To solve the expression \(-2 \frac{1}{2} - (-3 \frac{3}{5})\), we first convert the mixed numbers into improper fractions and then perform the calculations.
-
Convert \(-2 \frac{1}{2}\) to an improper fraction: \[ -2 \frac{1}{2} = -\frac{5}{2} \]
-
Convert \(-3 \frac{3}{5}\) to an improper fraction: \[ -3 \frac{3}{5} = -\frac{18}{5} \] Since we have a negative sign in front of this expression, we can write: \[ -(-3 \frac{3}{5}) = \frac{18}{5} \]
-
Now substituting these values back, the expression becomes: \[ -\frac{5}{2} + \frac{18}{5} \]
-
To add these two fractions, we need a common denominator. The least common multiple of \(2\) and \(5\) is \(10\). We convert both fractions: \[ -\frac{5}{2} = -\frac{25}{10} \quad \text{(multiply top and bottom by 5)} \] \[ \frac{18}{5} = \frac{36}{10} \quad \text{(multiply top and bottom by 2)} \]
-
Now, add the two fractions: \[ -\frac{25}{10} + \frac{36}{10} = \frac{-25 + 36}{10} = \frac{11}{10} \]
The final result is: \[ 1 \frac{1}{10} \] In the requested format, that is: \[ 1 [1]/[10] \]
So, the answer to your expression is: \[ 1 [1]/[10] \]