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Let's work through this problem step-by-step.

### Part a) Write \( 1 \frac{5}{6} \) as an improper fraction in its simplest form.

To convert a mixed number to an improper fraction:
- Multiply the whole number part (1) by the denominator (6).
- Add the result to the numerator (5).
- Keep the denominator the same.

So, for \( 1 \frac{5}{6} \):
\[
1 \times 6 + 5 = 6 + 5 = 11
\]
Thus, \( 1 \frac{5}{6} \) as an improper fraction is:
\[
\frac{11}{6}
\]

### Part b) Use your answer to part a) to work out \( \frac{1}{7} \div 1 \frac{5}{6} \). Give your answer as a fraction in its simplest form.

The division of fractions follows the rule:
\[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
\]
So, \( \frac{1}{7} \div \frac{11}{6} \) becomes:
\[
\frac{1}{7} \times \frac{6}{11}
\]
Now, multiply the numerators and the denominators:
\[
\frac{1 \times 6}{7 \times 11} = \frac{6}{77}
\]
Thus, the final answer is:
\[
\frac{6}{77}
\]

Do you want more details or have any questions?

Here are five related questions for practice:
1. Convert \( 2 \frac{3}{4} \) into an improper fraction.
2. Solve \( \frac{3}{5} \div \frac{7}{8} \) and simplify.
3. Convert \( 5 \frac{2}{3} \) into a fraction.
4. What is \( \frac{2}{9} \div \frac{4}{5} \)?
5. Multiply \( \frac{5}{8} \times \frac{3}{4} \) and simplify.

**Tip:** When dividing fractions, remember to multiply by the reciprocal of the second fraction!

a) Write 1 5/6 as an improper fraction in its simplest form.
b) Use your answer to part a) to work out 1/7 ÷ 1 5/6. Give your answer as a fraction in its simplest form.

Learn how to convert 1 5/6 to an improper fraction and divide 1/7 by the result. This solution involves key fraction concepts and is suitable for students in Grades 6-8.

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