Let's solve the expression step by step:

The expression is:

\[
\frac{5}{8} + \left( \frac{2}{3} - \frac{1}{4} \right)
\]

### Step 1: Solve \(\frac{2}{3} - \frac{1}{4}\)
To subtract these fractions, find a common denominator.

- The least common denominator (LCD) of 3 and 4 is 12.
- Rewrite the fractions with denominator 12:

\[
\frac{2}{3} = \frac{8}{12}, \quad \frac{1}{4} = \frac{3}{12}
\]

Now subtract:

\[
\frac{8}{12} - \frac{3}{12} = \frac{5}{12}
\]

### Step 2: Add \(\frac{5}{8} + \frac{5}{12}\)
Now, find the LCD of 8 and 12, which is 24.

- Rewrite the fractions with denominator 24:

\[
\frac{5}{8} = \frac{15}{24}, \quad \frac{5}{12} = \frac{10}{24}
\]

Now, add them together:

\[
\frac{15}{24} + \frac{10}{24} = \frac{25}{24}
\]

### Step 3: Simplify \(\frac{25}{24}\)
\(\frac{25}{24}\) is already in its simplest form, but it is an improper fraction. You can also express it as:

\[
1 \frac{1}{24}
\]

Thus, the final result is:

\[
\boxed{1 \frac{1}{24}}
\]

Would you like more details on any of these steps?

Here are some related questions:
1. How do you find the least common denominator (LCD) of fractions?
2. What is the difference between a proper and an improper fraction?
3. How do you convert improper fractions to mixed numbers?
4. How do you add fractions with different denominators?
5. How do you simplify fractions after performing operations?

**Tip:** Always find the least common denominator when adding or subtracting fractions with different denominators.

Learn how to solve the expression 5/8 + (2/3 - 1/4) with a detailed step-by-step solution. This problem covers key mathematical concepts, such as finding the least common denominator (LCD), adding and subtracting fractions with different denominators, and converting improper fractions to mixed numbers. Suitable for students in Grades 5-7.

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