To solve the expression \(\left( \frac{3}{4} \right) + \left( \frac{5}{12} \cdot \frac{1}{3} \right)\), we proceed step by step:

1. **Multiplication first**: \(\frac{5}{12} \cdot \frac{1}{3} = \frac{5 \cdot 1}{12 \cdot 3} = \frac{5}{36}\).

   Now the expression becomes:
   \[
   \frac{3}{4} + \frac{5}{36}
   \]

2. **Finding a common denominator**:
   The least common denominator (LCD) of 4 and 36 is 36.

   - Convert \(\frac{3}{4}\) to a fraction with a denominator of 36:
     \[
     \frac{3}{4} = \frac{3 \cdot 9}{4 \cdot 9} = \frac{27}{36}
     \]

3. **Adding the fractions**:
   \[
   \frac{27}{36} + \frac{5}{36} = \frac{27 + 5}{36} = \frac{32}{36}
   \]

4. **Simplifying the result**:
   \[
   \frac{32}{36} = \frac{8}{9}
   \]

So, the final answer is \(\frac{8}{9}\).

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you find the least common denominator for adding fractions?
2. Can you explain how to simplify fractions?
3. What is the process for multiplying fractions?
4. How do you convert mixed numbers to improper fractions for addition?
5. How can you check if two fractions are equivalent?

**Tip**: Always perform operations like multiplication or division before addition or subtraction when dealing with expressions.

Learn how to solve the mathematical expression (3/4) + (5/12 • 1/3) by following step-by-step instructions. This guide covers fraction multiplication, finding common denominators, and simplifying fractions. Perfect for students in Grades 6-8.

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