Question

evaluate and simplify the following complex fraction: \\(dfrac{dfrac{9}{-5}}{dfrac{-3}{8}} = \\)

Explanation:

Step1: Recall fraction division rule

Dividing by a fraction is multiplying by its reciprocal. So, \(\frac{\frac{9}{-5}}{\frac{-3}{8}}=\frac{9}{-5}\times\frac{8}{-3}\).

Step2: Multiply numerators and denominators

Multiply the numerators: \(9\times8 = 72\). Multiply the denominators: \((-5)\times(-3)=15\). So we get \(\frac{72}{15}\).

Step3: Simplify the fraction

Divide numerator and denominator by their greatest common divisor, which is 3. \(\frac{72\div3}{15\div3}=\frac{24}{5}\).

Answer:

\(\frac{24}{5}\)