https://file.aiquickdraw.com/mathbot/file/1730272612635lx0n036k.jpg

The image shows a mathematical expression. I'll write down and analyze it as best as I can from the image:

The expression is:
\[
\left( \frac{1}{3} - \frac{1}{2} \right) \div \frac{1}{4} + 1
\]

Let's break down the solution step-by-step.

### Step 1: Simplify the Parentheses
First, calculate \( \frac{1}{3} - \frac{1}{2} \).

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

### Step 2: Division by a Fraction
Now we have:
\[
-\frac{1}{6} \div \frac{1}{4} 
\]

Dividing by a fraction is the same as multiplying by its reciprocal:
\[
-\frac{1}{6} \times 4 = -\frac{4}{6} = -\frac{2}{3}
\]

### Step 3: Adding 1
Now add 1 to \(-\frac{2}{3}\):
\[
-\frac{2}{3} + 1 = \frac{-2 + 3}{3} = \frac{1}{3}
\]

### Final Answer
\[
\frac{1}{3}
\]

Would you like further details on this solution, or do you have any additional questions?

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Here are some related questions that might help expand understanding:

1. How do you handle division of fractions?
2. What is the process for finding a common denominator?
3. Can we simplify complex fractions differently?
4. How would the result change if a different operation were used instead of addition at the end?
5. How do parentheses affect the order of operations?

**Tip:** Always handle operations inside parentheses first to simplify complex expressions efficiently.

Solve the expression \( \left( \frac{1}{3} - \frac{1}{2} \right) \div \frac{1}{4} + 1 \).

This page provides a step-by-step solution to simplify the fractional expression \( \left( \frac{1}{3} - \frac{1}{2} \right) \div \frac{1}{4} + 1 \), covering concepts of fraction subtraction, division by a fraction, and order of operations. Suitable for students in Grades 6-8.

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