Final answer:
The two numbers that multiply to -8 and add to -7 are -8 and 1. These numbers satisfy the multiplication and addition rules for combining positive and negative numbers.
Step-by-step explanation:
The question asks for two numbers that multiply to -8 and add to -7. Considering the rules of multiplication and addition involving positive and negative numbers, two numbers that multiply to a negative number must have opposite signs (Rule 7), and when adding two negative numbers, the result will have a negative sign (Rule 6).
To find the numbers, let's consider the factor pairs of 8: 1 & 8, 2 & 4. Since the product needs to be -8, one number must be negative. To get a sum of -7, the greater number in absolute value must be negative because the sum of two numbers with opposite signs is equal to the difference between the absolute values of the numbers, taking the sign of the larger one (Rule 3).
The only pair that satisfies both conditions is -8 and 1. The number -8 multiplied by 1 equals -8, and -8 added to 1 equals -7. Thus, the correct answer is -8 and 1.