1) To solve the expression 4/7 : 5/11 + 3/7 : 5/11 - 1/5, we can simplify each fraction first.

4/7 : 5/11 can be rewritten as (4/7) * (11/5) = 44/35.

3/7 : 5/11 can be rewritten as (3/7) * (11/5) = 33/35.

Now we can rewrite the expression as 44/35 + 33/35 - 1/5.

To add the fractions, we need a common denominator. The least common multiple of 35 and 5 is 35. So we can rewrite the expression as (44/35) + (33/35) - (7/35).

Now we can add the fractions: (44 + 33 - 7)/35 = 70/35 = 2.

Therefore, the solution to the expression 4/7 : 5/11 + 3/7 : 5/11 - 1/5 is 2.

2) To solve the expression 1/3 x 4/5 + 1/3 x 1 x 1/5 + (-3/2)^2, we can simplify each part of the expression.

1/3 x 4/5 = (1/3) * (4/5) = 4/15.

1/3 x 1 x 1/5 = (1/3) * (1) * (1/5) = 1/15.

(-3/2)^2 = (-3/2) * (-3/2) = 9/4.

Now we can rewrite the expression as 4/15 + 1/15 + 9/4.

To add the fractions, we need a common denominator. The least common multiple of 15 and 4 is 60. So we can rewrite the expression as (4/15) + (1/15) + (135/60).

Now we can add the fractions: (4 + 1 + 135)/60 = 140/60 = 7/3.

Therefore, the solution to the expression 1/3 x 4/5 + 1/3 x 1 x 1/5 + (-3/2)^2 is 7/3.