0.5 + 6/17 - (2 2/5 - 1 1/4)

First, convert the mixed numbers to improper fractions:
2 2/5 = (52 + 2)/5 = 12/5
1 1/4 = (41 + 1)/4 = 5/4

Now the expression becomes:
0.5 + 6/17 - (12/5 - 5/4)

Next, find a common denominator for the fractions inside the parentheses:
The common denominator for 5 and 4 is 20. So, convert 12/5 and 5/4 to fractions with denominator 20:

12/5 = (124)/ (54) = 48/20
5/4 = (55)/(45) = 25/20

Now the expression becomes:
0.5 + 6/17 - (48/20 - 25/20)

Now subtract the fractions inside the parentheses:
48/20 - 25/20 = 23/20

Now the expression becomes:
0.5 + 6/17 - 23/20

Next, find a common denominator for all the fractions:
The common denominator for 17 and 20 is 340. So, convert 6/17 and 23/20 to fractions with denominator 340:

6/17 = (620)/(1720) = 120/340
23/20 = (2317)/(2017) = 391/340

Now the expression becomes:
0.5 + 120/340 - 391/340

Now subtract the fractions:
120/340 - 391/340 = -271/340

Now the final expression becomes:
0.5 - 271/340

To simplify this further, we need to find a common denominator for 2 and 340:

0.5 = 0.5*340/340 = 170/340

Now the expression becomes:
170/340 - 271/340

Finally, subtract the fractions:
170/340 - 271/340 = -101/340

Therefore, the final result of the expression 0.5 + 6/17 - (2 2/5 - 1 1/4) is -101/340.