The expression in the image is:

$\frac{5(3 + 4.625)}{8} \cdot \frac{-1.3 - 3 \frac{1}{4}}{4} \cdot \frac{7}{8}$

Let's break this down step by step.

Step 1: Simplify the first part $\frac{5(3 + 4.625)}{8}$

• Inside the parentheses: $3 + 4.625 = 7.625$
• Now multiply by 5: $5 \times 7.625 = 38.125$
• Divide by 8: $\frac{38.125}{8} = 4.765625$

Step 2: Simplify the second part $\frac{-1.3 - 3 \frac{1}{4}}{4}$

• First, convert the mixed fraction $3 \frac{1}{4}$ to an improper fraction: $3 \frac{1}{4} = \frac{13}{4}$
• Now simplify $-1.3 - \frac{13}{4}$. Convert $-1.3$ into a fraction: $-1.3 = -\frac{13}{10}$
• Now find a common denominator for $-\frac{13}{10} - \frac{13}{4}$: The least common denominator (LCD) between 10 and 4 is 20. $-\frac{13}{10} = -\frac{26}{20}, \quad \frac{13}{4} = \frac{65}{20}$ Now subtract: $-\frac{26}{20} - \frac{65}{20} = -\frac{91}{20}$
• Now divide by 4: $\frac{-\frac{91}{20}}{4} = \frac{-91}{80}$

Step 3: Simplify the third part $\frac{7}{8}$

This is already simplified: $\frac{7}{8}$.

Step 4: Multiply all parts together

Now multiply the results from steps 1, 2, and 3: $4.765625 \times \frac{-91}{80} \times \frac{7}{8}$ First, multiply $4.765625 \times \frac{-91}{80}$: $4.765625 \times \frac{-91}{80} = \frac{-433.671875}{80} = -5.4208984375$ Now multiply by $\frac{7}{8}$: $-5.4208984375 \times \frac{7}{8} = -4.7382861328125$

Final Answer:

The simplified value of the expression is approximately: $\boxed{-4.7383}$

Would you like a more detailed explanation on any step?

Here are some related questions:

1. How do you find the least common denominator (LCD) of fractions?
2. What is the process of converting mixed numbers to improper fractions?
3. How do you simplify complex fractions with multiple steps?
4. What are some tips for multiplying fractions with decimal numbers?
5. How can you check if a fraction is simplified correctly?

Tip: Always try to convert decimals into fractions when working with mixed arithmetic to avoid rounding errors during intermediate steps.