Equal Shares

Three friends run up a debt of 45 dollars and agree to share it equally. The debt is a negative amount, -45, and sharing equally means dividing. Use s for share: $s = \frac{-45}{3}$. A negative divided by a positive is negative, so the next line is $s = -15$. Each friend owes 15 dollars.

The sign makes sense: splitting a debt gives smaller debts, not money. Multiplying goes the other way round. Three shares of -15 put back together are $3 \cdot \left(-15\right)$, which is -45, the whole debt.

That reverse step is also how you check a share: multiply it by the number of people and you should get the total you started with, sign included.