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The given problem is:

\[
6 \div \frac{5}{6}
\]

To solve this, recall that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we rewrite the problem as:

\[
6 \times \frac{6}{5}
\]

Now, express \(6\) as a fraction:

\[
\frac{6}{1} \times \frac{6}{5}
\]

Multiply the numerators and the denominators:

\[
\frac{6 \times 6}{1 \times 5} = \frac{36}{5}
\]

Next, convert \(\frac{36}{5}\) to a mixed number. Divide 36 by 5:

\[
36 \div 5 = 7 \text{ remainder } 1
\]

Thus, \(\frac{36}{5} = 7 \frac{1}{5}\).

The correct answer is **\( 7 \frac{1}{5} \)**, which matches the second option.

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Do you want more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you multiply fractions?
2. What are reciprocal fractions and how are they used in division?
3. How can you simplify improper fractions into mixed numbers?
4. What is the relationship between multiplication and division of fractions?
5. How can you estimate the result of dividing a whole number by a fraction?

**Tip:** When dividing by a fraction, remember to always flip the fraction and multiply!

Solve this problem. Reduce to lowest terms. 6 ÷ 5/6 =

Learn how to solve the fraction division problem 6 ÷ 5/6 by multiplying by the reciprocal. This solution shows the process of dividing a whole number by a fraction and converting the answer into a mixed number. Suitable for Grades 6-8.

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