Translate the following math problem into English and solve it: е значение выражения a = 2,5. 6\frac{1}{6} - (2\frac{7}{9} + a), если a = 1,5.

Task: Find the value of the expression 6 1/6 - (2 7/9 + a) when a = 1.5.

Solution:

1. Convert mixed numbers to improper fractions:
   • 6 1/6 = (6*6 + 1) / 6 = 37/6
   • 2 7/9 = (2*9 + 7) / 9 = 25/9
2. Substitute the value of 'a' (1.5 = 3/2):
   • The expression becomes: 37/6 - (25/9 + 3/2)
3. Add the fractions inside the parentheses:
   • Find a common denominator for 9 and 2, which is 18.
   • 25/9 = 50/18
   • 3/2 = 27/18
   • 50/18 + 27/18 = 77/18
4. Subtract the result from the first term:
   • The expression is now: 37/6 - 77/18
   • Find a common denominator for 6 and 18, which is 18.
   • 37/6 = 111/18
   • 111/18 - 77/18 = 34/18
5. Simplify the fraction:
   • Divide both numerator and denominator by their greatest common divisor, which is 2.
   • 34/18 = 17/9
6. Convert the improper fraction back to a mixed number:
   • 17/9 = 1 8/9

Answer: 1 8/9