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19 answers

Your teacher is right... 2 ÷ 0 is undefined.

Division is the inverse operation to multiplication.
We know that 6 ÷ 3 = 2, because 2 × 3 = 6.

Okay, fill in the blank:
2 ÷ 0 = __. This means the same as __ × 0 = 2.

But this causes a big problem! Anything times zero is zero (not 2), and there is no number that you can use to fill in the blank. That's why 2 ÷ 0 is undefined.

You can do this with any nonzero number. 6 ÷ 0 is undefined... -37 ÷ 0 is undefined... any nonzero divided by zero is undefined.

The case of 0 ÷ 0 is quite different, though. Try the "fill in the blank" technique:
0 ÷ 0 = __. This means the same as __ × 0 = 0.

In this case, any real number makes the multiplication correct, and that causes a different problem. When a contradiction in math causes multiple possibilities for answers, this is called an indeterminate form. Indeterminates come up from time to time in the calculus when finding limits and derivatives. You don't have to worry about that 'til you get there, though. For the time-being, this should suffice:

n ÷ 0 is undefined for any n ≠ 0.
0 ÷ 0 is an indeterminate form.
In either case, dividing by zero is a definite math no-no!

2006-08-20 07:24:24 · answer #1 · answered by Anonymous · 0 1

Division by zero is undefined because such division leads to anomalies. For example, 4*0=0 and 5*0=0 . Dividing both sides by zero gives 4=5 which is anamolous and cannot be worked with.
If one has to criticize this rule , all that can be said is that division by zero would be defined some day when some arithmetic is invented to handle such anomalies as 4=5.

2006-08-20 07:45:48 · answer #2 · answered by rabi k 2 · 0 0

A lot of people have said your teacher's right, or just said you can't divide by zero, but I don't think anyone explained why.

Pick a number. 10 is a good one. Now divide it by 1, then by 0.1, then 0.01, then 0.001, and so on.

Now look at your answers. Starting with 10/1, you get 10, then 100, then 1000, etc.

When you divide by numbers that keep getting closer to zero, the answer keep going up, higher and higher. as the divisor approaches zero, the quotient approaches infinity.

That's why you can't divide by zero.

2006-08-20 08:01:16 · answer #3 · answered by bpiguy 7 · 0 0

As you divide any constant by smaller and smaller numbers you'll get greater and greater results. But you cannot tell what it is when divided by zero. Another point of view. 2 / 4 is 2 divided into 4 parts. Zero is nothing, how can you divide something into nothing parts.

2006-08-20 07:53:10 · answer #4 · answered by Joseph Binette 3 · 0 0

It appears the question was "WHAT IS THE ANSWER 4 (used in place of the word 'for') 2 DIVIDED by ZERO??" seeing as there is a space between the two numbers.

ANSWER: You cannot divide by zero...anything.

2006-08-20 07:33:49 · answer #5 · answered by wanna fanna out 2 · 0 0

Your teacher is right. They decide long ago that anything divided by zero would be undefined.

2006-08-20 07:28:06 · answer #6 · answered by iandanielx 3 · 0 0

If you have 42 dollars and divide it up among zero people, how would you do it? The answer is "Huh?" That is why it is undefined.

2006-08-20 07:26:56 · answer #7 · answered by Dougnuts38 2 · 1 0

Picture the graph
y =1/x
If x is positive and approaches 0, the result 1/x approaches infinity.
If x is negative and approaches 0, the result 1/x approaches negative infinity.

It is undefined because it cannot be both positive and negative infinity at the same time.

2006-08-20 15:25:26 · answer #8 · answered by PC_Load_Letter 4 · 0 0

the value for any number divided by zero is undefined...

some people may THINK it is infinity, but it is not...

I would go into more detail but I'm not sure of your grade and the real answer deals with "uniqueness"

2006-08-20 07:26:19 · answer #9 · answered by ♥Tom♥ 6 · 0 0

Your teacher is correct. I mean, work it out... try ANY number for your quotient... you'll always have a remainder which will always match the dividend. I've taught Math for over 20 years... it's hard to comprehend, isn't it? I think about it this way...if you're taking 42 and dividing by 0, you're really not dividing anything into groups, are you?

2006-08-20 07:24:28 · answer #10 · answered by Mike S 7 · 0 1

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