Question

what is \\( \frac{2}{5} \div \left( \frac{3}{5} \
ight) \\)? \\( \frac{6}{25} \\) \\( \frac{2}{3} \\) \\( \frac{5}{5} \\) \\( \frac{6}{5} \\)

Explanation:

Step1: Recall division of fractions

To divide by a fraction, multiply by its reciprocal. So, \(\frac{2}{5} \div \frac{3}{5}=\frac{2}{5}\times\frac{5}{3}\).

Step2: Multiply the numerators and denominators

Multiply numerators: \(2\times5 = 10\). Multiply denominators: \(5\times3 = 15\). So we have \(\frac{10}{15}\).

Step3: Simplify the fraction

Divide numerator and denominator by their greatest common divisor, which is 5. \(\frac{10\div5}{15\div5}=\frac{2}{3}\).

Answer:

\(\frac{2}{3}\) (corresponding to the option \(\frac{2}{3}\))