RWM101: Foundations of Real World Math

Photo by Scott Beale

Although zero serves as the additive identity for our numbers – literally leaving them all alone – it has a more destructive impact when used to multiply. Multiplying any number by $0$ always results in $0$. This is why some mathematicians call $0$ the annihilator: all other numbers or objects are annihilated when multiplied by $0$. For example, both $15\times0=0$ and $0\times (-33)=0$. While mathematicians accept this aspect of the additive identity as fact, there are good, everyday, real-world reasons for this rule, too.

For example, let's say your coffee shop manager tells an employee, Every time a customer orders a large coffee, we make $\$2.00$. When 45 customers order large coffees, multiplication tells us the shop earned $2\times 45=90$ dollars. However, if zero customers come in that day, clearly, the shop has earned $\$0.00$: $2\times 0=0$ in large coffee sales. We can generalize and adjust this common experience to see that $(any\:number)\times 0=0$.