Evaluate the expression.
1
5
÷
–
1
2
×
3
4
+
4
5
Write your answer as a fraction or as a whole or mixed number.

Let's evaluate the given expression step by step. The expression is:

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

### Step 1: Evaluate the multiplication \(-\frac{1}{2} \times \frac{3}{4}\)
\[
-\frac{1}{2} \times \frac{3}{4} = -\frac{1 \times 3}{2 \times 4} = -\frac{3}{8}
\]

### Step 2: Evaluate the division \(\frac{1}{5} \div -\frac{3}{8}\)
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{1}{5} \div -\frac{3}{8} = \frac{1}{5} \times -\frac{8}{3} = -\frac{1 \times 8}{5 \times 3} = -\frac{8}{15}
\]

### Step 3: Add \(-\frac{8}{15}\) to \(\frac{4}{5}\)
To add these fractions, we need a common denominator. The least common denominator between 15 and 5 is 15. Convert \(\frac{4}{5}\) to a fraction with a denominator of 15:
\[
\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}
\]
Now add the fractions:
\[
-\frac{8}{15} + \frac{12}{15} = \frac{-8 + 12}{15} = \frac{4}{15}
\]

### Final Answer:
The value of the expression is \(\frac{4}{15}\).

Would you like further details or have any questions? Here are some related questions:

1. How do you multiply and divide fractions with negative signs?
2. What is the importance of finding a common denominator when adding or subtracting fractions?
3. How do you convert a fraction into a mixed number?
4. What are the steps for simplifying fractions?
5. How do you handle complex fractions with multiple operations?

**Tip:** When performing operations on fractions, always keep track of the signs and ensure you follow the order of operations (PEMDAS).

Learn how to evaluate expressions involving fractions through division, multiplication, and addition with a step-by-step solution. This problem covers operations with fractions, including negative fractions and reciprocal multiplication. Suitable for students in Grades 6-8.

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