Final answer:
The three consecutive integers that sum to -51 are -18, -17, and -16. The product of half the smaller and half the largest is -72.
Step-by-step explanation:
In this problem, we are given that there are three consecutive integers that sum to -51. Let's represent these integers as x, x+1, and x+2 (where x is the smallest integer). The sum of these three integers can be expressed as x + (x+1) + (x+2) = -51. Simplifying this equation gives us 3x + 3 = -51. Solving for x, we find that x = -18. Therefore, the three consecutive integers are -18, -17, and -16.
To find the product of half the smaller and half the largest, we need to calculate (-18/2) * (-16/2) = 9 * (-8) = -72.