1. State the problem: Simplify the expression $$-\frac{7}{4} + \frac{7}{16} \times \frac{1}{8} \times 384 \times \frac{3}{28}$$. 2. First, calculate the product part $$\frac{7}{16} \times \frac{1}{8} \times 384 \times \frac{3}{28}$$ step-by-step. 3. Multiply numerator terms together and denominator terms together where possible: - Multiply numerators: $7 \times 1 \times 384 \times 3 = 8064$ - Multiply denominators: $16 \times 8 \times 1 \times 28 = 3584$ 4. So the product is $$\frac{8064}{3584}$$. 5. Simplify $$\frac{8064}{3584}$$ by dividing numerator and denominator by their greatest common divisor (GCD). The GCD is 64: - $\frac{8064 \div 64}{3584 \div 64} = \frac{126}{56}$. 6. Simplify $$\frac{126}{56}$$ further by dividing numerator and denominator by 14: - $\frac{126 \div 14}{56 \div 14} = \frac{9}{4}$. 7. Now, substitute this result back into the expression: $$-\frac{7}{4} + \frac{9}{4}$$. 8. Combine the fractions with a common denominator 4: $$\frac{-7 + 9}{4} = \frac{2}{4}$$. 9. Finally, simplify $$\frac{2}{4} = \frac{1}{2}$$. Answer: $$\frac{1}{2}$$.