how do i divide numbers by zero?

Question

2/0 how do i do it

Answer 1

Let's think of this in terms of similar problem and try to identify what we are doing when solving this task.  Identifying a pattern in our thinking can help us understand division by zero.

 

Let's say an elementary student was asked to answer this question and provide justification for their answer.  

 

10/5 = ?

 

There are two common ways I have seen students think through this type of problem.  One method is to imagine 10 pieces of candy sitting on the table.  Around the table are 5 friends.  They want to split the candy on the table evenly among them.  How many pieces do they each get?  Students often use a picture, similar to the one below, to communicate their thinking.  Each "x" represents a piece of candy.  The number next to them represent the five friends.  

 

x x      x x      x x      x x      x x

 1         2        3        4        5

 

You can see in the picture that person 1 has two pieces of candy, person 2 has two pieces, person 3, 4, and 5 also each have two pieces of candy.  Therefore, 10 divided by 5 is 2, because each person gets 2 pieces of candy.  This student answered this question by assigning each student one piece of candy at a time until all candy was distributed and each person had the same amount.

 

If we apply this same line of reasoning to 10/0 = ?, it would not be possible.  Ten pieces of candy divided evenly among zero friends is not possible because someone has to be present to receive the candy.  If there are zero people to give the candy, then it can't happen.  The ten pieces cannot be shared with anyone if no one is there.  This is why we say you cannot divide by zero.

 

Another approach I have seen students take is as follows…Say you have $10 in your pocket.  You are shopping and find a T-shirt you like that costs $5.  You like it so much that you want to buy more than one.  To determine how many shirts you want can buy, you take the $10 and divide it into groups of $5.  When you do this, you find that there are 2 groups of $5, and conclude that you can buy 2 T-shirts.  Therefore….

 

10/5=2

 

Rather than giving one piece of candy at a time to each friend until the ten pieces were all gone, this student sees the task as finding the number of groups of 5 that are in ten.  They count out 1,2,3,4,5 and leave that as one group.  They use the remaining to count out another group of 5.  Now, they have 2 groups of 5, and each group of five would represent one T-shirt.  An illustration for this approach might look something like this:

 

$1

$1

$1 -> This represents one T-shirt

$1

$1

 

$1

$1

$1 -> This represents a second T-shirt

$1

$1

 

So, if using this line of reasoning, we can say that 10/0 is not possible because you cannot break $10 into groups of zero.

 

Answer 2

As the denominator gets smaller, the answer gets bigger.  Therefore, anything divided by zero is infinitely large.  So, 

 

2/0 = ∞

 

 

 

Answer 3

Hello, friends!

One of the Math rules is you can't divide by zero. That's it!

Nicole M. Language Tutor

Answer 4

Well "Divide" from Richton Park, Il,

Yes, and no.

Both answers are correct, that dividing by zero is, 'by the rules,'

1) not allowed and

2) undefined.  

If that leaves you unsatisfied,

here's some more to consider... Rules are made to be broken.

 

In second grade, when you tried to subtract 5 from 2, the response

was "You can't do that!"  Now, after study with a number line, or

this past winter with a thermometer, (1) you know that you can have

a number that is "below zero."    

 

In fourth grade you learned your squares and square roots.

You had to open your eyes to accept that the square root of

sixteen is not only four ( 4 x 4 = 16 ),

but also NEGATIVE four ( -4 x -4 = 16 ).

Then when asked what is the square root of NEGATIVE 16,

the response was again, "You can't do that!"   UNTIL a nasty

little calculation called the Quadratic Equation came around, and

we WANTED to have a square root of a negative number, so

we made one up in our IMAGINATION, and gave it the name

"imaginary number" represented by lower case i to equal the

square root of negative one, which can then be factored.

 

So now here we are, trying to divide by zero.  Are you going

to accept someone telling you, "You can't do that!" after all

we just went through?  Of course not.  Let's look at an example

of division, where any number N divided by X equals Y or N/X=Y.

You will note that the X and the Y are inversely proportional.

That is to say that, as X gets smaller, Y gets larger.  What is

the smallest that X could be?  ZERO, of course. (2) So that makes

Y the largest it could be.  What is the largest number you can

think of? A million? A trillion?  A googol?  A googol-plex?

All our Saturday morning cartoon fans will remember the final

answer as we get larger and larger is "INFINITY!" However, it's

useless to calculate with infinity, because whatever we do to it,

it's still infinity.  So

1) to say we call dividing by zero "undefined"

ironically, gives it a definition.  And

2) it's not so much that we "can't" divide by zero, it's just useless

because once you get to infinity, anything else is meaningless.

Whatever you do from there is still infinity. (3)

 

So substituting in from your equation, two divided by zero gives us

 

2 / 0 = Y

 

or "Y" would you want to bother doing that?

 

I hesitate to add it to our history of disproved "I can't" statements.

Maybe someday, something like time travel will require that we

use the concept of dividing by zero, but until then,

the textbook answer that will get you points on a test is

"Dividing by zero is undefined." and trying to do it will leave

gaps on your grids, and nobody wants gaps on their grids.

 

Footnotes:

(1) Let's not mention my checkbook, please!

(2) Remember, there's a difference between "ZERO" and "Nothing"

but we promised we wouldn't mention my checkbook.

(3) Until we make another rule that says different.

Answer 5

Hi!

In mathematics, this is not allowed.  Anything with a zero in the denominator, such as in the example you provide...

2/0

is considered undefined.  (The denominator is also called the divisor.  We cannot divide by zero.)

However, anything with a zero in the numerator, for example...

0/2

is considered zero.