Task 1. Represent in the form of an irreducible fraction

$$
6 \frac{16}{2015} \times 9 \frac{17}{2016}-2 \frac{1999}{2015} \times 17 \frac{1999}{2016}-27 \times \frac{16}{2015}
$$
Answer: $17 / 224$.

Solution. First solution. Let $a=16 / 2015, b=17 / 2016$. Then

$$
\begin{aligned}
& 6 \frac{16}{2015} \times 9 \frac{17}{2016}-2 \frac{1999}{2015} \times 17 \frac{1999}{2016}-27 \times \frac{16}{2015}=(6+a)(9+b)-(3-a)(18-b)-27 a= \\
& \quad=54+9 a+6 b+a b-54+18 a+3 b-a b-27 a=9 b=9 \cdot \frac{17}{2016}=\frac{9 \cdot 17}{9 \cdot 224}=\frac{17}{224}
\end{aligned}
$$

Second solution. After replacing the mixed fractions with common fractions, we get that the original expression equals

$$
\begin{gathered}
\frac{12106}{2015} \cdot \frac{18161}{2016}-\frac{6029}{2015} \cdot \frac{36271}{2016}-\frac{432}{2015}=\frac{219857066-218677859-870912}{2015 \cdot 2016}= \\
=\frac{308295}{2015 \cdot 2016}=\frac{2015 \cdot 9 \cdot 17}{2015 \cdot 9 \cdot 224}=\frac{17}{224}
\end{gathered}
$$