To find the water level of the river at the end of summer, we first need to convert the measurements to improper fractions for easier addition.
- The initial water level is \(1 \frac{1}{2}\) meters below sea level, which is:
\[ 1 \frac{1}{2} = \frac{3}{2} \]
- During the summer, the river drops another \(2 \frac{1}{3}\) meters below sea level, which is:
\[ 2 \frac{1}{3} = \frac{7}{3} \]
Now, we need to combine these two measures of how far below sea level the river is. We will add these two fractions:
\[ \text{Total drop} = \frac{3}{2} + \frac{7}{3} \]
To add these fractions, we need a common denominator. The least common multiple of 2 and 3 is 6. We convert both fractions:
\[ \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \] \[ \frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6} \]
Now we can add the two fractions:
\[ \frac{9}{6} + \frac{14}{6} = \frac{9 + 14}{6} = \frac{23}{6} \]
This means that at the end of summer, the water level is \(\frac{23}{6}\) meters below sea level.
To express this in mixed number form, we divide 23 by 6:
\[ 23 \div 6 = 3 \quad \text{remainder} \ 5 \]
So,
\[ \frac{23}{6} = 3 \frac{5}{6} \]
Thus, the water level at the end of summer is \(3 \frac{5}{6}\) meters below sea level.
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