To solve these equations, we will follow the Order of Operations (PEMDAS) rule.

5/12 - 1/4 - (-1/3)
First, we will simplify the expression inside the parentheses:
5/12 - 1/4 + 1/3
To add or subtract fractions, we need to find a common denominator. The least common multiple of 12, 4, and 3 is 12.
(5/12) 3/3 - (1/4) 3/3 + (1/3) * 4/4
15/36 - 3/36 + 4/12
Now that we have the common denominator, combine the fractions:
(15 - 3 + 4) / 12
Now simplify the numerator:
16/12 = 4/3

(1/2)(-4) - 5
Multiply the fraction by the number:
(1/2) (-4) - 5
-2 - 5
-7

4/9 : (-2/3) + 1
First, we will simplify the expression inside the parentheses:
4/9 / (-2/3) + 1
To divide by a fraction, we multiply by its reciprocal:
(4/9) * (-3/2) + 1
-12/18 + 1
Simplify the fraction:
-2/3 + 1
Now find a common denominator:
-2/3 + 3/3
Combine the fractions:
(1 - 2) / 3
-1/3

Therefore, the solutions are:

5/12 - 1/4 - (-1/3) = 4/3(1/2)*(-4) - 5 = -74/9 : (-2/3) + 1 = -1/3