To solve the expression step-by-step, let's break it down while keeping track of the order of operations (parentheses, exponents, multiplication and division, addition and subtraction).
The expression is: \[ 2.34 : 0.39 \times (10.7 - 2.3) : ((8.9 - 5.7) \times (2.11 + 1.04)) \]
Start by evaluating the expressions inside the parentheses:
- \( 10.7 - 2.3 = 8.4 \)
- \( 8.9 - 5.7 = 3.2 \)
- \( 2.11 + 1.04 = 3.15 \)
Now substitute back into the expression: \[ 2.34 : 0.39 \times 8.4 : (3.2 \times 3.15) \]
Now calculate \( 3.2 \times 3.15 \): \[ 3.2 \times 3.15 = 10.08 \]
Substitute this back into the expression: \[ 2.34 : 0.39 \times 8.4 : 10.08 \]
Now we have: \[ 2.34 : 0.39 \times 8.4 : 10.08 \]
Let's compute \( 2.34 : 0.39 \): \[ 2.34 / 0.39 \approx 6 \]
Substitute this into the expression: \[ 6 \times 8.4 : 10.08 \]
Next, compute \( 6 \times 8.4 \): \[ 6 \times 8.4 = 50.4 \]
Substitute this back: \[ 50.4 : 10.08 \]
Finally, compute \( 50.4 : 10.08 \): \[ 50.4 / 10.08 \approx 5 \]
Therefore, the result of the expression is: \[ 5 \]