I understand that a negative times a negative equals a positive, are there any real world examples of this?
I know if I have 3 jars with 5 cookies each that’s 15 cookies
3×5=15
What about (-3) x (-5) = +15
How is that expressed in a simple scenario like above?
In:
Negative numbers are a construction. There just has to be an opposite of positive addition to complete simple arithmetic functions. This manifests as negative numbers once you subtract past zero. Negative numbers in general can represent bank account values and temperatures. It’s needed to calculate opposing forces too like buoyancy and drag.
The construct extends to arithmetic functions like multiplication and division. The operations all work the same, you just add a negative for when you need to represent values less than zero. The concept here is that negative values are the opposite of positive values.
So 5 x 3 = 15 is the same magnitude as -5 x -3 = 15
The second equation can be re-written as (-1)5 x (-1)3 = 15.
That is the numerical demonstration of the opposite of an opposite. You get the same value (positive) you started with.
This property of negative numbers is useful all the time in engineering & physics.
Imagine you’ve got a road, and the road has a gradient. If the road is going uphill, the gradient is positive, if the road is going downhill then the gradient is negative.
Now also imagine you’ve got a car on this road, and you know the car’s velocity. Positive velocity means the car is going forward, negative velocity means the car is reversing. I want to work out how quickly the car is ascending or descending. I can find this out by multiplying gradient by velocity.
If the slope is going downhill (-ve) and the car is reversing back up it (-ve), then the car is actually going uphill and the ascent rate is positive.
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