Solve Mixed Number Expression: 2⅕ - (2⅕ - 1½)

The given expression to evaluate is $2\frac{1}{5} - (2\frac{1}{5} - 1\frac{1}{2})$.

First, we perform the calculation inside the parentheses:

• Convert $2\frac{1}{5}$ to an improper fraction: $2\frac{1}{5} = \frac{11}{5}$.
• Convert $1\frac{1}{2}$ to an improper fraction: $1\frac{1}{2} = \frac{3}{2}$.

Now, perform the subtraction inside the parentheses:

$\left( \frac{11}{5} - \frac{3}{2} \right)$

To perform this subtraction, we need a common denominator. The least common denominator of 5 and 2 is 10.

• Convert $\frac{11}{5}$ to $\frac{22}{10}$.
• Convert $\frac{3}{2}$ to $\frac{15}{10}$.

Subtract the fractions:

$\frac{22}{10} - \frac{15}{10} = \frac{7}{10}$.

Now substitute this result back into the original expression:

$2\frac{1}{5} - \frac{7}{10}$.

Again, convert $2\frac{1}{5}$ to $\frac{11}{5} = \frac{22}{10}$.

Now perform the subtraction:

$\frac{22}{10} - \frac{7}{10} = \frac{15}{10}$.

Simplify the fraction $\frac{15}{10}$:

$\frac{15}{10} = \frac{3}{2}$.

Convert back to a mixed number if necessary, but here $\frac{3}{2} = 1\frac{1}{2}$.

The solution to the problem is therefore: $1\frac{1}{2}$.