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