10/1: 6 2/5

To solve the equation \( \frac{10}{1} : \frac{6}{5} \), we first rewrite it in a multiplication form by inverting the second fraction.

Here’s how it works step-by-step:

1. Rewrite \( 10/1 \) as \( 10 \).
2. Rewrite \( 6/5 \) as a fraction.
3. Change the division to multiplication by inverting \( 6/5 \):

\[ 10 \div \frac{6}{5} = 10 \times \frac{5}{6} \]

4. Now, perform the multiplication:

\[ 10 \times \frac{5}{6} = \frac{10 \times 5}{6} = \frac{50}{6} \]

5. Simplify \( \frac{50}{6} \):

\[ \frac{50}{6} = \frac{25}{3} \]

6. To convert \( \frac{25}{3} \) into a mixed number, divide 25 by 3:
   • 25 divided by 3 is 8, with a remainder of 1.

Thus,

\[ \frac{25}{3} = 8 \frac{1}{3} \]

So, \( \frac{10}{1} : \frac{6}{5} = 8 \frac{1}{3} \).