What happens when the denominator is zero

We can never divide by 0

A fraction really represents the division of its numerator by its denominator. For example, the fraction

$\frac38$

means “$3$ divided by $8$,” or "$3$ parts out of $8$ equal parts."

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One of the important things to remember about fractions is that we can never divide by $0$. Since we’re always dividing by whatever is in the denominator, this just means that we can’t have $0$ in the denominator of a fraction. It’s just one of those weird things in math that we can’t do. And so if we ever have $0$ in the denominator, all we can say is that the fraction is “undefined,” which means we never want to put $0$ in the denominator of a fraction.

Consider the idea of “parts of a whole.” The fraction $4/0$ could be read as, “$4$ parts out of $0$ equal parts.” But that doesn’t make sense. How can we take $4$ parts if the whole is $0$, or empty? We can’t, it’s impossible; and this is one explanation of why $4/0$ is undefined.

Keep in mind that this is totally different than having $0$ in the numerator of a fraction. If we have $0$ in the numerator, the value of the fraction is $0$. So something like

$\frac06$

is equal to $0$.

When fractions are undefined

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How to define a fraction with a 0 denominator

Example

Find the value of $3/0$.

Because we can’t have $0$ in the denominator of a fraction, all we can say is that this fraction is “undefined.” The value isn’t $0$, it isn’t $3$, it’s just undefined.

if we ever have 0 in the denominator, all we can say is that the fraction is “undefined.”

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