Let’s say you have a division. You’ve got 3/2, where 3 might be acres and 2 might be brothers so from there you could deduce that the division just means that the 3 acres of land will be distributed between two brothers. Summation and multiplication are quite straight forward, but what the hell does one do with multiplication and exponentiation? If I got 20 N-m of torque, wtf does the multiplication tells me there? If something follows a square root?
Please feel free to add any other operations to these. Thanks!
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Physics provides a lot of insight into representation of mathematical operations.
For multiplication, you can imagine a car going a certain rate of speed, e.g. 60 km/h. If it travels for 2 hours, how far will it go? Well, 60km/h * 2hrs = 120Km.
Taking your N-m of Torque example, you can imagine that as applying 1 newton of force over 1m of distance. The distance in this case is rotational instead of linear, but the idea is the same.
Exponentiation is similar, if you have a cube shaped tank with a side length of 2m, then how much water will fit inside it? (2m)^3 = 8 cubic meters. Cubic meters might seem a weird measurement, but it just means the volume taken up by a cube with a side length of 1m, so you could fill 8 1m side length cubes with the water from one cube with a side length 2m.
Square roots are just the opposite of squaring, in case you wanted to know the side length of a square given the area that it covers.
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