1) $0.75-05+2+\frac{13}{8} \times(-0.8)-1+(-0.6)=$
Answer (2)
First, perform the multiplication: 8 13 × ( − 0.8 ) = − 1.3 .
Then, perform the addition and subtraction from left to right: 0.75 − 0.5 + 2 − 1.3 − 1 − 0.6 .
Combine the terms: 0.25 + 2 − 1.3 − 1 − 0.6 = 2.25 − 1.3 − 1 − 0.6 = 0.95 − 1 − 0.6 = − 0.05 − 0.6 = − 0.65 .
The final result is: − 0.65 .
Explanation
Initial Analysis We are asked to evaluate the arithmetic expression: 0.75 − 0.5 + 2 + 8 13 × ( − 0.8 ) − 1 + ( − 0.6 ) = To solve this, we will perform the operations step by step, following the order of operations (PEMDAS/BODMAS).
Multiplication First, let's perform the multiplication: 8 13 × ( − 0.8 ) = 8 13 × 10 − 8 = 8 × 10 13 × ( − 8 ) = 80 − 104 = − 1.3 So the expression becomes: 0.75 − 0.5 + 2 − 1.3 − 1 − 0.6 =
Addition and Subtraction Now, let's perform the addition and subtraction from left to right: 0.75 − 0.5 = 0.25 0.25 + 2 = 2.25 2.25 − 1.3 = 0.95 0.95 − 1 = − 0.05 − 0.05 − 0.6 = − 0.65 So the final result is: − 0.65
Final Result Therefore, the value of the expression is: 0.75 − 0.5 + 2 + 8 13 × ( − 0.8 ) − 1 + ( − 0.6 ) = − 0.65
Examples
In everyday life, evaluating arithmetic expressions like this is essential for managing finances, calculating expenses, or determining discounts while shopping. For instance, if you're buying items with different prices and discounts, you need to perform similar calculations to find the final amount you owe. Understanding the order of operations ensures accurate results in such scenarios.
To evaluate the expression, we first perform the multiplication, which simplifies the overall expression. Then, we carry out addition and subtraction step by step. The final result of the expression is -0.65.
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