To find out how far you'll run today, we need to calculate $\frac{7}{8}$ of the total distance of 12 3/5 miles.

1. Convert the mixed number 12 3/5 into an improper fraction: $12 \frac{3}{5} = \frac{12 \times 5 + 3}{5} = \frac{60 + 3}{5} = \frac{63}{5}$

2. Now, multiply $\frac{7}{8}$ by $\frac{63}{5}$: $\frac{7}{8} \times \frac{63}{5} = \frac{7 \times 63}{8 \times 5} = \frac{441}{40}$

3. Convert $\frac{441}{40}$ into a mixed number by dividing 441 by 40: $441 \div 40 = 11 \text{ remainder } 1$ So, $\frac{441}{40} = 11 \frac{1}{40}$.

Thus, you'll run 11 1/40 miles today.

Would you like any further details or have any questions?

Here are 5 related questions you could explore:

1. What would happen if you only ran 3/4 of your training schedule?
2. How far would you run if the schedule said to run 15 miles, but you planned to do 7/8 of it?
3. What percentage of the total distance will you run today?
4. How do you convert mixed numbers to improper fractions and vice versa?
5. How much farther would you have to run to complete the full training distance?

Tip: When dealing with mixed numbers, always convert them to improper fractions for easier multiplication or division.