To solve \(\frac{7}{27} \div \frac{35}{36}\), we need to divide two fractions. The process involves multiplying by the reciprocal of the second fraction:

\[
\frac{7}{27} \div \frac{35}{36} = \frac{7}{27} \times \frac{36}{35}
\]

Now, multiply the numerators and the denominators:

\[
\frac{7 \times 36}{27 \times 35} = \frac{252}{945}
\]

Next, simplify \(\frac{252}{945}\). The greatest common divisor (GCD) of 252 and 945 is 63. Dividing both the numerator and the denominator by 63:

\[
\frac{252 \div 63}{945 \div 63} = \frac{4}{15}
\]

So, the final simplified result is:

\[
\frac{4}{15}
\]

Would you like further details or explanations? Here are 5 related questions to expand your understanding:

1. How do you find the reciprocal of a fraction?
2. What are the steps for simplifying a fraction?
3. How can you check if two fractions are equivalent?
4. Why does dividing by a fraction involve multiplying by its reciprocal?
5. What is the method to find the GCD of two numbers?

**Tip:** When dividing fractions, always remember to multiply by the reciprocal to avoid confusion!

Learn how to divide fractions with this example: 7/27 ÷ 35/36. The solution includes step-by-step instructions on multiplying by the reciprocal and simplifying the result using the greatest common divisor (GCD). Suitable for students in Grades 6-8.

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