# Division By Zero

Pronunciation: /dɪˈvɪ.ʒən baɪ ˈzɪər.oʊ/ Explain

 Click on the blue point and drag it to change the figure. Dragging the blue point, what is the value of f(x) at x=0? Manipulative 1 - Division by 0 Created with GeoGebra.

Division by zero is undefined. Any expression that includes division by zero can not be used because it has no mathematical meaning.

### Why is division by zero undefined?

Division answers the question, "Into how many groups do I need to divide the whole so that there are a certain number of items in each group?" For example, 10 ÷ 5 asks, "How many groups do I need to divide 10 into so that there are 5 in each group?" The answer, of course, is 2. 10 can be divided into 2 groups of 5. Now consider this statement: 10 ÷ 0. The question is "How many groups do I need to divide 10 into so that there are 0 in each group?" Here is the problem: No matter how many groups 10 is divided up into, there will never be zero in each group.

Manipulative 1 shows the function f(x) = a / x. Click on the blue point on the slider in manipulative 1 and drag it back and forth to change the value of a. Notice that on one side of x = 0, the graph goes to positive infinity and on the other side it goes to negative infinity. What is the value of f(x) at 0? The answer is that f(x) has no value at 0. f(x) is undefined at 0.

1. McAdams, David E.. All Math Words Dictionary, division by zero. 2nd Classroom edition 20150108-4799968. pg 65. Life is a Story Problem LLC. January 8, 2015. Buy the book

### Cite this article as:

McAdams, David E. Division By Zero. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/divisionbyzero.html.

### Revision History

4/20/2019: Updated equations and expressions to the new format (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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