1-4/9:16/27

To simplify the expression \( \frac{1 - 4}{9} : \frac{16}{27} \), we first need to simplify the first fraction. 1. Simplify \( \frac{1 - 4}{9} \): \[ 1 - 4 = -3 \] So, we have: \[ \frac{-3}{9} = -\frac{1}{3} \] 2. Now we need to divide \( -\frac{1}{3} \) by \( \frac{16}{27} \). Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{1}{3} \div \frac{16}{27} = -\frac{1}{3} \times \frac{27}{16} \] 3. Multiply the fractions: \[ -\frac{1 \times 27}{3 \times 16} = -\frac{27}{48} \] 4. Simplify \( -\frac{27}{48} \). The greatest common divisor (GCD) of 27 and 48 is 3: \[ -\frac{27 \div 3}{48 \div 3} = -\frac{9}{16} \] Thus, the final answer is: \[ -\frac{9}{16} \]