-7 3/10+10 1/2

To compute \(-7 \frac{3}{10} + 10 \frac{1}{2}\), we first need to convert the mixed numbers into improper fractions.

1. Convert \(-7 \frac{3}{10}\) into an improper fraction: \[ -7 \frac{3}{10} = -\left(7 \times 10 + 3\right)/10 = -\left(70 + 3\right)/10 = -\frac{73}{10} \]

2. Convert \(10 \frac{1}{2}\) into an improper fraction: \[ 10 \frac{1}{2} = \left(10 \times 2 + 1\right)/2 = \left(20 + 1\right)/2 = \frac{21}{2} \]

Next, we will add \(-\frac{73}{10}\) and \(\frac{21}{2}\). To do this, we need a common denominator. The least common multiple of 10 and 2 is 10.

3. Convert \(\frac{21}{2}\) to have a denominator of 10: \[ \frac{21}{2} = \frac{21 \times 5}{2 \times 5} = \frac{105}{10} \]

Now we can add the two fractions: \[ -\frac{73}{10} + \frac{105}{10} = \frac{-73 + 105}{10} = \frac{32}{10} \]

4. Simplify \(\frac{32}{10}\): \[ \frac{32}{10} = \frac{16}{5} \]

Converting \(\frac{16}{5}\) back to a mixed number: \[ \frac{16}{5} = 3 \frac{1}{5} \]

So, the result of \(-7 \frac{3}{10} + 10 \frac{1}{2}\) is: \[ 3 \frac{1}{5} \]