# Understanding Units: Multiply vs Divide

• polaris90
In summary, the conversation discusses the concept of having units being multiplied rather than divided, using examples such as Weber and Volt seconds. The concept is further explored with examples of other units such as meters per second and kilogram per meter squared. The conversation also touches on the idea of conceptual understanding versus mathematical calculations when dealing with unit multiplication. Ultimately, the key takeaway is that unit multiplication is an abstract concept and is defined by the units involved.
polaris90
What does it mean to have units being multiplied rather than divided. For example 1Weber which is equal to 1Vs. Saying 1 Volt second doesn't make much sense to me. I understand if it said for example N/m. In general what does it mean to have the units being multiplied rather than divided?

What does it mean if you have units like m^2 or m^3?

Well, if you are trying to cover your floor with tiles, and your room is 5m by 6m, you need 30m^2 of floor tiles. meter^2 is dimensionally different than meter, since it is a two-dimensional area, not a length. It has to be multiplied, not divided, because of how it scales. For example, a meter is 100 centimeters; therefore, a square meter is 100^2 square centimeters.

When you have a divided unit, for example, 1 meter per second--that's the same as 1 centimeter per centisecond, because you scaled down the numerator and denominator by a factor of ten.

1 volt second = 1 millivolt kilosecond, because milli and kilo cancel out when you multiply them. Capiche?

Velocity has units of m/s. Velocity is the DERIVATIVE of position with respect to time.

Weber has units of V*s. Magnetic flux (Weber) is the INTEGRAL of voltage with respect to time.

polaris90 said:
What does it mean to have units being multiplied rather than divided. For example 1Weber which is equal to 1Vs. Saying 1 Volt second doesn't make much sense to me. I understand if it said for example N/m. In general what does it mean to have the units being multiplied rather than divided?

does this make a difference for you?
1 Weber = 1 Vs
1 V = 1 Weber/second

If you have a problem with multiplying units, one can only imagine what you would think of more abstract units such as fractional dimensions...

@flatmaster
The only one with a reasonable answer, that helps understand it. I did some reading an you were correct about it. However, I my question was more general and used the Weber as an example. It is clearly understood when you have units such as meters per second, which means a change of a meter per every second. Or if we said one kilogram per meter squared, which means there is an amount of an kilogram for every meter in the x direction and meter in the y direction. In a more generalized form, it says a change of a unit for every change of this other unit. But if you have units being multiplied( not such as $m^2$ which I mentioned above), is there a more generalized way to explain it?

polaris90 said:
@flatmaster
The only one with a reasonable answer, that helps understand it. I did some reading an you were correct about it. However, I my question was more general and used the Weber as an example. It is clearly understood when you have units such as meters per second, which means a change of a meter per every second. Or if we said one kilogram per meter squared, which means there is an amount of an kilogram for every meter in the x direction and meter in the y direction. In a more generalized form, it says a change of a unit for every change of this other unit. But if you have units being multiplied( not such as $m^2$ which I mentioned above), is there a more generalized way to explain it?

So you are asking what a unit of measurement squared is? As in km² or m²?

No, as I already mentioned above in the text you quoted. My question is when you have two different units such as Newton Meters, which according to my reading is equal to the amount of force of one Newton applied to an arm perpendicularly which is one meter long. I understand how to work with the units when it comes to mathematical calculations. But I would like to have a more conceptual understanding of how the units work when they are being multiplied.

polaris90 said:
No, as I already mentioned above in the text you quoted. My question is when you have two different units such as Newton Meters, which according to my reading is equal to the amount of force of one Newton applied to an arm perpendicularly which is one meter long. I understand how to work with the units when it comes to mathematical calculations. But I would like to have a more conceptual understanding of how the units work when they are being multiplied.

I'm really baffled by that question. So, multiplying meter by meter to get m2 is OK, but multiplying meter by Newtons to get Nm some how is causing you conceptual difficulties. How come?

polaris90 said:
@flatmaster
The only one with a reasonable answer, that helps understand it.

I think there were other good answers. 256bits' answer was pretty good. You can't have division without multiplication.

dauto said:
I'm really baffled by that question. So, multiplying meter by meter to get m2 is OK, but multiplying meter by Newtons to get Nm some how is causing you conceptual difficulties. How come?
Good point, I guess it might be because I cannot simply visualize it in my head as easily as a $m^2$.

Stop trying to visualize it then. Ultimately unit multiplication is an abstract concept. You are performing a mathematical operation on non-numerical entities. A meter is not a number, it's a distance. A second is not a number, it's an amount of time. A meter per second is not a number, it's an amount of speed. Even though none of those things are numbers, it is correct to state that a meter per second is equal to a meter divided by a second. This operation is possible by definition. A meter per second is defined as a meter divided by a second (not as a meter for every second as you stated earlier), and a Weber is defined as a Volt times a second. That's all there is to it.

Is it that you have problems understanding N*m as an unit but you are OK with Newton by itself?
A force measured in Newtons does not raise conceptual problems?
If this is the case, remember that N=kg*m/s^2. Now you have a problem with N too?
And N/m which you say you "understand" is "actually" kg/s^2. How do you visualize the s^2?

SteamKing said:
What does it mean if you have units like m^2 or m^3?

m^2 is the unit of area whereas, m^3 is the units of Volume. Both the units are in SI system.

Hey, Gudiya... that thread is from 2 years ago. That's OK, I forget to check the date often too.

## What is the difference between multiplying and dividing units?

Multiplying units is used to find the total when the units are repeated a certain number of times, while dividing units is used to find the number of times a unit fits into another unit.

## How do I know when to use multiplication or division with units?

You should use multiplication when you are finding the total of a certain unit, and division when you are finding the number of times a unit fits into another unit.

## Can I use either multiplication or division to convert units?

Yes, you can use both multiplication and division to convert units. It depends on the specific conversion factor you are using.

## What happens to the units when multiplying or dividing?

In multiplication, the units are multiplied together. In division, the units are divided and the resulting unit will depend on the specific units being divided.

## How can I check my work when using multiplication or division with units?

You can check your work by making sure that the resulting unit makes sense in the context of the problem. You can also convert the final unit back to the original unit to see if you get the same value you started with.

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