Find the ratio and write in the simbleest form: \( 1 \frac{5}{6}, 1 \frac{11}{15} \) and \( 1 \frac{13}{30} \)

1. Convert each mixed number to an improper fraction. - For \(1 \frac{5}{6}\): \[ 1 \frac{5}{6} = \frac{6 \times 1 + 5}{6} = \frac{11}{6} \] - For \(1 \frac{11}{15}\): \[ 1 \frac{11}{15} = \frac{15 \times 1 + 11}{15} = \frac{26}{15} \] - For \(1 \frac{13}{30}\): \[ 1 \frac{13}{30} = \frac{30 \times 1 + 13}{30} = \frac{43}{30} \] 2. Express all fractions with a common denominator. The denominators are \(6\), \(15\), and \(30\). The least common denominator is \(30\). - Rewrite \(\frac{11}{6}\) as: \[ \frac{11}{6} = \frac{11 \times 5}{6 \times 5} = \frac{55}{30} \] - Rewrite \(\frac{26}{15}\) as: \[ \frac{26}{15} = \frac{26 \times 2}{15 \times 2} = \frac{52}{30} \] - \(\frac{43}{30}\) is already with denominator \(30\). 3. Write the ratio using the numerators: \[ \frac{55}{30} : \frac{52}{30} : \frac{43}{30} = 55 : 52 : 43 \] The ratio in its simplest form is: \[ 55:52:43 \]