https://file.aiquickdraw.com/mathbot/file/17261882091170x9zn13i.jpg

The expression provided is:

\[
\frac{7}{6} \div \frac{7}{4} \cdot \frac{1}{5}
\]

### Step 1: Division of Fractions
To divide fractions, multiply by the reciprocal of the divisor. So, divide \(\frac{7}{6}\) by \(\frac{7}{4}\) by multiplying by the reciprocal of \(\frac{7}{4}\), which is \(\frac{4}{7}\):

\[
\frac{7}{6} \div \frac{7}{4} = \frac{7}{6} \times \frac{4}{7} = \frac{7 \times 4}{6 \times 7} = \frac{28}{42} = \frac{2}{3}
\]

### Step 2: Multiplying Fractions
Now, multiply the result \(\frac{2}{3}\) by \(\frac{1}{5}\):

\[
\frac{2}{3} \times \frac{1}{5} = \frac{2 \times 1}{3 \times 5} = \frac{2}{15}
\]

### Final Answer:
The simplified result of the given expression is:

\[
\boxed{\frac{2}{15}}
\]

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

### Related Questions:
1. How do you multiply three fractions?
2. What is the general rule for dividing fractions?
3. How do you simplify fractions after multiplication?
4. What is the reciprocal of a fraction, and why is it used in division?
5. Can you explain why \(\frac{28}{42} = \frac{2}{3}\) in this case?

### Tip:
When dividing fractions, always remember to flip the second fraction (take the reciprocal) and change the division to multiplication!

This article provides a step-by-step solution to the math problem involving the division of fractions (7/6 ÷ 7/4) followed by the multiplication with another fraction (1/5). Learn how to use the reciprocal theorem and simplify fractions in this problem, suitable for Grades 6-8 students.

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