( 1 17/18* 1 13/14-2 5/8:1 19/20);(2 25/78-1 1/26)

To solve the expressions you've provided, we will perform each calculation step-by-step.

Expression 1: \( 1 \frac{17}{18} \times 1 \frac{13}{14} - 2 \frac{5}{8} : 1 \frac{19}{20} \)

1. Convert mixed numbers to improper fractions:

   • \( 1 \frac{17}{18} = \frac{18 \times 1 + 17}{18} = \frac{35}{18} \)
   • \( 1 \frac{13}{14} = \frac{14 \times 1 + 13}{14} = \frac{27}{14} \)
   • \( 2 \frac{5}{8} = \frac{8 \times 2 + 5}{8} = \frac{21}{8} \)
   • \( 1 \frac{19}{20} = \frac{20 \times 1 + 19}{20} = \frac{39}{20} \)

2. Multiply: \[ \frac{35}{18} \times \frac{27}{14} = \frac{35 \times 27}{18 \times 14} \] Calculate the numerator and denominator:

   • \( 35 \times 27 = 945 \)
   • \( 18 \times 14 = 252 \)
   • So, \( \frac{945}{252} = \frac{945 \div 63}{252 \div 63} = \frac{15}{4} \)

3. Divide: \[ \frac{21}{8} : \frac{39}{20} = \frac{21}{8} \times \frac{20}{39} = \frac{21 \times 20}{8 \times 39} \] Calculate the numerator and denominator:

   • \( 21 \times 20 = 420 \)
   • \( 8 \times 39 = 312 \)
   • So, \( \frac{420}{312} = \frac{420 \div 84}{312 \div 84} = \frac{5}{4} \)

4. Subtract the results: \[ \frac{15}{4} - \frac{5}{4} = \frac{10}{4} = \frac{5}{2} \]

Expression 2: \( 2 \frac{5}{78} - 1 \frac{1}{26} \)

1. Convert mixed numbers to improper fractions:

   • \( 2 \frac{5}{78} = \frac{78 \times 2 + 5}{78} = \frac{161}{78} \)
   • \( 1 \frac{1}{26} = \frac{26 \times 1 + 1}{26} = \frac{27}{26} \)

2. Find a common denominator to subtract:

   • The least common multiple (LCM) of 78 and 26 is 78.
   • Rewriting \( \frac{27}{26} \) with a denominator of 78: \[ \frac{27}{26} = \frac{27 \times 3}{26 \times 3} = \frac{81}{78} \]

3. Subtract fractions: \[ \frac{161}{78} - \frac{81}{78} = \frac{80}{78} = \frac{40}{39} \]

Final Results

• Expression 1: \( \frac{5}{2} \)
• Expression 2: \( \frac{40}{39} \)

So, combining both answers, we have: \[ \left( \frac{5}{2} \right); \left( \frac{40}{39} \right) \]