Final Answer:
The answer to the given expression [3 - 5 * 10 - 7 * 125] / [15 - 5 * 6 - 7] is -6. This result is obtained by simplifying the expression through step-by-step calculations following the order of operations in mathematics.
Step-by-step explanation:
To solve this expression, we follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). First, we calculate the values within the brackets:
[3 - 5 * 10 - 7 * 125] / [15 - 5 * 6 - 7]
= [3 - 50 - 875] / [15 - 30 - 7]
Next, perform the multiplication:
= [-47 - 875] / [-22]
Combine like terms:
= -922 / -22
Finally, divide:
= 42
Therefore, the final answer to the given expression is -6.
In the given expression, we start by evaluating the values within the brackets separately for the numerator and denominator. The multiplication operations are performed before subtraction. Once the values within the brackets are simplified, we proceed to perform the division. The final result is a fraction that simplifies to -6. This process adheres to the standard order of operations in mathematics, ensuring an accurate solution to the given expression.