Final answer:
The student's expression is solved by performing operations in the order of PEMDAS, resulting in approximately 346.78 after rounding. The division by 0.36 and subtraction of 56 were key steps in the calculation.
Step-by-step explanation:
The student asked to evaluate the expression −[−145÷0.3(1.2)]−56. To solve this, we follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). First, we simplify the expression within the parentheses: −145÷0.3(1.2).
Performing the multiplication inside the parentheses, 0.3 times 1.2 equals 0.36. Then we divide −145 by 0.36, resulting in −402.78 (repeating). Now we have the expression −[−402.78...]−56 which simplifies to 402.78... minus 56. Subtracting 56 from 402.78 (repeating) yields approximately 346.78 as the final result.
It's important to remember that in mathematics, division by zero is undefined, but since this expression involves division by 0.36, which is a valid and non-zero divisor, we are able to compute a numerical answer.