4. (5 points) A fraction, when the numerator is reduced by 1, equals $\frac{2}{3}$, and when the numerator is reduced by 2, equals $\frac{1}{2}$. What is this fraction?

保留源文本的换行和格式，所以翻译结果如下：

4. (5 points) A fraction, when the numerator is reduced by 1, equals $\frac{2}{3}$, and when the numerator is reduced by 2, equals $\frac{1}{2}$. What is this fraction?
【Solution】Solution: According to the problem, we can get: The denominator of this fraction should be a multiple of 6. Assuming the denominator is 6, i.e., $\frac{2}{3}=\frac{()-1}{6}$;

The denominator expands from 3 to 6, which is doubled. To keep the size of the fraction unchanged, the numerator also needs to be doubled, thus $2 \times 2=(\quad)-1$, so $(\quad)=5$,

Answer: This fraction is $\frac{5}{6}$.
Therefore, the answer is: $\frac{5}{6}$.