` 2 4/3 + 3 1/13 = `

To solve the problem `2 4/3 + 3 1/13`, first, we convert the mixed numbers into improper fractions.

1. Convert `2 4/3` to an improper fraction:
- The whole number part is `2`, which can be expressed as `2 * 3/3 = 6/3`.
- Adding the fractional part `4/3`, we get:
6/3 + 4/3 = 10/3.
- So, `2 4/3` = `10/3`.

2. Convert `3 1/13` to an improper fraction:
- The whole number part is `3`, which can be expressed as `3 * 13/13 = 39/13`.
- Adding the fractional part `1/13`, we get:
39/13 + 1/13 = 40/13.
- So, `3 1/13` = `40/13`.

Now, we need to add `10/3` and `40/13`. To do this, we first find a common denominator.

3. The least common denominator (LCD) of `3` and `13` is `39`.

4. Convert `10/3` to have a denominator of `39`:
- Multiply the numerator and denominator by `13`:
(10 13) / (3 13) = 130/39.

5. Convert `40/13` to have a denominator of `39`:
- Multiply the numerator and denominator by `3`:
(40 3) / (13 3) = 120/39.

Now we can add the two fractions:

6. Add `130/39` and `120/39`:
- Since the denominators are the same, add the numerators:
130 + 120 = 250.
- Thus, we have `250/39`.

7. Now, we can convert the improper fraction back into a mixed number:
- Divide `250` by `39`:
250 ÷ 39 = 6 with a remainder of `16`.
- Therefore, `250/39` can be expressed as `6 16/39`.

Final Answer: `2 4/3 + 3 1/13 = 6 16/39`.