Let's solve this step-by-step.

The expression given is:

$2 \cdot \left(-\frac{3}{5}\right) - \frac{3}{4} \div \frac{1}{2}$

Step 1: Multiply $2$ and $-\frac{3}{5}$

$2 \cdot \left(-\frac{3}{5}\right) = -\frac{6}{5}$

So, the expression now becomes: $-\frac{6}{5} - \frac{3}{4} \div \frac{1}{2}$

Step 2: Divide $\frac{3}{4}$ by $\frac{1}{2}$

Dividing by a fraction is the same as multiplying by its reciprocal: $\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \cdot 2 = \frac{6}{4} = \frac{3}{2}$

Now the expression is: $-\frac{6}{5} - \frac{3}{2}$

Step 3: Find a Common Denominator and Subtract

The common denominator for $\frac{6}{5}$ and $\frac{3}{2}$ is 10.

Convert each fraction: $-\frac{6}{5} = -\frac{12}{10}$ $\frac{3}{2} = \frac{15}{10}$

Now, subtract: $-\frac{12}{10} - \frac{15}{10} = -\frac{27}{10}$

Final Answer

$-\frac{27}{10} = -2.7$

So, the solution is:

$\boxed{-2.7}$

Would you like further details on any step or have any questions?

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1. What are the steps to multiply fractions with whole numbers?
2. How do you divide fractions by another fraction?
3. Why is finding a common denominator important when subtracting fractions?
4. How do you convert fractions to decimals?
5. What is the purpose of reciprocal in fraction division?

Tip: When working with fractions, always check if you can simplify intermediate results; it can make calculations easier.