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.
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