Question

which expression is equivalent to \\(\frac{4f^2}{3} \div \frac{1}{4f}\\)? \\(\frac{f}{3}\\) \\(\frac{16f^3}{3}\\) \\(\frac{3}{16f^3}\\) \\(\frac{3}{f}\\)

Explanation:

Step1: Recall division of fractions rule

To divide by a fraction, multiply by its reciprocal. So, \(\frac{4f^{2}}{3} \div \frac{1}{4f}=\frac{4f^{2}}{3}\times4f\)

Step2: Multiply the numerators and denominators

Multiply the coefficients: \(4\times4 = 16\). Multiply the variables: \(f^{2}\times f=f^{2 + 1}=f^{3}\). The denominator remains \(3\). So the result is \(\frac{16f^{3}}{3}\)

Answer:

\(\frac{16f^{3}}{3}\) (corresponding to the second option among the given choices)