To solve the expression \((-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)\), we will follow the order of operations and apply the properties of multiplication and division.
-
Division by a fraction: Dividing by a fraction is the same as multiplying by its reciprocal. \[ -3 ÷ \frac{3}{4} = -3 × \frac{4}{3} = -\frac{12}{3} = -4 \]
-
Now substitute -4 into the expression: \[ -4 × \frac{2}{7} × \frac{-5}{16} ÷ \frac{5}{7} \]
-
Again, convert the division by a fraction: \[ \frac{-5}{16} ÷ \frac{5}{7} = \frac{-5}{16} × \frac{7}{5} = \frac{-5 × 7}{16 × 5} = \frac{-35}{80} \] Simplifying \(\frac{-35}{80}\) (both numerator and denominator can be divided by 5): \[ \frac{-35 ÷ 5}{80 ÷ 5} = \frac{-7}{16} \]
-
Now substitute back into the expression: \[ -4 × \frac{2}{7} × \frac{-7}{16} \]
-
Now multiply: First, multiply \( -4 \) and \(\frac{-7}{16}\): \[ -4 × \left(\frac{-7}{16}\right) = \frac{28}{16} = \frac{7}{4} \quad \text{(simplifying)} \]
-
Now multiply by \(\frac{2}{7}\): \[ \frac{7}{4} × \frac{2}{7} \] Here, the \(7\) in the numerator and denominator cancel each other out: \[ = \frac{1 × 2}{4 × 1} = \frac{2}{4} = \frac{1}{2} \]
Thus, the final answer is: \[ \boxed{\frac{1}{2}} \]