(ii) \( \quad 6 \frac{3}{4} \div\left(21 \frac{1}{3} \times 2 \frac{1}{4}-21\right) \)

To simplify \( 6 \frac{3}{4} \div\left(21 \frac{1}{3} \times 2 \frac{1}{4}-21\right) \), first convert the mixed numbers to improper fractions. For \( 6 \frac{3}{4} \): \( 6 \times 4 + 3 = 27 \), so it becomes \( \frac{27}{4} \). For \( 21 \frac{1}{3} \): \( 21 \times 3 + 1 = 64 \), so it becomes \( \frac{64}{3} \). For \( 2 \frac{1}{4} \): \( 2 \times 4 + 1 = 9 \), so it becomes \( \frac{9}{4} \). Now calculate \( \left(21 \frac{1}{3} \times 2 \frac{1}{4}-21\right) \): Multiply the improper fractions: \( \frac{64}{3} \times \frac{9}{4} = \frac{576}{12} = 48 \). Subtract 21: \( 48 - 21 = 27 \). Now you have: \( 6 \frac{3}{4} \div 27 \) which is \( \frac{27}{4} \div 27 = \frac{27}{4} \times \frac{1}{27} = \frac{1}{4} \). So, the answer is \( \frac{1}{4} \).