Let's break down the expression:

$\frac{2}{3} + \left( -\frac{1}{8} + \frac{3}{4} \right)$

First, we solve the part inside the parentheses:

$-\frac{1}{8} + \frac{3}{4}$

To add these fractions, we need a common denominator. The least common denominator between 8 and 4 is 8. We can rewrite $\frac{3}{4}$ as:

$\frac{3}{4} = \frac{6}{8}$

Now, we can add:

$-\frac{1}{8} + \frac{6}{8} = \frac{5}{8}$

Now, substitute this back into the original expression:

$\frac{2}{3} + \frac{5}{8}$

Again, we need a common denominator to add $\frac{2}{3}$ and $\frac{5}{8}$. The least common denominator between 3 and 8 is 24. We rewrite the fractions with denominator 24:

$\frac{2}{3} = \frac{16}{24} \quad \text{and} \quad \frac{5}{8} = \frac{15}{24}$

Now, we can add the fractions:

$\frac{16}{24} + \frac{15}{24} = \frac{31}{24}$

So, the final result is:

$\frac{31}{24}$

This is an improper fraction, but you can also express it as a mixed number:

$1 \frac{7}{24}$

Would you like more details on any of the steps or have any further questions?

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Here are 5 related questions you might find interesting:

1. How do you add fractions with different denominators?
2. What are some methods to simplify improper fractions?
3. How do you convert an improper fraction to a mixed number?
4. How do you subtract fractions with different denominators?
5. What is the least common denominator, and how do you find it?

Tip: When adding or subtracting fractions, always find a common denominator first to ensure you’re working with equivalent fractions!