How to visualize this simple division?

R

RickQuest

New member
Joined
Apr 21, 2019
Messages
6
I have 6 marbles on the table.
Below are different situations that I can really visualize how the division works in real life.

Situation 1 : I put 6 marbles into 2 baskets, in math i solve it by using division , which is 6 marbles / 2 baskets = 3 marbles ( in each basket)
Situation 2 : I put 6 marbles into 3 baskets, in math i solve it by using division , which is 6 marbles / 3 baskets = 2 marbles ( in each basket)
Situation 3 : I put 6 marbles into 1 basket ,in math i solve it by using division , which is 6 marbles / 1 basket = 6 marbles ( in each basket)
but...
what about
Situation 4 : I put 6 marbles into 0.5 basket , how do I visualize this ? I know it sounds silly, but this is important to understand too. What I try to ask here is what 0.5 represents? basket? or what? If we follow the pattern of the situations above, 0.5 should be basket too.
Then, the next question : if I solve it I would get 6 marbles / 0.5 = 12 marbles.
The problem is, I only have 6 marbles, then how could it turn out to be 12 marbles as the final result?
 
Put a divider down the middle of your basket, and put your 6 marbles into only one half. If you had the same number of marbles in each half, you would have another 6 in the other half, making a total of 12 per basket.

Division assumes uniform distribution; your answer is a rate (marbles per basket), representing the number in each basket if every basket (or part of a basket) contains the same number.
 
Hi Dr.Peterson, Why can't I just put 3 marbles in each half of the basket? I'm having a hard time to differentiate this from 6 divided by 2, since a divider being put in the middle of the basket will divide the basket into two containers.
 
It sounds to me like you're getting confused because of the distinction between "divide" in the common English sense and "divide" as a mathematical term. In everyday English, the word "divide" can be used as a synonym for "split" or "separate." But in the world of math, "divide" specifically means to split/separate into equal parts.

You can try a simple example yourself at home. Grab six of any object and two containers. Put one object in one container and five in the other. In this way, you've divided (in the English sense) the objects into two groups. However, it should be clear that the result is not three objects in each container. Similarly, you can put two objects into one container and four into the other. This, too, is an example of division in the English sense of the word, but it's also not three objects in each container.

In short, mathematical division is a special case of "regular" division, in which all the groups are ensured to be the same size.
 
RickQuest said:
Hi Dr.Peterson, Why can't I just put 3 marbles in each half of the basket? I'm having a hard time to differentiate this from 6 divided by 2, since a divider being put in the middle of the basket will divide the basket into two containers.
Click to expand...
You can put 3 marbles in each half which is the same as putting all 6 marbles in one basket. Then the problem is the same as Situation 3 : I put 6 marbles into 1 basket ,in math i solve it by using division , which is 6 marbles / 1 basket = 6 marbles ( in each basket)
If you put all 6 marbles in half the basket then keeping the same rate how many marbles can you put in one whole basket?
 
Here is a completely different way to think about division. For example 10/2 = 5 which is the same as 2*5 = 10. That is a/b = c is the same as b*c=a.
If you did not know what 10/2 equals you could ask yourself 2 times what equals 10. The answer would be 5.
In your problem, 6/(1/2), you can ask yourself 1/2 times what is 6? Or even better, half of what is 6? The answer is 12.
I understand that this method may not answer your original question but maybe this will be enough for you.
 
ksdhart2 said:
It sounds to me like you're getting confused because of the distinction between "divide" in the common English sense and "divide" as a mathematical term. In everyday English, the word "divide" can be used as a synonym for "split" or "separate." But in the world of math, "divide" specifically means to split/separate into equal parts.

You can try a simple example yourself at home. Grab six of any object and two containers. Put one object in one container and five in the other. In this way, you've divided (in the English sense) the objects into two groups. However, it should be clear that the result is not three objects in each container. Similarly, you can put two objects into one container and four into the other. This, too, is an example of division in the English sense of the word, but it's also not three objects in each container.

In short, mathematical division is a special case of "regular" division, in which all the groups are ensured to be the same size.
Click to expand...
 
Jomo said:
Here is a completely different way to think about division. For example 10/2 = 5 which is the same as 2*5 = 10. That is a/b = c is the same as b*c=a.
If you did not know what 10/2 equals you could ask yourself 2 times what equals 10. The answer would be 5.
In your problem, 6/(1/2), you can ask yourself 1/2 times what is 6? Or even better, half of what is 6? The answer is 12.
I understand that this method may not answer your original question but maybe this will be enough for you.
Click to expand...
 
You must log in or register to reply here.
Top