a) To simplify the expression 1 - (2/3 + 1/6), we first need to find a common denominator for the fractions 2/3 and 1/6. The least common multiple of 3 and 6 is 6.

Converting 2/3 to have a denominator of 6, we get 4/6. Converting 1/6 to have a denominator of 6, we get 1/6.

Now, the expression becomes 1 - (4/6 + 1/6).

Combining the fractions inside the parentheses, we get 1 - (5/6).

To subtract fractions, we need a common denominator. The common denominator for 1 and 5/6 is 6.

Converting 1 to have a denominator of 6, we get 6/6.

Now, the expression becomes 6/6 - 5/6.

Subtracting the fractions, we get 1/6.

Therefore, a = 1/6.

b) To divide the mixed numbers 1 1/5 by 1 1/2, we need to convert them into improper fractions.

1 1/5 can be written as (5/5 + 1/5) = 6/5.

1 1/2 can be written as (2/2 + 1/2) = 3/2.

Now, the expression becomes 6/5 ÷ 3/2.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of 3/2 is 2/3.

Multiplying 6/5 by 2/3, we get (6/5) * (2/3) = 12/15.

Simplifying the fraction, we get 4/5.

Therefore, b = 4/5.