To find the water level of the river at the end of summer, we need to add the two depths below sea level together.
The initial water level is 1 1/2 meters below sea level, which can be expressed as: \[ 1 \frac{1}{2} = \frac{3}{2} \text{ meters below sea level} \]
During the summer, the river drops another 2 1/3 meters below sea level, which can be expressed as: \[ 2 \frac{1}{3} = \frac{7}{3} \text{ meters below sea level} \]
Next, we add these two amounts together: \[ \frac{3}{2} + \frac{7}{3} \]
To add these fractions, we need a common denominator. The least common multiple of 2 and 3 is 6.
Now, we convert each fraction: \[ \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \] \[ \frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6} \]
Now we can add the fractions: \[ \frac{9}{6} + \frac{14}{6} = \frac{9 + 14}{6} = \frac{23}{6} \]
Now we convert \(\frac{23}{6}\) back to a mixed number: \[ \frac{23}{6} = 3 \frac{5}{6} \]
Thus, the water level at the end of summer is \(3 \frac{5}{6}\) meters below sea level.
Answer: The water level is \(3 \frac{5}{6}\) meters below sea level.