Let a = (4 ÷ 3) ÷ 3 ÷ 4, b = 4 ÷ (3 ÷ 3) ÷ 4, c = 4 ÷ 3 ÷ (3 ÷ 4), The maximum value among the above three is?

Solution(By Examveda Team)

$$\eqalign{ & \,a = \left( {4 \div 3} \right) \div {\text{3}} \div {\text{4}} \cr & \,\,\,\,\,\,{\text{ = }}\frac{4}{3} \times \frac{1}{3} \times \frac{1}{4} \cr & \,\,\,\,\,\, = \frac{1}{9} \cr & b = 4 \div \left( {3 \div 3} \right) \div {\text{4}} \cr & \,\,\,\,\,{\text{ = 4}} \div 1 \div 4 \cr & \,\,\,\,\, = 1 \cr & c = 4 \div 3 \div \left( {3 \div 4} \right) \cr & \,\,\,\,\, = 4 \div 3 \div \frac{3}{4} \cr & \,\,\,\,\, = \frac{4}{3} \times \frac{4}{3} \cr & \,\,\,\,\, = \frac{{16}}{9} \cr & {\text{Clearly, c is the greatest}}{\text{.}} \cr} $$