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

To find the ratio of the three mixed numbers \( 1 \frac{5}{6}, 1 \frac{11}{15}, \) and \( 1 \frac{13}{30} \), we first convert them to improper fractions: 1. \( 1 \frac{5}{6} = \frac{6 + 5}{6} = \frac{11}{6} \) 2. \( 1 \frac{11}{15} = \frac{15 + 11}{15} = \frac{26}{15} \) 3. \( 1 \frac{13}{30} = \frac{30 + 13}{30} = \frac{43}{30} \) Now, let's express the ratio: \[ \text{Ratio} = \frac{11}{6} : \frac{26}{15} : \frac{43}{30} \] To simplify this, we can convert it to a single fraction. We find a common denominator, which would be 30: 1. \( \frac{11}{6} = \frac{55}{30} \) 2. \( \frac{26}{15} = \frac{52}{30} \) 3. \( \frac{43}{30} = \frac{43}{30} \) The ratio now becomes: \[ 55 : 52 : 43 \] Now, we need to make sure this is in the simplest form. The greatest common divisor (GCD) of 55, 52, and 43 is 1; hence, the ratio is already in its simplest form. Thus, the answer is: \[ \text{The ratio in simplest form is } 55 : 52 : 43. \]