How to Determine When a Numerical Expression is Undefined

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  • 0:01 Numerical Expression
  • 0:58 When Is It Undefined?
  • 1:56 How to Find When It Is…
  • 2:25 Example
  • 3:51 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

We get all kinds of problems in math. We sometimes get numerical expressions that are undefined. Watch this video lesson to learn what it means to be undefined and how to find when a numerical expression is undefined.

Numerical Expression

In math, we get all kinds of numerical expressions. We can have ones with just numbers and ones with variables. We have ones with one variable and ones with lots of variables. We have simple ones and not-so-simple ones. We have some without denominators and some with.

In this video lesson, we are going to be looking at the ones with variables and a denominator. It is only with denominators where you might end up with a point that is undefined. What does 'undefined' mean? 'Undefined' means there is no answer to the expression at that point. Think of it as the value where you end with more question marks at the end.

When Is It Undefined?

How do we know when a numerical expression is undefined? It is when the denominator equals zero. When we have a denominator that equals zero, we end up with division by zero. We can't divide by zero in math, so we end up with an expression that we can't solve. We end up with more question marks. Most calculators will tell you that you cannot divide by zero. Try it on your computer calculator and see.

There is no answer to a problem when you have division by zero. But if you are able to find the points where you have division by zero, then you can say that this numerical expression is valid except at these points.

How to Find When It Is Undefined

So how do we find the points where a numerical expression is undefined? We do this by solving our numerical expression's denominator for zero. What we do is set the denominator equal to zero and solve. The numbers that we get for our answer are the points where our numerical expression is undefined.

Let's look at an example to see how this is done.


We want to find the points where this numerical expression is undefined.

undefined expression

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