1-4/9:16/32

To simplify the expression \( 1 - \frac{4}{9} : \frac{16}{32} \), we need to first interpret the colon as division, so the expression becomes:

\[ 1 - \frac{4}{9} \div \frac{16}{32} \]

Next, let's simplify \( \frac{16}{32} \):

\[ \frac{16}{32} = \frac{1}{2} \]

Now substitute that back into the expression:

\[ 1 - \frac{4}{9} \div \frac{1}{2} \]

Dividing by a fraction is the same as multiplying by its reciprocal, so:

\[ \frac{4}{9} \div \frac{1}{2} = \frac{4}{9} \times 2 = \frac{8}{9} \]

Now the expression becomes:

\[ 1 - \frac{8}{9} \]

To perform this subtraction, we can write 1 as a fraction:

\[ 1 = \frac{9}{9} \]

Now we can subtract:

\[ \frac{9}{9} - \frac{8}{9} = \frac{1}{9} \]

Thus, the simplified result of the expression \( 1 - \frac{4}{9} : \frac{16}{32} \) is:

\[ \frac{1}{9} \]