4,05-(-2 1/2) (1 2/3:2,5-)

To solve the expression \( 4.05 - (-2 \frac{1}{2}) (1 \frac{2}{3} : 2.5) \), let's break it down step by step.

Step 1: Convert Mixed Numbers to Improper Fractions

1. Convert \( -2 \frac{1}{2} \) to an improper fraction: \[ -2 \frac{1}{2} = -\frac{5}{2} \]

2. Convert \( 1 \frac{2}{3} \) to an improper fraction: \[ 1 \frac{2}{3} = \frac{5}{3} \]

Step 2: Divide \( 1 \frac{2}{3} \) by \( 2.5 \)

Convert \( 2.5 \) to a fraction: \[ 2.5 = \frac{25}{10} = \frac{5}{2} \]

Now calculate: \[ \frac{5}{3} : \frac{5}{2} = \frac{5}{3} \times \frac{2}{5} = \frac{2}{3} \]

Step 3: Substitute Back into the Original Expression

Now the expression looks like this: \[ 4.05 - (-\frac{5}{2}) \cdot \frac{2}{3} \]

Step 4: Simplify the Multiplication

Calculate \( -\frac{5}{2} \cdot \frac{2}{3} \): \[ -\frac{5 \cdot 2}{2 \cdot 3} = -\frac{10}{6} = -\frac{5}{3} \]

Step 5: Substitute and Simplify

Now the expression is: \[ 4.05 - (-\frac{5}{3}) = 4.05 + \frac{5}{3} \]

Step 6: Convert \( 4.05 \) to a Fraction

Convert \( 4.05 \) into a fraction to combine: \[ 4.05 = \frac{405}{100} = \frac{81}{20} \]

Step 7: Find a Common Denominator

To add \( \frac{81}{20} \) and \( \frac{5}{3} \), we need a common denominator. The least common multiple of \( 20 \) and \( 3 \) is \( 60 \).

Convert both fractions: \[ \frac{81}{20} = \frac{81 \cdot 3}{20 \cdot 3} = \frac{243}{60} \] \[ \frac{5}{3} = \frac{5 \cdot 20}{3 \cdot 20} = \frac{100}{60} \]

Step 8: Add the Fractions

Now, add them: \[ \frac{243}{60} + \frac{100}{60} = \frac{243 + 100}{60} = \frac{343}{60} \]

Final Answer

The final result is: \[ \frac{343}{60} \quad \text{or approximately } 5.7167 \]

If you prefer the mixed number: \[ 5 \frac{43}{60} \]

Thus, \( 4.05 - (-2 \frac{1}{2}) (1 \frac{2}{3} : 2.5) = \frac{343}{60} \) or \( 5 \frac{43}{60} \).