Solve the Fraction Subtraction: 4/5 minus 6/10

To solve the problem of subtracting the fraction $\frac{6}{10}$ from $\frac{4}{5}$, follow these steps:

Step 1: Identify the least common multiple (LCM) of the denominators 5 and 10.
The LCM of 5 and 10 is 10.

Step 2: Convert each fraction to an equivalent fraction with the common denominator of 10.
- The fraction $\frac{4}{5}$ can be converted to have a denominator of 10 by multiplying both the numerator and the denominator by 2. Thus, $\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$.
- The fraction $\frac{6}{10}$ already has the denominator of 10, so it remains $\frac{6}{10}$.

Step 3: Subtract the second fraction from the first.
Subtract the numerators while keeping the common denominator: $\frac{8}{10} - \frac{6}{10} = \frac{8 - 6}{10} = \frac{2}{10}$.

Step 4: Simplify the resulting fraction.
The fraction $\frac{2}{10}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2: $\frac{2}{10} = \frac{2 \div 2}{10 \div 2} = \frac{1}{5}$.

Therefore, the solution to the problem is $\frac{1}{5}$, which corresponds to choice number 2.