The expression shown in the image is:

$- \left( \frac{3}{4} \right) \div \left( \frac{21}{4} \right)$

To solve this expression, we can follow the steps for dividing fractions:

Step-by-Step Solution

1. Rewrite the Division as Multiplication:

   Dividing by a fraction is the same as multiplying by its reciprocal. Thus:

   $- \left( \frac{3}{4} \right) \div \left( \frac{21}{4} \right) = - \left( \frac{3}{4} \times \frac{4}{21} \right)$

2. Simplify the Expression:

   The multiplication of fractions can be simplified by canceling any common factors in the numerator and denominator:

   $- \left( \frac{3 \cdot 4}{4 \cdot 21} \right)$

   Notice that the 4s in the numerator and the denominator can be canceled out:

   $- \left( \frac{3}{21} \right)$

3. Reduce the Fraction:

   Simplify the fraction $\frac{3}{21}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

   $- \left( \frac{1}{7} \right)$

Final Answer

$- \frac{1}{7}$

Would you like further details, or do you have any additional questions?

Related Questions

1. What is the reciprocal of a fraction and how is it used in division?
2. How do you simplify fractions to their lowest terms?
3. Why does dividing by a fraction involve multiplying by its reciprocal?
4. How do you handle negative signs when performing arithmetic operations?
5. Can you show a real-world example where dividing fractions is used?

Tip

Remember, when dividing fractions, always multiply by the reciprocal of the divisor to simplify the problem.