Question

The product of two rational numbers is minus 23 ⅓. If one of the numbers is minus 8 1/6, find the other number.

a. -3 2/3
b. -2 3/4
c. -1 5/6
d. -4 1/5

Answer 1

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.