If $\dfrac{12}{z}=60$, what is the value of $z$?

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Write both sides in fractional form and cross multiply.

$$\frac{12}{z}=60$$ $$\frac{12}{z}\xcancel{=}\frac{60}{1}$$ $$60(z)=12(1) \tag*{\tiny divide by 60 on both sides}$$ $$z=\frac{12}{60} \tag*{\tiny simplify}$$ $$\boxed{z=\frac{1}{5}}$$

Take the reciprocal of both sides. This is basically a shortcut that uses the method shown in approach 1.

$$\frac{12}{z}=60$$ $$\frac{z}{12}=\frac{1}{60} \tag*{\tiny multiply both sides by 12}$$ $$\boxed{z=\frac{1}{5}}$$