2. (5 points) After converting three simplest improper fractions with the same numerator into mixed numbers, they are $\mathrm{a} \frac{2}{3}, b \frac{3}{4}, c \frac{3}{5}$, where $a, b, c$ are natural numbers not exceeding 10, then $(2 a+b) \div c=$ $\qquad$ .
【Solution】Solution: Since the three simplest improper fractions with the same numerator are converted into mixed numbers, which are $\mathrm{a} \frac{2}{3} ， \mathrm{~b} \frac{3}{4} ， c \frac{3}{5}$, the original numerator is 1 less than a multiple of 12, i.e., it could be $11,23,35 \cdots$, and 3 more than a multiple of 20, i.e., it could be 23 , $43, \cdots$,

Since $a, b, c$ are natural numbers not exceeding 10, the original numerator can only be 23,
So $a=7, b=5, c=4$,
So $(2 a+b) \div c=(2 \times 7+5) \div 4=19 \div 4=4.75$.
Therefore, the answer is: 4.75.