Once the concept of division has been comprehended, many kids are faced with the issue of why division by zero doesn't work. After all, you are able to add, subtract and multiply by 0, 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 explain the idea of division is to tell various stories about sharing. Like, "There are 9 marbles here (have them physically there), and there are 3 kids who want to play with them. How do you divide the marbles equally among the three, so that everyone has the same number of marbles?"
Now transform that story into one about zero:
"You have 9 marbles and no-one wants to play with them. How does one divide the marbles equally among nobody?" This naturally doesn't make sense, because there simply is nobody to give the marbles to. (Which is also why the answer cannot be "9", because that would imply dividing by 1, not 0).
2. Use 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. Use 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. Invent a story
Probably the nicest way to explain the idea of division is to tell various stories about sharing. Like, "There are 9 marbles here (have them physically there), and there are 3 kids who want to play with them. How do you divide the marbles equally among the three, so that everyone has the same number of marbles?"
Now transform that story into one about zero:
"You have 9 marbles and no-one wants to play with them. How does one divide the marbles equally among nobody?" This naturally doesn't make sense, because there simply is nobody to give the marbles to. (Which is also why the answer cannot be "9", because that would imply dividing by 1, not 0).
2. Use 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. Use 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 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.
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