce{B}]$ in Equation $\text(2)$

$$\begin{align}
K_2&amp;=\frac {[\ce{C}]}{[\ce{B}]}\tag2\\[6pt]
K_2&amp;=\frac {[\ce{C}]}{K_1\cdot[\ce{A}]}\\[6pt]
\Leftrightarrow K_1\cdot K_2&amp;=\frac {[\ce{C}]}{[\ce{A}]}
\end{align}$$

Thus the equilibrium constant for the combined equilibrium is the product $K_2\cdot K_1$.