Evaluate the expression.
$-3+-2 \div(12--14 \times-1)$
Answer (1)
First, perform the multiplication within the parentheses: − 14 t im es − 1 = 14 .
Next, evaluate the subtraction within the parentheses: 12 − 14 = − 2 .
Then, perform the division: − 2 d i v − 2 = 1 .
Finally, complete the addition: − 3 + 1 = − 2 . The final answer is − 2 .
Explanation
Understanding the Expression We need to evaluate the expression − 3 + − 2 d i v ( 12 − − 14 t im es − 1 ) . To do this, we will follow the order of operations (PEMDAS/BODMAS).
Multiplication First, we evaluate the expression inside the parentheses. Within the parentheses, we have multiplication and subtraction. We start with the multiplication: − 14 t im es − 1 = 14 .
Subtraction Now we perform the subtraction inside the parentheses: 12 − 14 = − 2 . So the expression becomes − 3 + − 2 d i v − 2 .
Division Next, we perform the division: − 2 d i v − 2 = 1 . The expression is now − 3 + 1 .
Addition Finally, we perform the addition: − 3 + 1 = − 2 .
Examples
Understanding order of operations is crucial in many real-life calculations, such as calculating discounts, taxes, or financial returns. For instance, if you have a coupon for 20% off a product and then a further $5 off, you need to calculate the 20% discount first and then subtract the $5. This ensures you get the correct final price. Similarly, in programming, the order of operations determines how expressions are evaluated, which can affect the outcome of calculations in software applications.
