Final answer:
The product of −6.4 and −36.1 is 231.04, as the multiplication of two negative numbers results in a positive number. Using the rules for multiplying rational numbers, the calculation yields option a as the correct answer.
Step-by-step explanation:
To use properties of rational numbers to multiply −6.4×(−36.1), we should recognize that multiplying two negative numbers will result in a positive product. We multiply the absolute values of the numbers and then apply the sign rule.
Step 1: Multiply the absolute values: 6.4 × 36.1
Step 2: Calculate the product: 6.4 × 36.1 = 230.64
Since both numbers we started with are negative, the product is positive according to the rules of multiplying negative numbers.
Thus, −6.4×(−36.1) = 231.04
The correct answer is option a. 231.04.