Classify the materials commonly used at home into mixture and pure substances elements and compounds.?

Any number divided by zero is undefined (not infinity!). Here's why: Start with a division a/b, where a = 15 and be = 1. Okay, the answer is 15, right?

Now let be = 0.1, and the solution is 150. Let be = 0.01, and the answer is 1500. The smaller be gets, the larger a/b gets, right?

So it seems that as be approaches zero, a/b approaches infinity. Except for one problem; if be is negative, then 15/b approaches *negative* infinity as be approaches zero. So the limit of a/b as be --> zero is different, depending on which direction you're approaching from.

When that happens, we say that an expression is "undefined". There simply is no number or value that is equivalent to a/0, where a is equal to any real number. Here's another way to think about it.

If a/b = c, then b*c = a, right? So let's say that 15/0 = c, where c is some real answer. Rewriting the equation we get 0*c = 15.

But that's nonsense! Zero times *anything* is zero, not fifteen! There's no value for c that would make that equation work.

In the You-Didn't-Ask-But-I'm-Going-To-Mention-... Department, 0/0 is *also* undefined. For example, 0/0 = c. Rearranging we get: 0*c = 0.

Now we have the opposite problem: there are literally *infinite* numbers that you could substitute for c to make the equation work. We say that 0/0 is indeterminate and undefined, because it has no single real solution. I hope that helps.

Good luck!

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