Friday, March 29, 2019

algebra precalculus - Why is frac1frac10 undefined?




Is the fraction



110



undefined?



I know that division by zero is usually prohibited, but since dividing a number by a fraction yields the same result as multiplying the number by the fraction's reciprocal, you could argue that



110=(1)(01)=0




Is that manipulation permissible in this case? Why or why not?


Answer



Another way to think about this is order of operations:



110=1/(1/0)



I always compute what's inside the parenthesis first, which gives me undefined, and I have to stop there.


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