**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
The reality is, you already understand multiple unit math, you just don’t realize it yet.
Let’s say you have a big box of apples that you weigh, and find out there 100 lbs of apples in the box. You take out each apple and count it, and find out the box was holding 400 apples, you could take the average density of apples as:
400 apples / 100 lbs = 4 apples per pound, or 4 apples/lb
Then if you have another box that holds 200 lbs of apples, you could multiply it by the apple density you know of to find that the number of apples is: 200 lbs * (4 apples/lb) = 800 apples.
So the above is an example of units divided, IE apples / pound. Similar commonly used divided units are pressure, IE lbs/ square inch.
Let’s say you’re on a teeter-totter, and balancing with another friend. If each end of the teeter-totter is 4 ft from the pivot, and you’re sitting on it with a weight of 150 lbs, you’re applying a moment (torque) of M = F X R = 150 lbs * 4 ft = 600 ft*lbs.
If you add another 100-lb person to your side of the teeter-totter, you added a total torque of 100 lbs * 4 ft, or 400 ft * lbs.
So you’ve added 400 ft * lbs to 600 ft * lbs to get 1000 ft * lbs. So though the units are multiplicative (ft * lbs), because the sums you’re adding are the same, you can safely add them.
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