A6. What number must we add to the numerator and the denominator of the fraction $\frac{2}{5}$ to get a fraction that has the value $\frac{2}{3}$?
(A) -2
(B) 0
(C) 4
(D) 13
(E) Such a number does not exist.
A6. To the numerator and denominator of the fraction $\frac{2}{5}$, we must add 4. Then we indeed get $\frac{2+4}{5+4}=\frac{6}{9}=\frac{2}{3}$.

We can also solve it differently. For example, if we add the number $x$ to the numerator and denominator of the fraction $\frac{2}{5}$, then $\frac{2+x}{5+x}=\frac{2}{3}$, from which it follows that $6+3x=10+2x$ and $x=4$.