Let's break down and solve the expression step by step:

The given expression is:

\[
\left(-\frac{1}{2}\right) - \left(-\frac{7}{4}\right) \div \frac{3}{2} + \frac{11}{3} \times \left(-5\right)
\]

### Step 1: Handle the division and multiplication first, according to the order of operations (PEMDAS/BODMAS).

1. **Division:** \(\left(-\frac{7}{4}\right) \div \frac{3}{2}\)

   Division of fractions is equivalent to multiplying by the reciprocal:

   \[
   \left(-\frac{7}{4}\right) \times \frac{2}{3} = -\frac{7 \times 2}{4 \times 3} = -\frac{14}{12} = -\frac{7}{6}
   \]

2. **Multiplication:** \(\frac{11}{3} \times (-5)\)

   \[
   \frac{11 \times (-5)}{3} = \frac{-55}{3}
   \]

### Step 2: Substitute these values back into the expression.

\[
\left(-\frac{1}{2}\right) - \left(-\frac{7}{6}\right) + \left(\frac{-55}{3}\right)
\]

### Step 3: Simplify the expression.

1. **Simplify the subtraction:** \(\left(-\frac{1}{2}\right) - \left(-\frac{7}{6}\right)\)

   Subtraction of a negative is equivalent to addition:

   \[
   -\frac{1}{2} + \frac{7}{6}
   \]

   To add these, find a common denominator (which is 6):

   \[
   -\frac{1}{2} = -\frac{3}{6}
   \]

   So,

   \[
   -\frac{3}{6} + \frac{7}{6} = \frac{4}{6} = \frac{2}{3}
   \]

2. **Now, combine this result with the remaining term:**

   \[
   \frac{2}{3} + \frac{-55}{3}
   \]

   Since the denominators are the same, we can combine the numerators:

   \[
   \frac{2 - 55}{3} = \frac{-53}{3}
   \]

### Final Answer:

\[
\left(-\frac{53}{3}\right)
\]

So the final simplified expression is:

\[
-\frac{53}{3}
\]

This can also be expressed as a mixed number:

\[
-\frac{53}{3} = -17 \frac{2}{3}
\]

Do you want further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you find the reciprocal of a fraction?
2. What is the order of operations, and why is it important?
3. How do you convert improper fractions to mixed numbers?
4. What is the rule for multiplying and dividing negative numbers?
5. Can you solve a similar expression with different fractions?

**Tip:** Always simplify fractions as much as possible to make calculations easier.

Learn how to solve the mixed fraction expression -1/2 - (-7/4) ÷ 3/2 + 11/3 × (-5) step-by-step. This problem involves operations with fractions, including addition, subtraction, multiplication, and division. Suitable for Grades 7-9.

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