I am thinking of a fraction. Its numerator is 35 less than the denominator. The sum of the thought fraction and the same fraction in its simplest form is $\frac{16}{13}$. Which fraction am I thinking of?
From the assignment, it follows that the second added fraction was obtained by reducing the first one. And since the value of a fraction does not change by reducing it, we added two numbers with the same value. From this, we can calculate the second number (fraction in its simplest form):

$$
\frac{16}{13} : 2 = \frac{8}{13}
$$

The difference between the denominator and the numerator of this fraction is $13 - 8 = 5$. For the thought number, this difference is 7 times greater $(35 : 5 = 7)$, which means we need to expand the obtained fraction by seven. The thought fraction is $\frac{56}{91}$.

determining that both fractions have the same value - 2 points

calculating the second fraction - 1 point

calculating the thought fraction - 3 points

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