Perform the indicated operation:
$\frac{-[-45 \div(-5)(3)]}{(7-10)}$
Answer (1)
Evaluate the denominator: 7 − 10 = − 3 .
Evaluate the division within the brackets: − 45 ÷ ( − 5 ) = 9 .
Multiply within the brackets: 9 × 3 = 27 .
Simplify the numerator: − 3 − [ 27 ] = − 3 − 27 .
Perform the final division: − 3 − 27 = 9 .
$\boxed{9}
Explanation
Understanding the Expression First, we need to evaluate the expression ( 7 − 10 ) − [ − 45" , " ÷ ( − 5 ) ( 3 )] . This involves several arithmetic operations, and we must follow the order of operations (PEMDAS/BODMAS) to ensure we get the correct answer.
Simplifying the Denominator Let's start by simplifying the expression inside the parentheses in the denominator: 7 − 10 = − 3 .
Division Next, we simplify the expression inside the square brackets in the numerator. We have − 45 ÷ ( − 5 ) ( 3 ) . According to the order of operations, we perform division before multiplication. So, − 45 ÷ ( − 5 ) = 9 .
Multiplication Now, we multiply the result by 3: 9" , " × 3 = 27 . So, the expression inside the square brackets becomes 27.
First Negation Now we have − [ 27 ] in the numerator, which simplifies to − 27 . Then we have − [ − 45" , " ÷ ( − 5 ) ( 3 )] = − 27 .
Final Division Finally, we have the entire expression as − 3 − 27 . Dividing -27 by -3 gives us 9.
Examples
Understanding order of operations is crucial in many fields, such as engineering, computer science, and finance. For example, when calculating the trajectory of a rocket, engineers must follow the correct order of operations to ensure accurate results. Similarly, in finance, calculating investment returns requires precise application of the order of operations to avoid costly errors. This problem reinforces the importance of following these rules to achieve accurate outcomes in various real-world scenarios.
