(iii) \( \frac{\frac{3}{4}-\frac{7}{8}+\frac{1}{2}}{\frac{3}{4} \text { of }\left(\frac{7}{8}-\frac{1}{2}\right)} \)

Let's break down the expression step by step. First, simplify the numerator: 1. Convert all fractions to have a common denominator (which in this case could be 8): - \( \frac{3}{4} = \frac{6}{8} \) - \( \frac{1}{2} = \frac{4}{8} \) 2. Now substitute these values into the numerator: \[ \frac{6}{8} - \frac{7}{8} + \frac{4}{8} = \frac{6 - 7 + 4}{8} = \frac{3}{8} \] Now, simplify the denominator: 1. Calculate \( \frac{7}{8} - \frac{1}{2} \): - Again, converting \( \frac{1}{2} \) to eighths gives us \( \frac{4}{8} \): \[ \frac{7}{8} - \frac{4}{8} = \frac{3}{8} \] 2. Now find \( \frac{3}{4} \) of \( \frac{3}{8} \): \[ \frac{3}{4} \times \frac{3}{8} = \frac{9}{32} \] Now put it all together: \[ \frac{\frac{3}{8}}{\frac{9}{32}} \] 3. Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{3}{8} \times \frac{32}{9} = \frac{3 \times 32}{8 \times 9} = \frac{96}{72} \] 4. Simplifying \( \frac{96}{72} \) by dividing both numerator and denominator by 24 gives: \[ \frac{4}{3} \] Thus, the final result of the expression is: \[ \boxed{\frac{4}{3}} \]