To solve the expression \( 1 - \frac{1}{1 + \frac{3}{4 + \frac{1}{2 + \frac{1}{7}}}} \), we'll proceed step by step, starting from the innermost fraction and working our way out.

### Step 1: Simplify the innermost fraction
First, simplify the expression inside the innermost fraction:

\[
\frac{1}{7} \approx 0.142857
\]

### Step 2: Simplify the next fraction
Now, add this to 2:

\[
2 + \frac{1}{7} = 2 + 0.142857 = 2.142857
\]

### Step 3: Simplify the next fraction
Next, calculate the fraction with 3 in the numerator:

\[
\frac{1}{2.

1 - {1 ÷ [1 + 3 ÷ (4 + 1 ÷ (2 + (1 ÷ 7)))]} = ?

Discover how to solve the complex nested fraction problem 1 - {1 ÷ [1 + 3 ÷ (4 + 1 ÷ (2 + (1 ÷ 7)))]} with a detailed step-by-step explanation. This problem focuses on key arithmetic concepts like order of operations and nested fractions, suitable for students in Grades 6-8.

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