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The given image contains a mathematical expression that needs to be simplified, with four possible answer choices:

\[
4 - \frac{5}{1 + \frac{1}{3 + \frac{1}{2 + \frac{1}{4}}}}
\]

Let's break this expression down step by step, starting with the innermost fraction.

1. Simplify \( 2 + \frac{1}{4} \):
   \[
   2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}
   \]

2. Substitute into the next part:
   \[
   3 + \frac{1}{\frac{9}{4}} = 3 + \frac{4}{9} = \frac{27}{9} + \frac{4}{9} = \frac{31}{9}
   \]

3. Now substitute this into the next part:
   \[
   1 + \frac{1}{\frac{31}{9}} = 1 + \frac{9}{31} = \frac{31}{31} + \frac{9}{31} = \frac{40}{31}
   \]

4. Substitute this into the outer fraction:
   \[
   \frac{5}{\frac{40}{31}} = 5 \times \frac{31}{40} = \frac{155}{40} = \frac{31}{8}
   \]

5. Finally, subtract this from 4:
   \[
   4 - \frac{31}{8} = \frac{32}{8} - \frac{31}{8} = \frac{1}{8}
   \]

Thus, the correct answer is \( \frac{1}{8} \), which corresponds to option **(a)**.

Would you like a deeper explanation or more details on any step? Here are some additional questions for practice:

1. What happens if we change the value of 4 in the expression to 5?
2. How would the result change if the fraction \( \frac{1}{4} \) was replaced by \( \frac{1}{5} \)?
3. Can you generalize a method for simplifying such nested fractions?
4. What would the expression become if all fractions were halved?
5. How does the method of continued fractions help in simplifying such problems?

**Tip**: Always start simplifying the innermost part of the fraction and work your way outwards for complex nested expressions.

Solve the nested fractions problem: 4 - 5 / (1 + 1 / (3 + 1 / (2 + 1 / 4))). This step-by-step guide simplifies complex nested fractions and demonstrates key arithmetic techniques. Suitable for students in Grades 8-10.

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