To solve the expression \(-2 \frac{3}{8} + 6 \frac{1}{2}\), we first convert both mixed numbers into improper fractions.
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Convert \(-2 \frac{3}{8}\): \[ -2 \frac{3}{8} = -\left(2 \times 8 + 3\right)/8 = -\left(16 + 3\right)/8 = -\frac{19}{8} \]
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Convert \(6 \frac{1}{2}\): \[ 6 \frac{1}{2} = 6 \times 2 + 1 = 12 + 1 = 13/2 \]
Now we add the two improper fractions \(-\frac{19}{8}\) and \(\frac{13}{2}\). First, we need a common denominator. The least common multiple of 8 and 2 is 8.
Convert \(\frac{13}{2}\) to a fraction with a denominator of 8: \[ \frac{13}{2} = \frac{13 \times 4}{2 \times 4} = \frac{52}{8} \]
Now, we add the fractions: \[ -\frac{19}{8} + \frac{52}{8} = \frac{-19 + 52}{8} = \frac{33}{8} \]
Next, we convert \(\frac{33}{8}\) back to a mixed number:
- Divide 33 by 8 which gives us 4, with a remainder of 1.
Thus, we have: \[ \frac{33}{8} = 4 \frac{1}{8} \]
So, the final answer is: \[ 4 \frac{1}{8} \]
In the format \([] []/[__]\): \[ 4\ 1/8 \]