Divide. Write your answer in lowest terms.
\[
\frac{1}{7} \div \frac{8}{7}
\]
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Answer
Final Answer: The result of the division \( \frac{1}{7} \div \frac{8}{7} \) in lowest terms is \( \boxed{\frac{1}{8}} \).
Step 1 ：First, we need to remember that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
Step 2 ：So, we need to find the reciprocal of \( \frac{8}{7} \). The reciprocal of \( \frac{8}{7} \) is \( \frac{7}{8} \).
Step 3 ：Next, we multiply \( \frac{1}{7} \) by \( \frac{7}{8} \).
Step 4 ：The result of the multiplication is \( \frac{1}{8} \).
Step 5 ：Final Answer: The result of the division \( \frac{1}{7} \div \frac{8}{7} \) in lowest terms is \( \boxed{\frac{1}{8}} \).
