3.1 Introduction and Key Insights

Calculations and operations with negative numbers may seem strange at first compared to computations with positive ones. But there are plenty of real-world and mathematical scenarios that require them!

Temperature is a good example: the thermostat might read $50.0$ or $-50.0$ degrees Celsius. Profits and losses offer another example. We say a business is "in the red" when it owes money. It is "in the black" when there is a surplus. For example, a business that has a tally of negative $500.00 (or $-\$500.00$) is "in the red" by 500 dollars.

Our operations would be incomplete without negative numbers! The additive inverse property we discussed in Section 1.3 would no longer hold if negative numbers were not available. Also, we would not be able to cancel positive numbers.