### Instruction: Solve for $w$ and express as a common fraction: $\frac{1\frac16}w=\frac{42}3$.### Response: This problem involves fractions and mixed numbers, so I want to convert them to improper fractions to make the calculations easier.
To do that, I multiply the whole number by the denominator and add the numerator, so 1 1/6 becomes $\frac{6+1}{6}=\frac{7}{6}$.
Similarly, 42/3 becomes $\frac{42}{3}=\frac{42}{3}$.
Now I have the equation $\frac{7}{6w}=\frac{42}{3}$.
To solve for $w$, I want to isolate it on one side of the equation.
I can do that by cross-multiplying, which means multiplying the numerator of one fraction by the denominator of the other, and vice versa.
So I get $7\times 3=42\times 6w$, which simplifies to $21=252w$.
To get $w$ by itself, I need to divide both sides by 252, so $w=\frac{21}{252}$.
But this fraction can be simplified further by dividing the numerator and denominator by their greatest common factor, which is 21.
So $w=\frac{21}{252}=\frac{1}{12}$.