how to divide 0 by any number
Answers
Step-by-step explanation:
It doesn't matter how many groups of zero you have, because they would never add up to five since 0+0+0+0+0+0 = 0. You could even have one million groups of zero blocks, and they would still add up to zero. So, it doesn't make sense to divide by zero since there is not a good answer.
If you know a little bit about multiplication, you could look at it this way:
10/2 = 5 This means that 5 x 2 = 10
9/3 = 3 This means that 3 x 3 = 9
5/1 = 5 This means that 5 x 1 = 5
5/0 = ? This would mean that the answer x 0 = 5, but
anything times 0 is always zero.
So there isn't an answer.
- Dr. Margaret
Why can't you divide a number by 0?
For one thing, when you divide one number by another, you expect the result to be another number. Look at the sequence of numbers 1/(1/2), 1/(1/3), 1/(1/4), ... . Notice that the bottoms of the fractions are 1/2, 1/3, 1/4, ..., and that they're going to zero. If there's a limit to this sequence, we would take that number and call it 1/0, so let's see if there is.
Well, the sequence turns out to be 2, 3, 4, ..., and that goes to infinity. Since infinity isn't a real number, we don't assign any value to 1/0. We just say it's undefined.
But let's say we did assign a value. Let's say that infinity is a real number, and 1/0 is infinity. Then look at the sequence 1/(-1/2), 1/(-1/3), 1/(-1/4), ..., and notice again that the denominators -1/2, -1/3, -1/4, ..., are going to zero. So again, we would want the limit of this sequence to be 1/0. But looking at the sequence, it simplifies to -2, -3, -4, ..., and it goes to negative infinity. So which would we assign to 1/0? Negative infinity or positive infinity? Instead of just assigning one willy nilly, we say that infinity isn't a number, and that 1/0 is undefined.
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To find the probability of something happening, you find out how many different ways the thing you're looking at can happen, and then divide that by the total number of things that can happen. So you'd have zero, the number of different ways the sky can fall (if you really think it can't fall), divided by however many things you think CAN happen, which is probably some positive number. In any case, the denominator can't be zero, since that means that there are zero things that can happen.
The difference between 0/0 and 1/0 is sometimes complicated. For instance, if I look at these two sequences:
Sequence A: 5*1 5*1/2 5*1/3 5*1/4 5*1/5
----,------,------,------, ------, ...
1 1/2 1/3 1/4 1/5
Sequence B: 1 1 1 1 1
---, -----, -----, -----, -----, ...
1 1/2 1/3 1/4 1/5
The numerator and the denominator in Sequence A are both going to zero, so this sequence should be getting closer and closer to 0/0. But notice that every term in this sequence is 5. So the limit of this sequence is 5. And I could replace the 5 with any number I want, to get whatever limit I want for 0/0. So if you say that the probability of something happening is 0/0, you might be saying that it has probability 1, or .5, or anything at all.
In the second sequence though, notice that we could write it as 1,2,3,4,...which goes to infinity. The only way we can interpret 1/0 (or any nonzero real number over zero) is as positive or negative infinity. In general though, listen to the oft-heard words of advice: DON'T DIVIDE BY ZERO, but with the following addendum: if you do, make sure you're prepared to deal with what happens. In your case, you could have caused the sky to fall, because you said that the probability of it happening might be 1.
If you divided a number with 0 the answer will be 0.
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