In this context, \( \frac{3}{2} \) represents Leila's height in meters, and \( \frac{4}{5} \) is the fraction that represents how tall Leila is relative to Shanika. Specifically, it indicates that Leila is \( \frac{4}{5} \) of Shanika's height.
To understand what \( \frac{3}{2} \div \frac{4}{5} \) represents, we can calculate it:
\[ \frac{3}{2} \div \frac{4}{5} = \frac{3}{2} \times \frac{5}{4} = \frac{3 \times 5}{2 \times 4} = \frac{15}{8} \]
This result, \( \frac{15}{8} \), represents the height of Shanika in relation to Leila’s height. In other words, Shanika's height is \( \frac{15}{8} \) times the height of Leila. If needed, you could also express this as 1.875 meters, which is Shanika's height in meters when converted from the fraction.
So, \( \frac{3}{2} \div \frac{4}{5} \) tells you how many times Leila's height fits into Shanika's height, or gives you the ratio of Shanika's height to Leila's height.