Final answer:
To find the other number, we divide the product of the two numbers by the given number. The other number is 2 16/21, which is closer to -4 1/5.
Step-by-step explanation:
To find the other number, we need to divide the product of the two numbers by the given number. The product of two rational numbers is -23 1/3. One of the numbers is -8 1/6.
So, (-23 1/3) ÷ (-8 1/6) = (-(70/3)) ÷ (-(49/6)) = (70/3) ÷ (49/6). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore,
(70/3) ÷ (49/6) = (70/3) × (6/49) = (70 × 6)/(3 × 49) = 420/147.
Simplifying 420/147 gives us (2 16/21). Therefore, the other number is 2 16/21, which is closer to option d. -4 1/5.