The expression in the image is:

$\left(6 \frac{1}{8} \cdot \frac{1}{7} - 2 \frac{11}{14} \cdot \frac{1}{13}\right) \cdot \frac{3}{5}$

Let's solve it step by step.

Step 1: Convert mixed fractions to improper fractions

1. $6 \frac{1}{8} = \frac{49}{8}$
2. $2 \frac{11}{14} = \frac{39}{14}$

Step 2: Rewrite the expression with improper fractions

$\left(\frac{49}{8} \cdot \frac{1}{7} - \frac{39}{14} \cdot \frac{1}{13}\right) \cdot \frac{3}{5}$

Step 3: Simplify the products inside the parentheses

1. $\frac{49}{8} \cdot \frac{1}{7} = \frac{49}{56} = \frac{7}{8}$ (simplify by dividing by 7)
2. $\frac{39}{14} \cdot \frac{1}{13} = \frac{39}{182}$ (no simplification possible)

Now the expression becomes:

$\left(\frac{7}{8} - \frac{39}{182}\right) \cdot \frac{3}{5}$

Step 4: Find a common denominator for the subtraction

The denominators are $8$ and $182$. Their least common denominator (LCD) is $728$.

1. Rewrite $\frac{7}{8}$: $\frac{7}{8} = \frac{637}{728}$
2. Rewrite $\frac{39}{182}$: $\frac{39}{182} = \frac{156}{728}$

Now the subtraction becomes: $\frac{637}{728} - \frac{156}{728} = \frac{481}{728}$

Step 5: Multiply by $\frac{3}{5}$

$\frac{481}{728} \cdot \frac{3}{5} = \frac{1443}{3640}$

Final Answer:

$\frac{1443}{3640}$

This is the simplified result of the given expression. Let me know if you'd like further clarification or steps explained.

Follow-up Questions:

1. How is the least common denominator (LCD) calculated?
2. What are mixed fractions and how do they convert to improper fractions?
3. Why do we simplify fractions before performing operations?
4. How can you check the accuracy of this solution?
5. What are some common tips for solving fractional arithmetic efficiently?

Tip: Always simplify fractions early to make calculations easier.