Let's go step by step to solve the given expression from your image:

$\left( \frac{5}{8} + 4.625 \right) \times \left( -1.2 - 3 \frac{1}{4} \right) \times \frac{1}{4}$

Step 1: Simplify each term individually

Term 1: $\frac{5}{8} + 4.625$

Convert 4.625 to a fraction: $4.625 = \frac{4625}{1000} = \frac{37}{8}$ So, the expression becomes: $\frac{5}{8} + \frac{37}{8} = \frac{42}{8} = 5.25$

Term 2: $-1.2 - 3 \frac{1}{4}$

Convert $3 \frac{1}{4}$ to an improper fraction: $3 \frac{1}{4} = \frac{13}{4}$ Now simplify: $-1.2 = -\frac{6}{5}$ We need a common denominator to subtract these: $-\frac{6}{5} - \frac{13}{4} = -\frac{24}{20} - \frac{65}{20} = -\frac{89}{20} = -4.45$

Term 3: $\frac{1}{4}$

Step 2: Multiply the simplified terms

Now multiply: $5.25 \times (-4.45) \times \frac{1}{4}$

Start by multiplying $5.25 \times (-4.45)$: $5.25 \times (-4.45) = -23.3625$

Now multiply the result by $\frac{1}{4}$: $-23.3625 \times \frac{1}{4} = -5.840625$

Final Answer:

The simplified result is approximately $-5.841$.

Would you like further clarification or details?

Related Questions:

1. How do you convert decimals to fractions?
2. What are some strategies for simplifying mixed fractions?
3. How can you find a common denominator for different fractions?
4. What is the importance of negative signs when performing arithmetic operations?
5. How does multiplying by fractions affect the size of a number?

Tip:

Always check if terms can be simplified early in the process to make calculations easier!