12/5:15/2

To simplify the expression \( \frac{12}{5} : \frac{15}{2} \), we can rewrite the division of fractions as multiplication by the reciprocal:

\[ \frac{12}{5} \div \frac{15}{2} = \frac{12}{5} \times \frac{2}{15} \]

Now, multiply the fractions:

\[ = \frac{12 \times 2}{5 \times 15} = \frac{24}{75} \]

Next, we can simplify \( \frac{24}{75} \):

The greatest common divisor (GCD) of 24 and 75 is 3.

Now, divide both the numerator and the denominator by 3:

\[ \frac{24 \div 3}{75 \div 3} = \frac{8}{25} \]

Thus, the final simplified result of \( \frac{12}{5} : \frac{15}{2} \) is:

\[ \frac{8}{25} \]