Solve: 11/10 - 4/5 + 1/2 | Fraction Operation Challenge

To solve this problem, we'll follow these steps:

• Step 1: Determine the least common multiple (LCM) of the denominators $10$, $5$, and $2$.
• Step 2: Convert each fraction to have this common denominator.
• Step 3: Perform the subtraction and addition operations sequentially.

Now, let's work through each step:
Step 1: The denominators are $10$, $5$, and $2$. The LCM of these numbers is $10$.
Step 2: Convert each fraction:
- $\frac{11}{10}$ already has the denominator $10$.
- Convert $\frac{4}{5}$ to have a denominator of $10$:
$\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$.
- Convert $\frac{1}{2}$ to have a denominator of $10$:
$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$.
Step 3: Perform the operations:
- First, subtract: $\frac{11}{10} - \frac{8}{10} = \frac{11 - 8}{10} = \frac{3}{10}$.
- Then, add: $\frac{3}{10} + \frac{5}{10} = \frac{3 + 5}{10} = \frac{8}{10} = \frac{4}{5}$ after simplifying.

Therefore, the solution to the problem is $\frac{4}{5}$.