### Instruction: Simplify $\dfrac{111}{9999} \cdot 33.$.### Response: I notice that both 111 and 9999 are divisible by 9, so I can simplify the fraction by canceling out a factor of 9 from the numerator and the denominator.
This gives me $\dfrac{37}{3333} \cdot 33.$
Now I can multiply 37 by 33 and get 1221.
Then I can divide 1221 by 3333 and get a decimal approximation.
I can use long division or a calculator to find the decimal approximation.
I get about 0.3663366...
I could also write this as a fraction in lowest terms, which would be $\dfrac{1221}{3333}.$