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- Why is negative times negative = positive? 40 answers
Why is a negative number multiplied by a negative number a positive number?
I'm trying to know what does multiplying by a negative number mean.
If you think of multiplication as a "groups of" ($3 \times 5$ meaning $3$ groups of $5$ then it's confusing what a "negative number of groupsof $X$" could mean.
A lot of mathematics can be and was done without reference to "negative" numbers—whatever that unfathomable silliness might mean! The first several chapters of Stillwell's Mathematics and its History cover rational points on the circle, irrational numbers, distance, conic sections, rational curves, Pell's equation, chords and tangents, prime numbers, Chinese remainder theorem all without reference to negative numbers. You could do Platonic solids or spiric sections as well without ever venturing in that direction.