I apologize, but it seems that there was a mistake in the given work as well as Paul's work. Let's go step by step to solve the problem correctly.
The given expression is 1/4 + (5/8 + 1/2).
First, let's simplify the innermost parentheses by adding 5/8 and 1/2:
5/8 + 1/2 = 5/8 + 4/8 = 9/8.
Now, the expression becomes 1/4 + 9/8.
To add these fractions, we need to have a common denominator. The least common multiple of 4 and 8 is 8.
Converting 1/4 into a fraction with a denominator of 8:
1/4 = 2/8.
Now, the expression becomes 2/8 + 9/8.
When the fractions have the same denominator, we can add their numerators directly:
2/8 + 9/8 = 11/8.
Therefore, the correct simplified form of the expression is 11/8, and Paul made his first error when he calculated 1/4 + 9/8 as 8/36.