To solve the expression you've provided, we need to break it down into manageable parts. Your expression is:
\[ |2002| + |-640| \cdot |8 \frac{12}{11}| - \frac{-820}{-4.1} - |8.9| \cdot |-1.5| \]
Let's calculate step by step:
Absolute Values:
- \(|2002| = 2002\)
- \(|-640| = 640\)
- \(|8 \frac{12}{11}| = 8 + \frac{12}{11} = \frac{88}{11} + \frac{12}{11} = \frac{100}{11}\) (or approximately 9.09)
- \(|-4.1| = 4.1\)
- \(|8.9| = 8.9\)
- \(|-1.5| = 1.5\)
Calculating the Expression: Now substituting in the absolute values: \[ 2002 + 640 \cdot \frac{100}{11} - \frac{-820}{-4.1} - 8.9 \cdot 1.5 \]
Multiply and Divide:
First, calculate \(640 \cdot \frac{100}{11}\): \[ 640 \cdot \frac{100}{11} = \frac{64000}{11} \approx 5818.18 \]
Next, calculate \(\frac{-820}{-4.1}\) (considering that both negatives cancel): \[ \frac{820}{4.1} \approx 200 \]
Then calculate \(8.9 \cdot 1.5\): \[ 8.9 \cdot 1.5 \approx 13.35 \]
Combine Results: Substitute back into the main expression: \[ 2002 + 5818.18 - 200 - 13.35 \]
Now calculate this step-by-step:
First, add: \[ 2002 + 5818.18 = 7820.18 \]
Then subtract: \[ 7820.18 - 200 = 7620.18 \] \[ 7620.18 - 13.35 = 7606.83 \]
Thus, the final result of the expression is approximately:
\[ \boxed{7606.83} \]