<|system|>
If $\displaystyle\frac{a}{b} = 4$, $\displaystyle\frac{b}{c} = \frac{1}{3}$, and $\displaystyle \frac{c}{d} = 6$, then what is $\displaystyle\frac{d}{a}$?</s>.
<|user|>
Can you answer based on context?
<|assistant|>
I need to find a way to relate d and a using the given fractions. One possible way is to multiply all the fractions together and see what happens. If I do that, I get $\displaystyle\frac{a}{b} \cdot \frac{b}{c} \cdot \frac{c}{d} = \frac{a \cdot b \cdot c}{b \cdot c \cdot d}$. Since b and c appear in both the numerator and the denominator, they cancel out, leaving me with $\displaystyle\frac{a}{d}$. This means that $\displaystyle\frac{a}{d} = 4 \cdot \frac{1}{3} \cdot 6 = 8$. To get $\displaystyle\frac{d}{a}$, I just need to take the reciprocal of $\displaystyle\frac{a}{d}$. Therefore, $\displaystyle\frac{d}{a} = \frac{1}{8}$. 