Ari will be a teenager in \( 1 \frac{3}{4} \) years. His little sister Anna will be one in \( 3 \frac{1}{4} \) years. How much longer does Anna have to wait than Ari?

To find out how much longer Anna has to wait than Ari, we first need to determine how many years each of them has until they reach their respective teenage and one-year-old milestones. Ari will be a teenager in \( 1 \frac{3}{4} \) years, which can be converted to an improper fraction: \( \frac{7}{4} \) years. Anna will be one year old in \( 3 \frac{1}{4} \) years, which can also be converted to an improper fraction: \( \frac{13}{4} \) years. Next, we subtract Ari's waiting time from Anna's: \[ \frac{13}{4} - \frac{7}{4} = \frac{6}{4} = \frac{3}{2} \text{ years} \] So, Anna has \( 1 \frac{1}{2} \) years to wait longer than Ari.