1 - 4/9 : 16/27

To solve the expression \(1 - \frac{4}{9} : \frac{16}{27}\), we first need to clarify the division represented by the colon (:).

The expression can be interpreted as:

\[ 1 - \frac{4}{9} \div \frac{16}{27} \]

Dividing by a fraction is equivalent to multiplying by its reciprocal, so we change the division into multiplication:

\[ 1 - \frac{4}{9} \times \frac{27}{16} \]

Now, multiply \(\frac{4}{9}\) by \(\frac{27}{16}\):

\[ \frac{4 \times 27}{9 \times 16} = \frac{108}{144} \]

Next, simplify \(\frac{108}{144}\):

\[ \frac{108 \div 36}{144 \div 36} = \frac{3}{4} \]

Now we substitute this back into the expression:

\[ 1 - \frac{3}{4} \]

Convert \(1\) to a fraction with a denominator of \(4\):

\[ 1 = \frac{4}{4} \]

Now we compute:

\[ \frac{4}{4} - \frac{3}{4} = \frac{1}{4} \]

So, the final answer is:

\[ \frac{1}{4} \]