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. Invent 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 transform 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. Make use of Multiplication
The second way is to look at multiplication. We know that multiplying a number simply means adding that number a given number of times to itself. For example, 5 * 3 = 5 + 5 + 5 = 15. And 15/5 = 3. In this example, we are really asking, how many times must I add 5 in order to get to 15? But if we have 15/0, we are asking, how many times must I add 0 in order to get to 15. The answer of course is: it is impossible. Regardless of how many times we add 0 to itself, it'll never become more than 0.
3. Examine fractions
The final way is to have a look at fractions. As an example, 1/2 means we have one pie and we would like to divide it into 2 pieces. 1/3 means we have 1 pie and want to divide it into 3 pieces. 1/1 means divide the pie into one piece. But what about 1/0? Regardless of how we try and cut the pie, we can never cut it into zero pieces. We could of course, eat the pie, but that would be a different operation to division. :-).
Below are three ways that you can use to show why division by zero does not compute:
1. Invent 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 transform 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. Make use of Multiplication
The second way is to look at multiplication. We know that multiplying a number simply means adding that number a given number of times to itself. For example, 5 * 3 = 5 + 5 + 5 = 15. And 15/5 = 3. In this example, we are really asking, how many times must I add 5 in order to get to 15? But if we have 15/0, we are asking, how many times must I add 0 in order to get to 15. The answer of course is: it is impossible. Regardless of how many times we add 0 to itself, it'll never become more than 0.
3. Examine fractions
The final way is to have a look at fractions. As an example, 1/2 means we have one pie and we would like to divide it into 2 pieces. 1/3 means we have 1 pie and want to divide it into 3 pieces. 1/1 means divide the pie into one piece. But what about 1/0? Regardless of how we try and cut the pie, we can never cut it into zero pieces. We could of course, eat the pie, but that would 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 children master math early on and improve their confidence in the process. Discover useful tips for homework help for parents or get the free trial software.
