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