https://file.aiquickdraw.com/mathbot/file/17261448376836b4gm7yx.jpg

The expression in the image appears to be a complex fraction:

\[
\frac{\frac{12}{7}}{\frac{9}{14}}
\]

To simplify this expression, follow these steps:

1. Recognize that dividing by a fraction is the same as multiplying by its reciprocal. So, rewrite the expression as:

\[
\frac{12}{7} \times \frac{14}{9}
\]

2. Multiply the numerators and the denominators:

\[
\frac{12 \times 14}{7 \times 9} = \frac{168}{63}
\]

3. Simplify the fraction by finding the greatest common divisor (GCD) of 168 and 63, which is 21:

\[
\frac{168 \div 21}{63 \div 21} = \frac{8}{3}
\]

Thus, the simplified result is:

\[
\frac{8}{3}
\]

Would you like more details on this solution, or do you have any specific questions? 

Here are 5 related questions for deeper practice:

1. How do you simplify more complex nested fractions?
2. What is the process for finding the GCD of two numbers?
3. How can improper fractions be converted to mixed numbers?
4. What is the relationship between division of fractions and multiplication by the reciprocal?
5. How can you use cross-cancellation to simplify fractions before multiplying?

**Tip:** Always check if you can cancel factors between the numerator and denominator before multiplying, as this can save time in simplification!

Simplify the complex fraction \(\frac{\frac{12}{7}}{\frac{9}{14}}\).

Learn how to simplify the complex fraction \(\frac{\frac{12}{7}}{\frac{9}{14}}\) using multiplication by the reciprocal and finding the greatest common divisor (GCD). This solution is suitable for middle school students in Grades 6-8.

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