To find the water level of the river at the end of summer, we need to add the two decreases in elevation below sea level.
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The water level is initially at \(1 \frac{1}{2}\) meters below sea level, which we can convert to an improper fraction: \[ 1 \frac{1}{2} = \frac{3}{2} \text{ meters below sea level} \]
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During the summer, the water level drops another \(2 \frac{1}{3}\) meters below sea level, which we also convert to an improper fraction: \[ 2 \frac{1}{3} = \frac{7}{3} \text{ meters below sea level} \]
Now, we need to add these two values together. To do this, we first need a common denominator. The least common multiple of \(2\) and \(3\) is \(6\).
Now, we convert both fractions:
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For \(\frac{3}{2}\): \[ \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \]
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For \(\frac{7}{3}\): \[ \frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6} \]
Now we can add the two fractions: \[ \frac{9}{6} + \frac{14}{6} = \frac{9 + 14}{6} = \frac{23}{6} \]
Thus, the water level at the end of summer is \(\frac{23}{6}\) meters below sea level. To express this as a mixed number, we can do the division: \[ \frac{23}{6} = 3 \frac{5}{6} \]
So, the water level at the end of summer is \(3 \frac{5}{6}\) meters below sea level.