Task 1. Represent in the form of an irreducible fraction

$$
7 \frac{19}{2015} \times 6 \frac{19}{2016}-13 \frac{1996}{2015} \times 2 \frac{1997}{2016}-9 \times \frac{19}{2015}
$$
Answer: $19 / 96$.

Solution. First solution. Let $a=19 / 2015, b=19 / 2016$. Then

$$
\begin{aligned}
& 7 \frac{19}{2015} \times 6 \frac{19}{2016}-13 \frac{1996}{2015} \times 2 \frac{1997}{2016}-9 \times \frac{19}{2015}=(7+a)(6+b)-(14-a)(3-b)-9 a= \\
& \quad=42+6 a+7 b+a b-42+3 a+14 b-a b-9 a=21 b=21 \cdot \frac{19}{2016}=\frac{21 \cdot 19}{21 \cdot 96}=\frac{19}{96}
\end{aligned}
$$

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

$$
\begin{gathered}
\frac{14124}{2015} \cdot \frac{12115}{2016}-\frac{28191}{2015} \cdot \frac{6029}{2016}-\frac{171}{2015}=\frac{171112260-169963539-344736}{2015 \cdot 2016}= \\
=\frac{803985}{2015 \cdot 2016}=\frac{2015 \cdot 21 \cdot 19}{2015 \cdot 21 \cdot 96}=\frac{19}{96}
\end{gathered}
$$