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