4/15:2/3

To simplify the ratio \( \frac{4}{15} : \frac{2}{3} \), you can start by converting the colon (:) into a fraction. The ratio can be expressed as:

\[ \frac{4}{15} \div \frac{2}{3} \]

To divide by a fraction, you multiply by its reciprocal:

\[ \frac{4}{15} \times \frac{3}{2} \]

Now, perform the multiplication:

\[ \frac{4 \times 3}{15 \times 2} = \frac{12}{30} \]

Next, simplify \( \frac{12}{30} \):

\[ \frac{12 \div 6}{30 \div 6} = \frac{2}{5} \]

So, the simplified ratio \( \frac{4}{15} : \frac{2}{3} \) is:

\[ 2 : 5 \]