-2 2/7 + 4 3/5

To add the mixed numbers \(-2 \frac{2}{7}\) and \(4 \frac{3}{5}\), we can first convert them to improper fractions.

1. Convert \(-2 \frac{2}{7}\): \[ -2 \frac{2}{7} = -\left(2 \times 7 + 2\right)/7 = -\left(14 + 2\right)/7 = -16/7 \]

2. Convert \(4 \frac{3}{5}\): \[ 4 \frac{3}{5} = \left(4 \times 5 + 3\right)/5 = \left(20 + 3\right)/5 = 23/5 \]

Now we need to add \(-\frac{16}{7}\) and \(\frac{23}{5}\). To do this, we find a common denominator. The least common multiple of 7 and 5 is 35.

Convert both fractions to have a denominator of 35:

• For \(-\frac{16}{7}\): \[ -\frac{16}{7} = -\frac{16 \times 5}{7 \times 5} = -\frac{80}{35} \]

• For \(\frac{23}{5}\): \[ \frac{23}{5} = \frac{23 \times 7}{5 \times 7} = \frac{161}{35} \]

Now we can add the fractions: \[ -\frac{80}{35} + \frac{161}{35} = \frac{161 - 80}{35} = \frac{81}{35} \]

Now we can convert \(\frac{81}{35}\) back to a mixed number: \[ 81 \div 35 = 2 \quad (\text{with a remainder of } 11) \] So, \(\frac{81}{35} = 2 \frac{11}{35}\).

Thus, the final result is: \[ -2 \frac{2}{7} + 4 \frac{3}{5} = 2 \frac{11}{35} \]