Once the concept of division has been comprehended, many children are faced with the seemingly perplexing question of why division by zero doesn't work. After all, you are able to add, subtract and multiply by nil, so why can't you divide by it?
Below are three ways that you can use to show why division by zero does not compute:
1. Make up a story
Probably the nicest way to give an explanation for the concept of division is to make up some stories about sharing. Such as, "There are nine marbles here (have them physically there), and there are 3 friends who all want to play with them. How does one divide the marbles equally among the three, so that everybody gets the same number of marbles?"
Now convert that story into one about zero:
"You have nine marbles and nobody wants to play with them. How do you divide the marbles equally among no-one?" This of course does not seem sensible, as there simply is no-one to give the marbles to. (Which is also the reason why the answer can't be "9", because that would suggest dividing by 1, not zero).
2. Using Multiplication
The second way is to have a look at multiplication. We all know that multiplying a number actually means adding that number a specified number of times to itself. For instance, 5 * 3 = 5 + 5 + 5 = 15. And 15/5 = 3. In this example, we are actually asking, how often must I add 5 to get to 15? Now, if we have 15/0, we are asking, how often must I add 0 to get to 15. The answer naturally is: it's not possible. No matter how many times we add zero to itself, it will never amount to more than zero.
3. Examine fractions
The final way is to take a look at fractions. For example, 1/2 means we have one pie and we want to divide it into two pieces. 1/3 means we have 1 pie and will divide it into 3 slices. 1/1 means divide the pie into one piece. But how about 1/0? Irrespective of how we try and slice the pie, we will not be able to slice it into zero pieces. We could of course, eat the pie, but is be a different operation to division. :-).
Below are three ways that you can use to show why division by zero does not compute:
1. Make up a story
Probably the nicest way to give an explanation for the concept of division is to make up some stories about sharing. Such as, "There are nine marbles here (have them physically there), and there are 3 friends who all want to play with them. How does one divide the marbles equally among the three, so that everybody gets the same number of marbles?"
Now convert that story into one about zero:
"You have nine marbles and nobody wants to play with them. How do you divide the marbles equally among no-one?" This of course does not seem sensible, as there simply is no-one to give the marbles to. (Which is also the reason why the answer can't be "9", because that would suggest dividing by 1, not zero).
2. Using Multiplication
The second way is to have a look at multiplication. We all know that multiplying a number actually means adding that number a specified number of times to itself. For instance, 5 * 3 = 5 + 5 + 5 = 15. And 15/5 = 3. In this example, we are actually asking, how often must I add 5 to get to 15? Now, if we have 15/0, we are asking, how often must I add 0 to get to 15. The answer naturally is: it's not possible. No matter how many times we add zero to itself, it will never amount to more than zero.
3. Examine fractions
The final way is to take a look at fractions. For example, 1/2 means we have one pie and we want to divide it into two pieces. 1/3 means we have 1 pie and will divide it into 3 slices. 1/1 means divide the pie into one piece. But how about 1/0? Irrespective of how we try and slice the pie, we will not be able to slice it into zero pieces. We could of course, eat the pie, but is be a different operation to division. :-).
About the Author:
Thomas Brand is an IT Software Designer and father of 2 elementary school aged children. He created the math facts game MathRider to help youngsters master math early on and improve their confidence in the process. Discover helpful tips for homework help for parents or get the free trial software.
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