Solve: 1/10 + 3/5 - 1/2 Mixed Fraction Operations

To solve the exercise $\frac{1}{10} + \frac{3}{5} - \frac{1}{2}$, we must follow these steps:

Step 1: Find the Least Common Denominator (LCD).
The denominators we have are 10, 5, and 2. The LCD for these numbers is 10.

Step 2: Convert each fraction to have the common denominator of 10.
- $\frac{1}{10}$ is already with the denominator 10.
- Convert $\frac{3}{5}$:$\frac{3}{5} \times \frac{2}{2} = \frac{6}{10}$
- Convert $\frac{1}{2}$:
$\frac{1}{2} \times \frac{5}{5} = \frac{5}{10}$

Step 3: Perform the addition and subtraction.
Now operate: $\frac{1}{10} + \frac{6}{10} - \frac{5}{10} = \frac{1 + 6 - 5}{10} = \frac{2}{10}$

Step 4: Simplify the result.
The fraction $\frac{2}{10}$ simplifies to $\frac{1}{5}$ because both the numerator and denominator are divisible by 2.

Therefore, the solution to the problem is $\frac{1}{5}$.