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I was wondering what is the concept behind negative numbers? 2x3 is same as 3+3 but when we multiply -2x-3 why is it not the same as -3+-3 ? I am curious behind the reason of this and why do negative numbers behave like this.

Thank you!!! have a great day !!!!

JMoravitz
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Mr.Farmer john
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  • Welcome to math SE. Have a look at mathjax to improve your mathematical expressions. – Alain Remillard Jan 29 '20 at 16:27
  • Thinking of multiplication as repeated addition is fine for when you are first exposed to arithmetic as a very young child... but you should try to grow past that as "adding something a negative number of times" or "adding something a fraction number of times" or worse "adding something an irrational number of times" doesn't make any sense. Thinking of it as repeated addition only really makes sense if the number of times you are adding the thing is a positive whole number of times. – JMoravitz Jan 29 '20 at 16:28
  • Welcome to Mathematics Stack Exchange. $2\times-3=-3+-3$ – J. W. Tanner Jan 29 '20 at 16:29
  • ... and so $-2 \times -3 = -(2 \times -3) = -(-3 + -3) = -(-6) = 6$ – gandalf61 Jan 29 '20 at 16:30
  • @Mr.Farmerjohn The claim that ""adding something a negative number of times" or "adding something a fraction number of times" or worse "adding something an irrational number of times" doesn't make any sense." is bogus. It makes as much sense as negative numbers, or zero, or rational numbers, or irrational numbers. One defines them and just like one defines them, one can define negative or irrational times of doing something. In other words, not a reason to stop thinking about multiplication, among other ways, as repeated addition. – OscarRascal Jan 29 '20 at 16:37
  • irrational wouldn't be easy... for negative you can simply treat it as direction modificatiin instruction, start at 0 turn back step size=2 then walk nackwards 3 steps, you'll be at 6. –  Jan 30 '20 at 12:00

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