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An Example of Subtraction of Negative Numbers

move
initial depth i
-85
final depth f
-10
f - i = -10m - (-85)m = 75m
A puzzling issue for educators in elementary education is how to explain arithmetic operations between negative numbers: why, for example, subtracting a negative number is the same as adding a positive number or why the product of two negatives gives a positive. A related problem is to find good examples in which these operations appear in the "real world" and that students find sensible.
Here the immersion of a submarine to a certain depth is interpreted as a negative quantity, where the surface of the sea is taken as zero depth; a change from an initial depth
i
to a final depth
f
requires manipulation of negative quantities. When the submarine dives, the result of the subtraction
f-i
corresponding to the difference of depths is negative and when the submarine rises this result is positive.
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