https://file.aiquickdraw.com/mathbot/file/172841143747564j2pq0z.jpg

The image shows a mathematical expression involving fractions. The given expression is:

\[
\frac{1}{1 + \frac{1}{2 + \frac{1}{2}}}
\]

Let’s simplify this step by step.

### Step 1: Simplify the innermost fraction
We start by simplifying the innermost part of the expression, which is \(\frac{1}{2}\).

\[
\frac{1}{2} = 0.5
\]

So, the expression now becomes:

\[
\frac{1}{1 + \frac{1}{2 + 0.5}}
\]

### Step 2: Simplify \(2 + 0.5\)
Adding 2 and 0.5 gives:

\[
2 + 0.5 = 2.5
\]

Thus, the expression becomes:

\[
\frac{1}{1 + \frac{1}{2.5}}
\]

### Step 3: Simplify \(\frac{1}{2.5}\)
Next, simplify the fraction \(\frac{1}{2.5}\):

\[
\frac{1}{2.5} = 0.4
\]

Now the expression is:

\[
\frac{1}{1 + 0.4}
\]

### Step 4: Simplify \(1 + 0.4\)
Adding 1 and 0.4 gives:

\[
1 + 0.4 = 1.4
\]

### Step 5: Simplify \(\frac{1}{1.4}\)
Finally, simplify \(\frac{1}{1.4}\):

\[
\frac{1}{1.4} = 0.714
\]

So, the value of the expression is approximately **0.714**.

---

Would you like further details or explanations on any of the steps? 

Here are some related questions for further exploration:
1. How can you express the exact value of \(\frac{1}{1.4}\) as a fraction?
2. What would happen if the denominator structure continued infinitely?
3. How does this expression relate to continued fractions?
4. How can similar nested fractions be simplified in a general case?
5. How is this type of problem relevant in number theory?

**Tip:** Simplifying nested fractions is easier when you simplify from the innermost fraction outwards.

Simplify the expression \(\frac{1}{1 + \frac{1}{2 + \frac{1}{2}}}\).

Learn how to simplify the nested fraction expression \(\frac{1}{1 + \frac{1}{2 + \frac{1}{2}}}\). This solution involves step-by-step simplification of fractions, addition, and division, making it suitable for students in Grades 6-8.

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