#### Question

# So why isnt everything divided by zero undefined?

so im doing my math hw

and they gave me -15/0 and i thought it was 0 so i go check my answer and its undefined but then they give me 0/12 and the answer is 0.Can someone explain why the first wouldnt be zero?

#### Answer

Anything DIVIDED by zero is undefined.

Zero divided by ANYTHING is zero.

In one, the zero is the denominator. The zero can never be in the denominator, hence it is always undefined when a zero is in the denominator.

In the other, the zero is the numerator. This is always zero.

Think about the way you say it:

"Any number DIVIDED BY ZERO is undefined."

"Zero divided by ANY NUMBER is zero".

So:

"Seven divided by zero is undefined."

"Twenty divided by zero is undefined."

--Whenever any number is divided by zero, the answer is always undefined.

On the other hand:

"Zero divided by seven is zero."

"Zero divided by twenty is zero."

Notice where the "zero" is in each of these statements.

-15 divided by 0 is undefinded because NOTHING times 0 can equal -15

0 divided by 12 is 0 because 12 times 0 is 0

Numerator is on top and denominator on theb ottom.

Just try making the denominator smaler, i.e. see what happens as it tenmds to 0

-15/1

= 15

-15/0.5 = -30

-15/ 0.2 = 72

So as the denomintaor gets smaller the expression gets bigger

For the first question, you could say that zero goes into 15 infinitely many times. That is, you can keep adding 0 + 0 + 0 + 0 +.... and you'll never get to 15. So -15/0 is infinity, which is not really a number, it's undefined.

The second question is the opposite case. 12 doesn't go into zero at all, or in other words it goes into zero, zero times. So the answer to 0/12 is just zero.

If you divide by 0, the answer is undefined because it is infinite.

If you mulitply by 0, the answer is 0, because you are saying , zero lots of something.

but if you divide by 0 you are saying, how many time does zero go into this number, and the answer is infinite.

Think about dividing by 2, then you get half of the original number.

Now think about dividing by 1, then you get the number you began with - so yiur anser is getting bigger.

So if you divide by the smallest number possible, you are going to get the biggest number possible, so big that you cannot define it. Hence, it is undefineable or undefined! Infinity is undefined. You cant say exactly what it is, it is without bounds.