14/5:7/2

To divide the fraction \( \frac{14}{5} \) by \( \frac{7}{2} \), you can multiply by the reciprocal of the second fraction.

The reciprocal of \( \frac{7}{2} \) is \( \frac{2}{7} \). So, you perform the operation as follows:

\[ \frac{14}{5} \div \frac{7}{2} = \frac{14}{5} \times \frac{2}{7} \]

Now, multiply the fractions:

\[ \frac{14 \times 2}{5 \times 7} = \frac{28}{35} \]

Next, simplify \( \frac{28}{35} \). Both the numerator and the denominator can be divided by their greatest common divisor, which is 7:

\[ \frac{28 \div 7}{35 \div 7} = \frac{4}{5} \]

Thus, \( \frac{14}{5} : \frac{7}{2} = \frac{4}{5} \).