**Title: What does it mean to multiply units?**
I can’t grasp what it represents in the real world
Addition/Subtraction: only makes sense in same units and increases/decreases the value like moving forwards/backwards or inreasing/decreasing the amount of force on an object etc…
Division: a ratio, how much of x per y: how many meters you move in one second, how much force is put on an area etc….
Multiplication: no idea. The unit of force: kg / m×s^(2,) mass per whatever m×s^(2) means or F = m×g what does m*g represent? Obviously there is a mathematical proof for this equation but what is the actual reason beyond: the math works out
Or imagine I am in the process of figuring out a brand new equation (in Physics/Chemistry/Geometry/…) how do I know that I need a multiplication right here beyond it’s the math?
**EDIT:** An Attempt to clarify the problem I have
At some point in school we learn that multiplication can describe areas: 7*5 = 35 is the number of pieces in a rectangle if said rectangle is divisible into 7 rows with 5 pieces each or 7 columns with 5 pieces each or the opposite.
Multiplication can also describe an event occuring multiple times if I run 5 km in 7 hours then I ran 35 km total
in probability multiplication can also describe the number of possible uniqe iteration
and I definitly forgot a few things.
But what does Multiplication describe in nature sciences or physics especially? Perhaps in the example of F = m*g but also in general
In: 0
When you multiply, it doesn’t matter what the units are, it always works the same. You multiply both the numbers and the units. If it’s “4 cookies” times “$2 per cookie”, then the result is $8, because “cookies” * “per cookie” cancel out.
If you multiply “3 feet” by “3 feet”, the result is 9 square feet.
If you multiply “10 miles per second” with “60 seconds”, the result is 600 miles, because the “per second” and “seconds” cancel out.
It’s no different with any of the other examples you’re giving.
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If you want to visualize it, multiplication always adds a dimension. If you multiply two values which are one-dimensional, e.g. 3 meters and 2 meters, which are just “lengths” of a one-dimensional line, the result is two-dimensional: a rectangle of 2 by 3 meters length, i.e. an “area”. If you then multiply that again by another 4 meters, which again is a one-dimensional value, the result is three-dimensional, i.e. a block of 2 by 3 by 4 meters called “volume”. It’s easier to visualize if all three components have the same type of unit, but it doesn’t actually matter at all for the concept itself. Energy consumption is measured in kWh, which can be visualized as the two-dimensional area of a rectangle with some amount of Energy (kW) in one dimension and some other amount of time (h) in another dimension. Whether it’s 1 hour of 2000 kW consumption or 2000h of 1kW consumption doesn’t matter, the total energy consumption (i.e. the area of the rectangle) is the same in both cases.
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How do you know if you have to multiply something? That’s easy – correlation. If something grows when something else grows, you have to multiply it. If something gets smaller while something else grows, you have to divide by that. Like the formula for gravity. Gravitational force gets bigger the bigger the two masses are, so both masses have to be multiplied. The force gets smaller the bigger the distance is between those masses, so we have to divide by the distance. We actually see that this reduction is not just proportional, but actually exponential, so it’s really divided by distance squared. Then you only need to calibrate the formula with some constant factor to make the numbers work out, and there you go – Newton’s formula of gravitic force, derived quite easily just from basic observations.
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