1. Calculate: $\frac{2 \frac{5}{8}-\frac{2}{3} \times 2 \frac{5}{14}}{\left(3 \frac{1}{12}+4.375\right) \div 19 \frac{8}{9}}$
1.【Solution】Original expression $=\frac{\frac{21}{8}-\frac{2}{3} \times \frac{33}{14}}{\left(\frac{37}{12}+\frac{35}{8}\right) \div \frac{179}{9}}=\frac{\frac{21}{8}-\frac{11}{7}}{\frac{179}{24} \times \frac{9}{179}}=\left(\frac{21}{8}-\frac{11}{7}\right) \times \frac{8}{3}=7-4 \frac{4}{21}=2 \frac{17}{21}$

Solution two: Original expression $=\frac{\frac{21}{8}-\frac{2}{3} \times \frac{33}{14}}{\left(\frac{37}{12}+\frac{35}{8}\right) \times \frac{179}{9}}=\frac{\frac{21}{8}-\frac{11}{7}}{\frac{179}{24} \times \frac{9}{179}} \times \frac{56}{56}=\frac{147-88}{21}=2 \frac{17}{21}$
When solving this problem, note the following two points:
（1）In multiplication and division operations, mixed numbers should be converted to improper fractions, and simplification should be done promptly;
（2）In addition and subtraction operations, if fractions and decimals appear simultaneously, either convert all to fractions or all to decimals.

Here, it is also important to point out: the decimal forms of $\frac{1}{2}, \frac{1}{4}, \frac{3}{4}, \frac{1}{8}, \frac{3}{8}, \frac{5}{8}, \frac{7}{8}$, which are $0.5, 0.25, 0.75, 0.125, 0.375, 0.625, 0.875$, should be very familiar, as they can save time in specific calculations.